University of Ghana http://ugspace.ug.edu.gh A THEORETICAL STUDY OF THE PRODUCTION OF TECHNETIUM-99M 99m ( Tc) USING A CYCLOTRON A THESIS SUBMITTED TO THE DEEPARTMENT OF NUCLEAR SCIENCES AND APPLICATIONS GRADUATE SCHOOL OF NUCLEAR AND ALLIED SCIENCES UNIVERSITY OF GHANA BY NYAABA, RUDOLF ANYOKA (10363144) BSc. (UDS), 2007 IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF A MASTER OF PHILOSOPHY DEGREE IN APPLIED NUCLEAR PHYSICS JULY 2013 i University of Ghana http://ugspace.ug.edu.gh DECLARATION I, Nyaaba Rudolf Anyoka hereby declare that, with the exception of references to other peoples work which have been duly acknowledged, this work is the result of my own research undertaken under the supervision of Dr. G.K. Banini and Rev. Dr. Samuel Akoto Bamford and has not been presented for any other degree in this university or elsewhere either in part or in whole ………………………………… ……..………………………. NYAABA RUDOLF ANYOKA Date (Student) …………………………………… ……………………………… DR.G.K.BANINI Date (Supervisor) ………………………………… ……………………………......... REV. DR. S. AKOTO BAMFORD Date (Co-Supervisor) ii University of Ghana http://ugspace.ug.edu.gh DEDICATION This work is dedicated to my mother, Adugibiire Nyaaba, for her invaluable pieces of advice and prayers for me throughout my life. It is also dedicated to my lovely wife, Anasthasia Akambonga, for her understanding, prayers and care for me throughout this work. Finally, I would like to dedicate this work to my two lovely kids, Bertrand Awinegana Nyaaba and Nina Awinebota Nyaaba for their prayers, understanding and patience for me throughout this work. May the almighty God bless us all. iii University of Ghana http://ugspace.ug.edu.gh ACKNOWLEGEMENTS I would like to express my profound gratitude and appreciation to my supervisors: Rev Dr. Samuel Akoto Bamford and Dr. G. K. Banini for making time out of their busy schedules to offer critical scrutiny, constructive criticisms and guidance throughout this work. Moreover, I am very thankful to Prof. J. J. Fletcher for suggesting the thesis topic to me as well as for his fatherly words of encouragement and good pieces of advice. Furthermore, I am very grateful to Prof. Samuel Dampare for his concern for my work and the words of encouragement he offered me throughout this work. I am also very grateful to Mr. Daniel Nii Adjei, Mr. Raymond Agalga and Miss Sheila Victoria Gbormittah at RPI; Mr. Emmanual Boafoh , Miss Rita Ewura Abena Appiah and Mr. Mathew Asamoah all at (GHARR-1);Mr Enerst Kwame Ofori at (SNAS ICT LAB); Mr. Amadu Confeh and Mr. Bambara Look (students of Medical Physics) for their various assistance in the course of this work. Finally to all my friends and to all those who contributed in diverse ways to make this work a success, I say thank you and may God richly bless you all. iv University of Ghana http://ugspace.ug.edu.gh ABSTRACT 99m A theoretical study of the production of Technetium-99m ( Tc) using a cyclotron has been conducted. A nuclear reaction model code (Talys code) was used to generate 100 99m reaction cross sections as functions of particle energies for Mo (p, 2n) Tc 99m reaction channel which would lead to the direct production of Tc. Excitation 99m function for the desired reaction channel for the production of Tc and excitation functions for the reaction channels of competing products (contaminants) were plotted and analyzed. From the analysis, the optimum energy range for the production of 99m Tc was obtained to be 10-20 MeV. This result compared favorably with experimental as well as theoretical works in literature. Using the radionuclide production yield equation (Celler et al, 2011), the saturated thick target radionuclide production yield in this work was estimated to be 565MBq/µAh. To investigate the effects of certain operational parameters on the saturated thick 99m target yield of Tc, a numerical solution was obtained in this work for the saturated thick target radionuclide production yield equation by employing Newton‘s Forward Difference (NFD) formula and, concluding deductions made. The findings drawn from these theoretical considerations confirmed that a cyclotron 99m production of Tc may be a feasible alternative to the reactor-based production. v University of Ghana http://ugspace.ug.edu.gh Table of Contents DECLARATION ....................................................................................................................... ii DEDICATION .......................................................................................................................... iii ACKNOWLEGEMENTS ......................................................................................................... iv ABSTRACT ............................................................................................................................... v TABLE OF CONTENT………………………………………………………………………………………………………………vi LIST OF TABLES .................................................................................................................... ix LIST OF FIGURES ................................................................................................................... x CHAPTER ONE ........................................................................................................................ 1 INTRODUCTION ..................................................................................................................... 1 1.1 Background .......................................................................................................................... 1 1.1.1 Radioisotope Production Methods ............................................................................ 2 1.1.2 Production of Radioisotope Using Reactors ............................................................ 2 1.1.3 Production of Radioisotopes using Accelerators ..................................................... 2 1.1 3.1 Linear Energy Accelerators (Linacs) ................................................................. 2 1.1.3.2 Producing Isotopes using Electron Accelerators............................................... 3 1.1.3.3 Producing Isotopes using Cyclotrons .................................................................... 3 99 99m 1.1.4 Accelerator-based methods of Mo/ Tc productions .............................................. 6 100 99m 1.1.4.1 Reaction Mo (p,2n) Tc .................................................................................. 6 238 99 1.1.4.2 Reaction U (γ,f) Mo .......................................................................................... 7 100 99 1.1.4.3 Reaction Mo(γ,n) Mo ................................................................................... 7 100 99 1.1.4.4 Reaction Mo(n,2n) Mo ..................................................................................... 7 235 99 1.1.4.5 Reaction U(n,f) Mo using spallation neutron sources ...................................... 7 99m 1.1.5 Direct production of Tc ............................................................................................ 8 1.2 Statement of the Problem ..................................................................................................... 9 1.3Objectives ........................................................................................................................... 10 1.4 Justification of the Study ................................................................................................... 10 1.5 The Scope of the Study ...................................................................................................... 11 1.6 Structure of the thesis ....................................................................................................... 12 CHAPTER TWO ..................................................................................................................... 13 LITERATURE REVIEW ........................................................................................................ 13 2.1 Molybdenum and Technetium in Nuclear Medicine ......................................................... 13 99 99m 2.2 Major Options for Mo/ Tc Production ......................................................................... 14 2.2.1 Reactor Options ................................................................................................... 14 99 2.2.1.1 Production of Molybdenum-99, Mo .................................................................. 14 vi University of Ghana http://ugspace.ug.edu.gh 2.2.1.2 Production of Technetium-99m, Tc-99m ......................................................... 15 2.2.2 Accelerator options ..................................................................................................... 16 2.3 Overview of Current Reactors in Production of Mo-99..................................................... 17 2.3.1 Present Medical Isotope Producers ............................................................................. 20 2.4 Alternative Medical Isotope Production Technologies ...................................................... 21 99 99m 2.4.1 Accelerator Based Technologies for the Production of Mo/ Tc ........................... 22 2.4.1.1. Proton activation ................................................................................................. 23 2.4.1.2 Photo-neutron process ...................................................................................... 24 2.4.1.3 Photo-fission ........................................................................................................ 26 2.4.2 Type of Accelerator Technologies for Radioisotope Production ................................ 26 2.4.2.1 Linear accelerator technology .......................................................................... 26 2.4.2.2 Cyclotron Option Technology for the Production of Radioisotopes .................... 27 2.5 Cyclotron Suppliers ........................................................................................................... 32 99m 2.6 Direct production of Tc using cyclotrons ...................................................................... 33 99m 2.6.1 Production yield of Tc ............................................................................................ 36 METHODOLOGY .................................................................................................................. 40 3.1 Materials and Methods ....................................................................................................... 40 3.1.1 Generation of Nuclear Reaction Cross Sections ......................................................... 40 3.1.2Determination of Stopping Power................................................................................ 42 3.2 Determination of Saturated Thick Target Radionuclide Production Yield ........................ 44 3.2.1 Numerical method for the estimation of Saturated thick target radionuclide production yield (Simpson numerical integration) ................................................................................. 44 3.2.2 Numerical estimation of saturated thick target radionuclide production yield using Newton forward difference formula ........................................................................... 45 CHAPTER FOUR .................................................................................................................... 52 RESULTS AND DISCUSSION .............................................................................................. 52 4.0 Results ................................................................................................................................ 52 4.1 Variation of Proton Energy with Reaction Cross Sections for different (p+Mo) Reaction Channels ................................................................................................................... 52 4.2 Variation of Proton Energy with Reaction Cross Section for Different Molybdenum Targets through (p, n) Reactions .............................................................................................. 57 4.3 Variation of reaction cross sections with proton energies for different molybdenum isotopic targets through (p, 2n) reactions. ................................................................................ 60 4.4 Comparison of Excitation Functions of this Work and Works Done by Previous Researchers .............................................................................................................................. 64 4.5 Variation of Saturated Thick Target Yield with Operational Parameters of a Cyclotron .. 70 4.5.1 Variation of Saturated Thick Target Yield with Proton Energy .......................... 72 vii University of Ghana http://ugspace.ug.edu.gh 4.5.2 Comparison of saturated yields obtained by Newton‘s Forward Difference (N.F.D) formula and Simpson Numerical Integration (S.N.I) method. ............................................. 75 4.5.3 Variation of Saturated Thick Target Yield with Irradiation Time. ............................. 77 4.5.4 Variation of Saturated Thick Target Yield with Target Thickness. ............................ 78 4.6 DISCUSSION .................................................................................................................... 79 4.6.1 Excitation Functions ....................................................................................................... 79 4.6.2 Comparisons with Experimental Data ........................................................................ 80 4.6.3 Radionuclide Production Yield ................................................................................... 82 4.6.4 Investigation of the effects of some operational parameters on saturated ........... 83 thick target radionuclide production yield. .......................................................................... 83 CHAPTER FIVE ..................................................................................................................... 85 CONCLUSION AND RECOMMENDATIONS..................................................................... 85 5.1 Conclusion ......................................................................................................................... 85 5.2 Recommendation ............................................................................................................... 86 REFERENCES ........................................................................................................................ 87 APPENDIX .............................................................................................................................. 94 viii University of Ghana http://ugspace.ug.edu.gh LIST OF TABLES Table 3.1.1 Values of Δf as functions of particle energies…………………. .….48 Table 3.1.2 Values of some constants in the radionuclide production yield equation…………………………………………………………….. 50 Table 3.1.3 Values of some variables and constants in equations (3.9-3.19)…………………………………………………………....50 Table 4.1.1 Particle Energy and Reaction Cross Sections for Different Radionuclide Products………………………………………………54 Table 4.2.1 Particle energy and cross sections for (p,n) reactions leading to different technetium products……………………………………58 Table 4.3.1 Particle energy and reaction cross sections of (p,2n) reactions leading to the production of different technetium products………...61 Table 4.4.1 Particle energy, cross sections by Talys code and cross sections 100 99m from EXFOR data for Mo (p,2n) Tc reaction by Levkovskij (1991); Scholten et al ( 1999); Celler et al, (2011);Takacks (2003)……………………………………………………………….65 Table 4.5 Particle energy, values of reaction cross section for 100 99m Mo(p,2n) Tc, values of Stopping Power for Mo target and values of quotient of cross sections and stopping power(σ(E)/S(E).……………………………………………………71 Table 4.5.1(a) Particle Energies and Corresponding saturated thick target Radionuclide Production Yields at different times of irradiation (Simpson‘s Rule)……………………………………………………72 Table 4.5.1(b) Table of Particle Energy Ranges and Corresponding saturated thick target Radionuclide Production Yields (Newton‘s Formula)……...................................................................74 Table 4.5.2 Particle energy ranges and saturated yield values for N.F.D and S.N.I…………………………………………………………………75 Table 4.5.3: Saturated Thick Target Yields for Different Irradiation times…........77 Table4.5.4. Values of Saturated Thick target Radionuclide Production Yield and Various Thicknesses of the Target Material................................78 ix University of Ghana http://ugspace.ug.edu.gh LIST OF FIGURES Figure1.1 The schematic of a typical cyclotron (Contemporary Physics Education Project (CPEP), 2003) ……………………………………5 99 99m Figure1.2: Summary of potential accelerator-based Mo/ Tc production technologies (OECD, 2010). ……………………………...8 Figure 2.1: Molybdenum-99 Producers Using Highly Enriched Uranium (An Internal European Commission AD HOC Interservice Group, 2009).......................................................................................................19 Figure 3.1 Flow chart of the Talys code system. …………………………….…...41 Figure 3.2 Graphical User Interface of the SRIM software package ……….…..43 Figure 3.2.1 Flow chart system of SRIM software package …………….………..44 100 Figure 4.1.1: Excitation functions corresponding to the Mo+p reaction products with the highest cross sections in the investigated energy range...………………………………………………………………..56 100 99m Figure 4.2.1: Comparison of the Mo (p,n) Tc excitation function to the six other Technetium isotopes which are produced through the (p,n) reaction………………………………………………………....59 100 99m Figure 4.3.1: Comparison of the Mo (p, 2n) Tc excitation function to the other technetium isotopes which are produced through the (p,2n) reaction.................................................................................................63 Figure 4.4.1 Comparison of excitation functions (cross sections vrs energy) obtained by this work and by (Takacs et al, 2003) for 100 99m the Mo(p,2n) Tc reaction. ……………………………………….66 x University of Ghana http://ugspace.ug.edu.gh Figure 4.4.2 Comparison of excitation functions (cross sections vrs energy) obtained by this work and by (Scholten et al, 1999) for the 100 99m Mo(p,2n) Tc reaction……………………………………………67 Figure 4.4.3 Comparison of excitation functions (cross sections vrs energy) obtained by this work and by (Levkovskij, 1991) for the 100 99m Mo(p,2n) Tc reaction. …………………………………………..68 Figure 4.4.4 Comparison of excitation functions obtained by this work and by 100 99m (Celler et al, 2011) for the Mo(p,2n) Tc reaction. ……………...69 Figure 4.5 A graph of saturated thick target radionuclide production yield versus particle energy (Simpson‘s Rule). …………………………73 Figure 4.5.1. A Graph of saturated thick target Radionuclide Production Yield Versus Particle Energy (Newton‘s Formula). ………………...74 Figure 4.5.2 Graphs of particle energy against saturated yields for N.F.D and S.N.I………………………………………………………………….76 Figure 4.5.3: A graph of saturated thick target radionuclide production yield against irradiation time. …………………...………………………..77 Figure 4.5.4: A graph of saturated thick target radionuclide production yield versus various thickness of the target. ………………….……………79 xi University of Ghana http://ugspace.ug.edu.gh CHAPTER ONE INTRODUCTION 1.1 Background The development of nuclear technology was one of the significant achievements of the twentieth century and this technology and its derivatives are currently used in almost every field of human endeavor (IAEA, 2008). Radioisotopes which are the main products of this technology were first practically used by G. de Hevesy in 1911(IAEA, 2008). Radioisotopes or radionuclides are artificially produced, unstable atoms of a chemical element, which have a different number of neutrons in the nucleus, but the same number of protons and the same chemical properties. Many live for only minutes. Their existence is measured in ―half-lives.‖ i.e. the time (or how long) it takes for half of the radioisotopes to disappear. To produce radioisotopes, a stable isotope is bombarded with fast neutrons that are produced in a nuclear reactor or a particle accelerator. Radioisotopes which emit gamma rays are used today in medical diagnostics, to provide information about how certain organs—the thyroid, bones, heart, liver, and so on—is functioning, without surgery. Radioisotopes can also be used to image the progress of certain treatments, such as shrinking tumors. The radiation does not stay in the body, and there are no side-effects. Radioisotopes are also used in disease treatment, especially cancer, where gamma-emitting isotopes are attached to some kind of carrier, such as a monoclonal antibody, which targets particular cancer cells. The carrier delivers the radioisotope to the cancer site, where the gamma rays destroy the cancerous cells, with minimal damage to surrounding tissue. The use of radioisotopes in the physical and biological sciences can be broken down into three general categories; imaging, radiotherapy and radiotracers. These 1 University of Ghana http://ugspace.ug.edu.gh isotopes however need to be generated for their respective applications through two broad methods as discussed below 1.1.1 Radioisotope Production Methods There are broadly two methods of radioisotope production namely (i) production via reactor and (ii) production via accelerators. These two are discussed briefly below: 1.1.2 Production of Radioisotope Using Reactors Radioisotopes can be produced in reactors by exposing suitable target materials to the intense reactor neutron flux for an appropriate time. A wide range of isotopes are made at reactors, from as light as Carbon-14 to as heavy as Mercury-203, with irradiations lasting minutes to weeks. For example, Mo-99 (the parent to the widely used medical diagnostic radioisotope Tc-99m) is usually produced via neutron- induced fission of targets with U-235 using a four (4) to eight (8) day irradiation time(IAEA, 2009). 1.1.3 Production of Radioisotopes using Accelerators Particle accelerators and, in particular, cyclotrons, were very important in the preparation of radioisotopes during the years from 1935 to 1941. After World War II, reactors were used to produce radioactive elements, and the use of accelerators for this purpose became less common. As the techniques for using radiotracers became more sophisticated, it became clear that reactor produced radionuclides could not completely satisfy the growing demand and, therefore, accelerators were needed to produce new radioisotopes that could be used in new ways in both industry and medicine (IAEA, 2009). 1.1 3.1 Linear Energy Accelerators (Linacs) The principle of acceleration used in all accelerators is the fact that a charged particle has its energy changed when it is acted on by an electric field. In the linac, this change 2 University of Ghana http://ugspace.ug.edu.gh in energy is applied by an alternating potential, which must be applied in exactly the proper sequence to keep accelerating the particle. In practice, this is achieved with the use of hollow electrodes called drift tubes, which allow the particle to drift at constant velocity within the tube and then be accelerated between the tubes. The particle is accelerated into the tube by an electric field that is opposite in sign to the charge on the particle. As the particle passes through the hollow tube, the phase of the electric field is changed and, at the exit of the tube, the particle is accelerated with a push from the field which now has the same sign as the particle (IAEA,2008). 1.1.3.2 Producing Isotopes using Electron Accelerators In this case instead of the bombarding particles being protons (or neutrons from a reactor), they are photons or light rays. The photons are generated by directing an electron beam from a high-powered electron accelerator onto a heavy metal such as liquid mercury or water-cooled tungsten called a converter. High-energy photons known as bremsstrahlung radiation are produced by the electron beam as it interacts and loses energy in the converter target. The photons can then be used to irradiate another target material placed just behind the convertor, in this case 100 99 Mo-100, to produce Mo-99 via the reaction Mo(γ,n) Mo. The produced Mo-99 would then be incorporated into a generator system which provides Tc-99m periodically through the decay of the longer lived Mo-99 (66 hours) as compared to the half-life of Tc-99m (Ruth, 2009). 1.1.3.3 Producing Isotopes using Cyclotrons The first artificially produced radioisotopes were created on Lawrence's cyclotrons in1932, but it took another 30 years before accelerator produced radioisotopes began to play a major role in production of radiopharmaceuticals. 3 University of Ghana http://ugspace.ug.edu.gh The principle of the cyclotron is based on the application of small accelerating voltages repeatedly. Hollow cavities called dees because of their shape serve as the electrodes for the acceleration. A radio frequency (RF) oscillator is connected to the dees such that the electrical potential on the dees is alternatively positive and negative with respect to each other. By placing the dees between the poles of a strong magnet so that the magnetic field is perpendicular to the plane of motion, the charged particle undergoing acceleration will move in a circular path. As the particle gains energy it moves in a spiral outward from the centre. With the source of negative ions at a point in the centre of the cyclotron the positive dee will accelerate the ions toward that dee with magnetic field forcing them to move in a curved path. Once inside the cavity the particles no longer experience an electric force. Continuing in the circular path the particles will exit the cavity and enter the gap between the dees where the second dee has changed its potential to be an attracting force, accelerating the particles to that dee. The dees reverse their potential when the particles are inside the dees so that at each crossing of the gap the particles receive an increase in energy of the order of 20- 50keV. Lawrence discovered the equations defining this principle of operation in 1929 and built the first cyclotron in 1931. Below is the diagram of a typical cyclotron (Ruth, 2009). 4 University of Ghana http://ugspace.ug.edu.gh University of Ghana http://ugspace.ug.edu.gh Tomography) as well as the production of several PET isotopes. The SPECT isotopes have medium half-lives and production generally takes place in dedicated facilities. The longer half-lives permit isotope delivery to more distant users and this leads to dedicated production facilities with high power targets and larger throughput. (iii) Cyclotron providing protons with energies of greater than 35 MeV are used in the production of a number of the isotopes used for radio-therapy. The primary need is for high current cyclotrons with currents in the 1mA range (Schmor, 2010) 99 99m 1.1.4 Accelerator-based methods of Mo/ Tc productions 99 99m The most widely discussed accelerator-based routes of Mo or Tc production are 99 99m summarized in Figure 1.2. In the proton accelerator technologies, the Mo or Tc is produced directly via the interaction of bombarding particles with the target material as follows: 100 99m 1.1.4.1 Reaction Mo (p,2n) Tc 99m In this route Tc is directly produced for immediate use, via the reaction of 100 99m an accelerated proton with a Mo nucleus yielding Tc and two neutrons. This is 99m only useful for a local production because Tc is a short-lived radioisotope. In the electron or deuteron accelerator technologies the primary accelerated charged particles (electrons, protons, deuterons, etc.) are used to produce energetic secondary particles (photons, neutrons) that then interact with the target material to produce 99 Mo. The indirect production is intrinsically more complicated than the direct one and usually goes through different routes of reaction as follows: 6 University of Ghana http://ugspace.ug.edu.gh 238 99 1.1.4.2 Reaction U (γ,f) Mo The photo-fission of depleted uranium is induced by energetic gamma rays that are produced via Bremsstrahlung (i.e. deceleration radiation) of high-energy electrons provided by an accelerator. The processing of irradiated targets is similar to the one in the reactor-based fission routes. 100 99 1.1.4.3 Reaction Mo(γ,n) Mo Molybdenum-99 may be produced through the photon-to-neutron reaction (γ,n) 100 on a molybdenum target with enriched Mo. Photons for this reaction are provided, as in the previous technology, from the electrons deceleration radiation. 100 99 1.1.4.4 Reaction Mo(n,2n) Mo 100 99 Molybdenum-99 is produced through the Mo (n,2n) Mo reaction using an 100 enriched Mo target. High-energy neutrons for this reaction are provided by energetic deuterons bombarding a natural carbon target. 235 99 1.1.4.5 Reaction U(n,f) Mo using spallation neutron sources In this route neutrons are generated by spallation reactions induced by energetic protons bombarding a heavy metal target. These neutrons are used for fashioning the uranium nuclei in a target, as in a nuclear reactor. The process works in the same way as the reactor-based fission production route, but the system remains subcritical and can be operated by changing the proton beam intensity (OECD, 2010). 7 University of Ghana http://ugspace.ug.edu.gh University of Ghana http://ugspace.ug.edu.gh 1.2 Statement of the Problem Technetium-99m is the radioisotope commonly used in nuclear medicine. It offers many advantages as compared to many other radionuclides, due to its very good physical and chemical characteristics. The gamma radiation emitted has the appropriate energy, 140KeV to provide a good image whilst keeping low radiation 99m dose to the patient (also because Tc is a nearly pure gamma emitter: 89%). Technetium-99m accounts for nearly 85% of all nuclear medicine imaging studies (IAEA, 1999). The clinical uses of this important radioisotope enables diagnostic imaging to be carried out in many areas in the human body such as respiratory and renal systems, musculoskeletal, the central nervous systems and other body systems. 99m Despite the above importance of Tc, Ghana is not able to produce this radionuclide (Tc-99m) locally to feed its medical facilities. Due to the absence of its production locally, there is always frequent shortage of the radionuclide in our medical facilities causing unnecessary delays in medical examinations and treatment. In the absence of the local capacities for Tc-99m production, it is necessary to undertake a theoretical study to investigate the possible production locally in Ghana in the near future using cyclotrons. 9 University of Ghana http://ugspace.ug.edu.gh 1.3 Objectives Main Objective The main objective of the research is to carry out a theoretical study on the 99m production of Tc using a cyclotron. Specific objectives i. To investigate appropriate operational parameters to be adopted for a cyclotron facility to be used in Ghana and to utilize a Nuclear Reaction Model Code (Talys code) for calculating nuclear reaction cross sections for the cyclotron. 99mii. To obtain the optimum production yield for the production of Tc on an enriched molybdenum-100 target over a given range of proton-energy using the cyclotron. iii. To investigate theoretically the effects of the various operational parameters on the radioisotope production yield. 1.4 Justification of the Study 99m The use of Tc (6.02 h) in nuclear medicine is well established worldwide. Its supply and distribution is largely based on the use of reactor technologies to produce 99 235 its parent Mo (66 h), mostly by fissioning U with neutrons or, to a lesser extent, 98 by the neutron bombardment of Mo targets. After separating and purifying "Mo 99 99m from the fissioned or the activated targets, it is used to prepare Mo -» Tc generators for distribution worldwide (Lagunas-Solar et al, 1996). 10 University of Ghana http://ugspace.ug.edu.gh However the high cost of these generators is making it impossible for a developing country like Ghana to acquire them to feed all its medical facilities. A way to alleviate this situation is to develop many alternative supply centers with capabilities for local or regional supply and based upon more affordable and reachable technologies. 99m Preliminary investigations to develop alternative methods for producing Tc with accelerators were conducted in the mid 1970's. The technical feasibility of using 99m modern cyclotrons for the production of Tc was analyzed by Egan et al. (1994. Because of the above scenario it was concluded that, accelerator methods to provide 99m 99 either a direct source of Tc and/or of its parent Mo are needed as potential 99 alternatives to the reactor based production of Mo.The main advantages of the use of cyclotrons in the production of radioisotopes are as follows: (i) The high specific activity (SA) that can be obtained via the nuclear reactions that produce an isotope that is chemically different from the target element. (ii) The smaller amount of radioactive waste generated in particle reactions compared to reactor based reactions (TRIUMF, 2012). Considering the above analysis it is justifiable enough for a developing country like Ghana to acquire a cyclotron with the associated benefits stated above to produce Tc-99m to feed its medical faculties. 1.5 The Scope of the Study The study will cover calculations of cross- sections for various proton- induced nuclear reactions on molybdenum-100 target that leads to the production of various technetium products over an energy range of 5MeV-35MeV. Besides the study will 100 99m involve the comparison of excitation function of Mo (p,2n) Tc reaction to the excitation functions of other technetium isotopes which are produced through (p,2n) 11 University of Ghana http://ugspace.ug.edu.gh and (p,n) reactions. Additionally, the study will cover the estimation of the optimum 99m production yield of Tc within the optimum energy range. Finally, a numerical solution for the saturated radionuclide production yield equation using the Newton‘s forward difference formula will be attempted which aims at investigating the effects of the various operational parameters on the yield. 1.6 Structure of the Thesis This research work has been organized into five chapters. Chapter one is the introduction of the thesis. It highlights the background of the thesis, the statement of the problem of the research, the objectives, the scope, the justification as well as the structure the thesis. Chapter two is the literature review of the thesis which takes a critical review of previous works that have been done both experimentally and theoretically in line with the production of Technetium-99m. Chapter three spells out the materials and the methodology used in carrying out this research. Chapter four deals with presentation of results. Here the various results obtained during the research are presented in tables and graphs and are thoroughly discussed. Chapter five is the last chapter and it talks about the conclusion and the recommendations for the research. 12 University of Ghana http://ugspace.ug.edu.gh CHAPTER TWO LITERATURE REVIEW This chapter presents a review of literature in the fields of isotope production as a foundation for a better understanding of this study. 2.1 Molybdenum and Technetium in Nuclear Medicine Molybdenum is used as a target material for the production of medically important 99m 99 96(m+g) 94m 94m radioisotopes, such as Tc/ Mo, Tc and Tc. Tc (t½=52min), has shown 96 its applicability as a PET isotope (Fabbender, et al., 1994; Hohn, et al., 2008). Tc with a have life of 4.28 days (t½=4.28d) has been proposed for the use in prevention of coronary restenosis by Fox (2001). Despite of favorable moderate half-life, other 93 94 95 isotopes of Technetium, like, Tc (t½=2.75h), Tc (t½=4.883h) and Tc (t½=20.0h) 94 are seldom discussed. Specially, radiological half-life of Tc is ideal for diagnostic 95 purposes. Tc (t½=20.0h), due to its comparatively longer half-life is also promising for tracking long processes, like, metabolic pathways for brain and heart, studies with 93 proteins, anti-bodies, etc. Among short-lived radionuclides, Tc (t½=2.75 h) is another promising isotope for imaging as suggested by (Lambrecht and Montner, 99m 1982). One of the most important medical radioisotopes is Tc (T½= 6.01 h), which has a gamma ray energy of about 140 keV. The fact that both its physical half-life and its biological half-life are very short, leads to a very fast clearing from the body after an imaging process. A further advantage is that the gamma is a single energy, not accompanied by beta emission, and that permits a more precise alignment of imaging detectors. 99m 99 Tc is obtained from the decay of its parent isotope Mo. It was discovered in 1937, 99 99m and the first Mo/ Tc generator was invented at the Brookhaven National 99m Laboratory in the U.S. in 1957 (Googhand et al, 2009). General usage of Tc began 13 University of Ghana http://ugspace.ug.edu.gh in the early seventies when the Chalk River Laboratory established routine production 99 99m of Mo, its parent isotope (Tammemagi and Jackson, 2009; Ullyett, 1997). Tc is versatile and can be used to produce some 20 different compounds of radiopharmaceuticals. There are various technological options for the production of 99m 99 Tc/ Mo (Alharbi et al. 2011). 99 99m 2.2 Major Options for Mo/ Tc Production 99 99m There are broadly two major ways to produce Mo/ Tc, that is via reactors and accelerators for which typical nuclear reactions are outlined below. 2.2.1 Reactor Options 235 Through fission of U: 235 →99 n+ U Mo + xn + other fission products (2.1) where x = number of neutrons 235 U= Uranium-235 isotope 99 Mo= Molybdenum-99 isotope 98 Or through the neutron activation of Mo: 98 99 n + Mo→ Mo (2.2) 99 2.2.1.1 Production of Molybdenum-99, Mo 99 The usual production of Mo for nuclear medicine depends on: 1. 235The neutron induced fission of U, which results in expensive but high specific 99 activity Mo (IAEA-TECDOC, 1999), 98 2. The (n) nuclear reaction with Mo, 24% using natural Molybdenum, resulting 99 in inexpensive but low-specific activity Mo. Thus, for either method, at least 14 University of Ghana http://ugspace.ug.edu.gh one neutron is required for the reaction. Neutrons can be produced from accelerator reactions where the charged particles strike heavy atoms, also from alpha or gamma reactions with light atoms, such as beryllium or lithium. However, to produce the large quantities of neutrons needed for production of 99 useful quantities of Mo, the most effective source is a critical nuclear reactor operating at powers in the range of megawatts. Each fission process of an atom 235 of U produces an average of about 2.5 neutrons. In an operating reactor, these neutrons either are absorbed by materials in the reactor or escape from the 235 boundaries of the reactor. One neutron must cause fission in another U atom. Of the remaining 1.5 neutrons from each fission process in a critical reactor, some small fractions are available for production. The most appropriate target 99 material for low specific activity Mo production is molybdenum trioxide 98 99 (MoO3); neutron activation occurs via the reaction Mo (n,x) Mo. 2.2.1.2 Production of Technetium-99m, Tc-99m Derived from the man-made element technetium, Tc-99m emits radiation without causing significant damage to the patient and its 6-hour half-life is long enough for a medical examination and short enough to allow a patient to leave the hospital soon 99 afterwards. More importantly, Tc-99m is generated from Molybdenum-99 ( Mo or Mo-99), whose half-life of 66 hours allows for transport over long distances. Mo-99 is mostly produced at nuclear reactors where the beam of neutrons comes from the fission reaction in uranium in the reactor core. Also the target material contains uranium (U-235) that after irradiation is split in various completely different elements including Mo-99. The raw irradiated target material from the reactor, containing a variety of radioisotopes, then travels to a separate facility. It is dissolved in either 15 University of Ghana http://ugspace.ug.edu.gh nitric acid or alkaline solutions for one to three hours, after which the Mo-99 can be recovered and purified by a variety of processes. Mo-99 is send to the manufacturer of Tc-99m generators, which is often located close to the Mo-99 producer. The Tc-99m generators must then quickly be forwarded to hospitals and other users. A radiopharmacy in the hospital will recover Tc-99m from the generator and add this to the nonradioactive components of radiopharmaceuticals. In case of molecular imaging, Tc-99m will be combined with the relevant biomolecules to form the specific radiopharmaceutical for administration to a patient (Gelder and Herder , 2010). 2.2.2 Accelerator options 238 Through the Photo-fission of U: 238 99 Photon + U→ Mo + xn + other fission products (2.3) Where x= the number of neutrons and other symbols have their usual meanings. 238 99 U= Uranium-238 isotope, Mo= Molybdenum-99 isotope 100 Through the Mo transmutation: 100 99 Photon + Mo→ Mo + n (2.4) 100 Where p= proton, Mo= Molydenum-100 isotope and n= neutron Through the Direct 99mTc production: 100 →99m p + Mo Tc + 2n (2.5) 16 University of Ghana http://ugspace.ug.edu.gh 100 99m where p= proton, Mo= Molydenum-100 isotope, n= neutron and Tc= Technetium-99 metastable isotope. The potential use of accelerators for these purposes is another issue of current scientific and technological interest. Recently, a matter of concern has been the 99 availability and supply of Mo for the manufacturing of generators. These concerns arose from several factors including, amongst others, the shutdown of some nuclear reactors, uncertainty of reliable operating condition for radioisotope production and 235 easy availability of enriched U target materials. More recently, the utilization of charged particle accelerators, either LINAC's or cyclotrons, has been discussed as a potential alternative technology to the fission route. These discussions have been prompted by basic research concerns as well as the need to explore Radioisotope – applications in bio-medical science, new production routes to offset the perceived 99 situation of future problems with the availability of Mo if no new dedicated reactors 99 100 are licensed. The production of Mo via the Mo(p,pn) reaction was evaluated. A good agreement was found among the different excitation functions available. However, because of the rather low cross-section values found in these 99 measurements, the production of Mo via this potential process was found to be largely impractical (Alharbi, et al., 2011). 2.3 Overview of Current Reactors in Production of Mo-99 Reactors used in the production of Mo-99 can be classified into two categories. Those producers using highly enriched Uranium (proportion of U-235 is higher than 25% - HEU) and low enriched Uranium (proportion of U-235 is lower than 25% - LEU) targets (Hansell, 2008) .All of the organizations that currently produce Mo-99 utilize government-owned research/test reactors to irradiate targets (Interservice Group, 17 University of Ghana http://ugspace.ug.edu.gh 2009). In some cases also the Mo-99 recovery/processing facilities are government- owned. The principal producers worldwide: i. MDS Nordion (Canada): MDS Nordion provides approximately 40 percent of world supply. It obtains raw Mo-99 from the Atomic Energy of Canada Limited (AECL), a Canadian government-owned Crown Corporation. AECL is responsible for (HEU) target fabrication, target irradiation, and target processing to recover a solution containing Mo-99. Irradiation takes place in the NRU (National Research Universal) reactor at the Chalk River Site in Ontario, Canada. The targets are processed at their Chalk River. The separated Mo-99 is shipped to MDS Nordion‘s plant in Ottawa for purification and preparation for distribution. (Interservice Group, 2009) ii. Mallinckrodt–Covidien (The Netherlands): Mallinckrodt produces about 1/4 of world supply. Production is carried out at the Petten Site in the Netherlands in a joint venture with NRG (Nuclear Research and Consultancy Group) the reactor operator. iii. Institute National des Radioéléments (Belgium): IRE produces approximately 20 percent of the world supply of Mo-99. Its production takes place at Fleurus, Belgium. The HEU targets are irradiated in the HFR reactor, which is located at the Petten Site. The BR2 reactor, which is located in Belgium, and the Osiris Reactor, which is located in France are used as backup. After irradiation, the targets are processed in a facility at the Petten Site. (Interservice Group, 2009) iv. NTP Radioisotopes (South Africa); NTP, part of the South African Nuclear Energy Corporation (NECSA), produces about 10% world supply of Mo-99. It produces Mo-99 from HEU (45% enriched) targets, which are irradiated in the 18 University of Ghana http://ugspace.ug.edu.gh University of Ghana http://ugspace.ug.edu.gh 2.3.1 Present Medical Isotope Producers 99 While radioisotopes, and especially Mo, are at present commonly produced in research reactors, not all research reactors in the world are able or willing to produce them. The analytical and research capabilities of a research reactor are determined primarily by the available thermal neutron flux. The database of International Atomic Energy Agency (IAEA) keeps record of operational research reactors in the world and categorizes them as a low flux, medium flux, or high flux reactor according to the following levels of thermal neutron flux: i. 12 2107 low flux reactors (≤ 1 x 10 n/cm /s). 12 2 14 2 ii. 85 medium flux reactors (> 1 x 10 n/cm /s and < 1 x 10 n/cm /s) 14 2 iii. 55 high flux reactors (≥ 1 x 10 n/cm /s) The amount of radioactivity of radioisotopes formed is proportional to the neutron flux: the higher the neutron flux, the higher the radio activity. This explains the importance of nuclear research reactors with high power or high neutron flux for the 99 99 production of radioisotopes, especially Mo. The worldwide production of Mo basically depends on six nuclear reactors: the OPAL in Australia, the BR2 reactor in Belgium, the NRU in Canada, the High Flux Reactor (HFR) in the Netherlands, SAFARI-1 in South Africa and, to a lesser extent, the OSIRIS in France. The production schedules of these reactors are matched to comply with the need for medical isotopes. These producers of medical isotopes are aging. In 2009 the NRU was shut down again for necessary, but unscheduled, repairs. Because of the risk that a possible break down of more than one reactor at the same time will result in medical isotope shortage, many people involved argue that new reactors are needed to safeguard the supply of medical isotopes. Plans for new reactors are being developed, taking a lot of time and investments. For example, the construction of Pallas 20 University of Ghana http://ugspace.ug.edu.gh (Netherlands) is estimated at € 500 million and Jules Horrowitz (France) at € 500 million. Besides these six major producers, other reactors do produce radioisotopes for application in nuclear medicine, but only in small amounts and for the national market. However, most reactors are dedicated for research and are not equipped with the necessary facilities to regularly produce medical isotopes. When looking for alternative production methods to avoid the disadvantages of nuclear reactors, the 99 challenge is to identify those techniques which have high yields of Mo and high specific radioactivity. It is also important to consider the necessary facilities for the 99m production of Tc generators and the infrastructure for transport to hospitals, 99 because a constant and reliable supply of Mo is critical for nuclear medicine (Gelder and Herder, 2010). 2.4 Alternative Medical Isotope Production Technologies 99 All of these technologies should be able to produce high yields of Mo with high 99 specific radio activity, guaranteeing a constant and reliable supply of Mo to the 99m manufacturers of Tc generators and from there to hospitals and other users. The alternative technologies are grouped in four groups, based on the basic technology used: i. Accelerators ; ii. Nuclear reactors; iii. Accelerator driven systems; iv. Generators. However, in this work we would like to focus on only accelerators method as an alternative method for medical isotope production due to its numerous advantages spelt out under the justification. 21 University of Ghana http://ugspace.ug.edu.gh 99 99m 2.4.1 Accelerator Based Technologies for the Production of Mo/ Tc An accelerator (also called a cyclotron) is a high voltage machine made to accelerate particles. The energy of the particles may range from a few electronvolts (eV) up to nearly teraelectron-volts (1000 billion eV). Electrons, protons, and all kind of charged particles are accelerated to produce X-rays, neutrons, charged particle beams and radioisotopes for use in research and technology. Accelerators can vary in size between one small enough to fit on a table, up to huge machines tens of kilometres in length. They can be linear or circular, can operate in continuous or pulsed modes, and utilize many techniques to accelerate ion beams. A few hundred accelerators are used worldwide to produce short-lived medical isotopes, needed for producing medical 11 13 15 18 isotopes required for positron-emission tomography procedures ( C, N, O, F). These isotopes cannot be produced in nuclear reactors (Gelder and Herder , 2010 ). An accelerator based approach has some major advantages over nuclear reactors: i. The accelerator can be turned on and off at will and without consequence ii. The accelerator does not produce radioactive waste from its operation although waste from chemical processing of irradiated targets to recover 99 and extract the Mo would be similar to a reactor-based approach iii. An accelerator is safe, no risk of nuclear accidents iv. The technology is scalable: additional accelerators can be built or turned on and off as needed v. Higher predictability of schedule, cost and licensing than for a reactor. The main facility costs and licensing issues should be reasonably low in risk vi. At end-of-life, an accelerator is comparatively inexpensive to decommission as major components are less prone to become radioactive 22 University of Ghana http://ugspace.ug.edu.gh over time than occurs in the high neutron environment of an operating reactor. Furthermore, accelerators are devices that impart high energies to particles by accelerating them through electrical or magnetic fields. These high energy particles when directed on a target nuclide may lead to the formation of an unstable nucleus thus inducing radioactivity. The production of radionuclides with an accelerator requires that particles beams are delivered with two specific characteristics. The beams must have sufficient energy to bring about the required nuclear reactions and sufficient beam current to give practical yields. The source of particles for accelerators produces electrically charged particles, because most accelerating devices use electrical and magnetic field effects for acceleration. The sources may provide negative ions, electrons or positive ions. The latter are the most common, especially protons, deuterons, and alpha particles. Some particle accelerators include Cockcroft-Walton accelerator, Van de Graff accelerator, Linear accelerator, Cyclotron and synchrotron (PA, 2011). 99 There are various options by which accelerators can be used to produce Mo the 99m parent atom of Tc. These options are briefly described below (Gelder and Herder, 2010). 2.4.1.1. Proton activation Irradiation of stable elements with protons in accelerators also results in radioisotopes of the irradiated element. An accelerator can for example be used for facilitating the 100 99 100 Mo (p,pn) Mo reaction, taking one neutron from the stable Mo. An accelerator 99 with high beam power can only produce 0,64 Ci Mo/hour from 100% enriched 100 Mo. This means that there are about 160 accelerators needed to produce an 99 equivalent of Mo as for example the High Flux Reactor in Petten is able to produce 23 University of Ghana http://ugspace.ug.edu.gh through fission of uranium targets. With the current available accelerators it is not 99 (yet) possible to produce the amount of Mo that hospitals need. Advantages of this approach i. No use of HEU or LEU for targets ii. No high level radioactive waste, because no reactor is operated 99miii. In case of Tc production, local and regular production is possible Disadvantages of this approach: 100 99 i. Only part of the expensive Mo converts into Mo, other Mo- isotopes will cause competitive reactions and production of harmful Tc-isotopes 99 99mii. Lesser quality of end product than reactor produced Mo or Tc iii. A hospital would need its own production and manufacturing facilities (Gelder and Herder , 2010 ) 2.4.1.2 Photo-neutron process The photo-neutron process uses a high-powered electron accelerator to irradiate a high-Z converter target such as liquid mercury or water-cooled tungsten. High-energy photons (known as Bremsstrahlung) radiation is produced by the electron beam as it interacts and loses energy in the converter target. The photons can then be used to 100 irradiate another target material placed just behind the convertor, in this case Mo, to 99 produce Mo. In short: an intense photon beam generated by an electron accelerator 100 99 removes a neutron from a Mo target to produce Mo (stimulating the reaction 100 99 Mo(γ,n) Mo). According to the Task Force on Alternatives for Medical Isotope 100 Production ―some research and development work to examine the Mo target 24 University of Ghana http://ugspace.ug.edu.gh 99m chemistry for direct extraction of Tc could be considered. If successful, it could make the possibility of very small, self contained generator systems being possible for central radio-pharmaceutical labs for a group of hospitals, very similar to PET cyclotrons.‖ Advantages of this approach i. There would be nearly no waste stream, except waste from chemical 99 processing of irradiated targets to recover and extract the Mo; ii. Higher predictability of schedule, cost, and licensing than for a reactor; iii. The main facility costs and licensing issues should be reasonably low risk; iv. Scalable: it can be built as a small (low power) facility or large facility, because; v. technology is equally useful over a wide range of powers; vi. No high level radioactive waste, because no reactor is operated. Disadvantages of this approach i. A major change in the generator technology would be needed because of the different target; ii. An accelerator-based production facility would require substantially more electrical power than a reactor-based facility; iii. Pharmaceutical authorities need to approve these new products; 100 iv. The cost of manufacturing Mo targets and the cost of separating 100 99 100 Mo from Mo would likely be quite high, because Mo comprises less than 10% of naturally occurring molybdenum and the separated 25 University of Ghana http://ugspace.ug.edu.gh isotope presently costs dollars per milligram (Gelder and Herder, 2010). 2.4.1.3 Photo-fission The present-day technique uses a neutron to split uranium. An alternative solution uses a photon instead to fission the uranium nucleus. The proposed photo-fission accelerator approach would produce high-energy photons to split natural uranium U- 100 238 with the same fractional production of Mo as produced by neutrons. According to a 2008 study of TRIUMF, the photo-fission accelerator technique has several key advantages and the authors highly recommend further research and investments. This 99 technology is expected to generate sufficient quantities of Mo to supply a significant fraction of the North American demand. The conceptual design is not established yet and there are substantial uncertainties in the capital cost and eventual operating costs. However, according to TRIUMF construction of such an accelerator will be much faster than design and construction of a new reactor, such as Pallas (which will take probably ten years). 2.4.2 Type of Accelerator Technologies for Radioisotope Production 2.4.2.1 Linear accelerator technology 100 99 Another proposed technology that transforms Mo into Mo is the linear accelerator technology, using beams of electrons. A linear particle accelerator (often shortened to linac) is a type of particle accelerator that greatly increases the velocity of charged subatomic particles or ions by subjecting the charged particles to a series of oscillatingelectric potentials along a linearbeamline; this method of particle acceleration was invented by Leó Szilárd. It was patented in 1928 by Rolf Widerøe, 26 University of Ghana http://ugspace.ug.edu.gh who also built the first operational device and was influenced by a publication of Ising Gustav (http://en.wikipedia.org/wiki/Linear_particle_accelerator). Linacs have many applications: they generate X-rays and high energy electrons for medicinal purposes in radiation therapy, serve as particle injectors for higher-energy accelerators, and are used directly to achieve the highest kinetic energy for light particles (electrons and positrons) for particle physics. For the production of technetium-99m, the electron beams are fired at a metal screen, 100 99 where they produce X-rays that irradiate Mo, producing Mo that decays into 99m Tc. Linear accelerators could be distributed directly to hospitals to manufacture 99m 99 and use Tc directly. Alternately, offsite linear accelerators could produce Mo, 99m and hospitals will extract the Tc. Teams developing this technology include a consortium led by Canadian Light Source, and another led by the Prairie Isotope Production Enterprise (PIPE), including the University of Winnipeg and the University of Manitoba (Science Media Centre of Canada, 2012). 2.4.2.2 Cyclotron Option Technology for the Production of Radioisotopes Among the above listed particle accelerators, cyclotrons, which use positive ions as particle source are the most commonly used for the production of radioisotopes employed in medicine and industry. The cyclotron was devised by E. O. Lawrence in 1931, to accelerate charged particles like protons, deuterons and alpha particles, and was awarded the Nobel Prize in 1939 for its development (Lawrence, 2010). These particles are accelerated to high energy levels and are allowed to strike the target material thereby inducing nuclear reactions. The cyclotron and its later modifications quickly became favorite research tools for nuclear scientists due to their ability to 27 University of Ghana http://ugspace.ug.edu.gh accelerate charged particles to energies of hundreds of MeV with beam currents of hundreds of microamperes. Generally, the target and product nuclides in a cyclotron are different chemical elements. This makes it possible to find suitable chemical or physical methods to separation. High specific activity (S.A) is obtained owing to the target and product being different elements and fewer radionuclide impurities are produced by selecting an appropriate target material. Radioisotope production with cyclotrons offers many advantaged over a nuclear reactor due to the following reasons: the production is centralized in that the cyclotrons can be located at the site of application (e.g. hospital etc), thereby enhancing the delivery of radiopharmaceuticals to patients on time. Additionally, the volume of radioactive waste generated by cyclotrons is far less and much less hazardous than the radioactive waste of nuclear reactors. Besides, the risk of nuclear transport accidents is practically zero. Moreover, there is no risk due to nuclear power accidents because there is no need for controlled chain reactions. Finally there is no proliferation risk associated with cyclotrons (IAEA, 2009). According to Schmor (2010), Cyclotrons are the primary tool for producing the shorter-lived proton-rich radio-isotopes currently used in the biosciences. He added that, although the primary use of the cyclotron produced short-lived radio-isotopes is in PET/CT and SPECT diagnostic medical procedures, cyclotrons are also used in producing longer-lived isotopes for therapeutic procedures. Commercial suppliers are responding by providing a range of cyclotrons in the energy range of 3 to 70 MeV. Cyclotrons generally have multiple beams servicing multiple targets. Schmor (2010) sought to provide a comparison of some of the capabilities of the various cyclotrons currently in existence. The use of nuclear medicine and the number of cyclotrons 28 University of Ghana http://ugspace.ug.edu.gh providing the needed isotopes is increasing. In the future it is expected that there will be a new generation of small 'table top' cyclotrons providing patient doses on demand. Cyclotrons have become the tool of choice for producing the short-lived, proton-rich radio-isotopes used in biomedical applications (Milton, 1996). Industry has responded with a variety of cyclotrons to address the particular needs of different users groups. Most of these machines have been installed in hospitals, institutes for academic research, and commercial facilities specializing in producing and selling of radio- isotopes. Schmor (2010) further stated that cyclotrons for biomedical radionuclide production are generally compact, accelerate light ions (proton, deuteron or helium) and are primarily used to produce short-lived, proton-rich radio-nuclides. He said, the main use of these unstable isotopes is for diagnostics and therapy in biomedicine. Other fields using radio nuclides as tracers include agriculture (bio-kinetics in plants and soil), biology (bio-chemical and toxicological studies), ecology (pollution, environmental impact, and ecology studies), Geology (migration of elements in soils and waters) and pharmacology (metabolic studies). He added that the use and need of radio-active isotopes for biomedical applications continues to increase worldwide, however, the list of radio nuclides and the applications have not changed significantly over the past 20 years. Five years after demonstrating the first cyclotron in1931, G. Lawrence was producing phosphous-32 with an accelerator and for injection into a patient with chronic leukemia. Other isotopes generated by his cyclotron also had important applications in medicine (Schmor, 2010). 99m 100 99m Feasibility of cyclotron production of Tc via the Mo(p,2n) Tc reaction was demonstrated in the early seventies (Beaver and Hupf 1971). Subsequently, a number of theoretical and experimental studies investigated cross sections, yields, as well as other aspects of accelerator-based isotope production (Sholten et al. 1999, Takacs et 29 University of Ghana http://ugspace.ug.edu.gh al. 2003, Gagnon et al 2011). Various Institution and governments have also help carried our various accelerator based projects to investigate the commercial 99 99m production of Mo and/or Tc. Notable amongst them is the Government of Canada which sponsored four such projects which have been reported by various scientists 100 99 100 (Ruth, 2012). Two were based on the photo transmutation of Mo into Mo ( Mo 99 100 99m (μ,n) Mo) and two based on proton irradiation of Mo to produce Tc directly 100 99m ( Mo(p,2n) Tc). One of the cyclotron teams involved collaborations between the University of Alberta, the University of Sherbrook and ACSI. i. Establish optimal irradiation conditions to maximize yield and purity which involves defining the beam energy range (effecting yield and purity), current (which effects yield). ii. 100Target characteristics (the enrichment of Mo, the isotopic composition of other Mo isotopes which will impact purity, establish the target plate capable of being irradiated at high beam current, the encapsulation of the target to enable target transfer, and establish the 100 ability to recycle the enriched Mo) iii. The optimal time of irradiation will impact the production, cooling (Ruth, 2012). Nuclear medicine applications of the cyclotron produced radiopharmaceuticals are being increasingly utilized for both research and routine clinical diagnosis and therapy of an extensive variety of diseases (Ibrahim et al, 2012). He added that numbers of medium energy cyclotrons world-wide have rapidly increased specially after the introduction of Positron Emission Tomography (PET) and this number is expected to 99 grow in the future. He said due to the major shortage supply of the Mo-99 ( Mo) caused by the prolonged shutdown of various reactors, the need to explore alternative 30 University of Ghana http://ugspace.ug.edu.gh methods of producing Technetium-99m isotope using medium energy cyclotron is well justified to allow continued use of all existing radiopharmaceuticals designed for 99m Tc in nuclear medicine. Recently, a numbers of countries have embarked on 99 research programs to investigate the use of accelerators for the production of Mo or 99m 100 99 Tc directly. These approaches make use of the Mo(γ,n) Mo and 100 99m Mo(p,2n) Tc reactions, respectively. Early indications have shown that the cyclotron approach holds promise for at least being able to supplement generator availability with production rate of 17mCi/μAh. At this rate it is possible for the existing cyclotrons with proton energies of 16-19 MeV and beam current ranging 99m from 60-100 μA to produce significant amounts of Tc for local use on a daily basis. (Ibrahim et al, 2012) Contributing to the alternative methods for the production of Mo-99/Tc-99m instead 99m of the reactor methods, Suzanne et al (2012) stated that Tc is the most commonly used isotope in diagnostic nuclear medicine with over 16 million scans using this isotope performed annually in the United States and over 40 million scans performed annually worldwide (Orienstein, 2009) . Common procedures using this isotope include bone scans, heart studies and more recently, targeted molecular imaging in 99m oncology using agents such as Tc octreotide analogues (Cwikla et al, 2008). From 99m their research, Tc is commonly available in a generator form. In this system, the 99 parent radionuclide Mo (t1/2 = 2.75 d) is bound to a solid phase column and the 99m daughter isotope, Tc, is continuously ‗milked‘ off the column with a saline eluant and incorporated into an appropriate radiopharmaceutical. In this manner hospital nuclear medicine departments can have a generator delivered approximately once a 99m week for ongoing maintenance of Tc supplies for diagnostic patient procedures. 31 University of Ghana http://ugspace.ug.edu.gh 99 They reported that, presently, the majority of the United States supply of Mo is generated by Canadian reactors. These reactors are ageing and have become unreliable with several recent unexpected shutdowns. Over the last few years the 99m Tc isotope supply has been drastically reduced due to issues with the Canadian reactors and with other suppliers in the world. In addition to this vulnerability in supply due to the reactors‘ age, these reactors run using highly enriched (weapons 99 grade) uranium fuel (HEU) for the production of Mo, HEU is a proliferation risk and thus there are significant security issues associated with the current route of production (Suzanne et al., 2012) 2.5 Cyclotron Suppliers Commercial companies have responded to the varied user specifications with a number of basic cyclotrons with optional add-ons in an attempt to satisfy each particular need and budget. A short comparative summary of cyclotrons contained in a table can be found in Appendix at the end of this thesis. The table lists some of the important characteristics of the cyclotrons offered by many of the current industrial suppliers. Most manufacturers have the option of self-shielding for the cyclotrons when the maximum energy is less than 15 MeV. The customer must choose between vault (concrete) shielding versus the more expensive but compact arrangement of close packing steel around the cyclotron and targets. (Schmor, 2010) 32 University of Ghana http://ugspace.ug.edu.gh 99m 2.6 Direct production of Tc using cyclotrons 99m 100 The direct production of Tc using lower energy medical accelerators via the Mo (p,2n) reaction has several advantages, some of which are listed below: 99m Cyclotrons already in operation could be used to produce Tc, thus alleviating the problem without having to invest in new infrastructure. The ability to produce these isotopes onsite at hospitals will result in less shipping, thus reducing costs and loss of the radionuclide due to decay. This method is an alternative to using HEU and thus solves the proliferation risk associated with current methods of production. Overall this is a straightforward solution to the current isotope crisis which also addresses the proliferation issues associated with the current method of production. The sharing of this technology with institutes in developing nations will enhance the supply, utilization and hence the reliability of these important radiotracers (TRIUMF, 2012). According to Mayeen et al, (2006), beside the general interest of basic nuclear physics, intermediate energy activation cross-sections data are of increasing importance for a wide variety of applications. The remarkable applications are in the field of space and environmental sciences, medical sciences (radioisotope production, dosimetry application, radiation therapy etc.). They introduced a systematic study of medium energy proton induced reactions on some important structural and instrumental materials. Their study of proton induced activation reactions on natural molybdenum was a part of the above systematic measurements due to its importance 33 University of Ghana http://ugspace.ug.edu.gh as structural materials, and the rigorous use of activation cross-section of molybdenum for proton beam over a wide energy range. 99m The report that, the production cross-section of Tc was calculated through the analysis of 140.51keV gamma peak. Basically, this radionuclide can be produced in 100 99m two processes. One is direct process through the reaction Mo(p,2n) Tc and the 100 99 99m other is indirect process via Mo(p,pn) Mo→ Tc reaction. 98 99m Although theoretically, the reaction Mo(p,γ) Tc has little contribution in the 99m production cross section of Tc, they neglected this contribution in the present case. 99m This is because; the process has no practical relevance for the production of Tc. They found a good agreement with evaluated data MENDL-2P. According to them, the data reported by Scholten et al is quite higher than our data but the trend of peak formation agrees to each other. In their experiment, they worked with the 97.4% and 100 98 99.5% enriched Mo and Mo sample, respectively but we performed the present experiment using natural molybdenum sample. Moreover, it should be emphasized 100 99m that the Mo(p,2n) Tc reaction cannot be compared to a normal (p,2n) reaction, since the product activity is an isomeric state. An accurate experimental data base is thus crucial to consider the feasibility of this reaction for a possible production of 99m Tc at a cyclotron. A limiting factor in this regard would be the level of co- 99g produced long-lived Tc impurity. Experimentally, this is very hard to determine and was outside the scope of the present work. Technetium-99m has emerged as the most widely used radionuclide in medicine and 99 99m is currently obtained from a Mo/ Tc generator system (Gagnon, 2012). At present, there are only a handful of ageing reactors worldwide capable of producing large 99 quantities of the parent isotope, Mo, and owing to the ever growing shutdown 34 University of Ghana http://ugspace.ug.edu.gh 99m periods for maintenance and repair of these ageing reactors, the reliable supply Tc has been affected in recent years. With an interest in alternative strategies for producing this key medical isotope, Gagnon, (2012) thesis focuses on several 99m technical challenges related to the direct cyclotron production of Tc via the 100 99m 100 Mo(p,2n) Tc reaction. Highly enriched Mo was required as the target material 99m for Tc production and a process for recycling of this expensive material is presented. An 87% recovery yield was reported, including metallic target preparation, 99m irradiation, Tc extraction, molybdate isolation, and finally hydrogen reduction to the metal. Further improvements are expected with additional optimization experiments. A method for forming structurally stable metallic molybdenum targets had also been developed which are capable of withstanding more than a kilowatt of 99m beam power and the reliable production and extraction of Curie quantities of Tc. 99m Cyclotron-produced Tc has been extensively compared with relevant United States 99 99m Pharmacopeia (USP) specifications for the existing Mo/ Tc production strategy, 99m 99m including biodistribution studies of [ Tc] pertechnetate and [ Tc]disofenin in both mice and rabbits (Gagnon, 2012). Takács 99 99m et al (2003) reported that, the use of the Mo→ Tc generator in nuclear 99 medicine is well established world- wide. The production of the Mo (T1/2 = 66 h) 235 parent as a fission product of U is largely based on the use of reactor technology. From the early 1990's accelerator based production methods to provide either direct 99m 99 produced Tc or the parent Mo, were studied and suggested as potential 99 alternatives to the reactor based production of Mo. A possible pathway for the 99m 99 charged particle production of Tc and Mo is irradiation of molybdenum metal 100 99m 100 99 with protons via the reaction Mo(p,2n) Tc and Mo(p,pn) Mo, respectively. 35 University of Ghana http://ugspace.ug.edu.gh 100 99m In Scholten et al, (1999) excitation functions for the Mo(p,2n) Tc, 98 99m 100Mo(p,pn)99Mo and Mo(p,γ) Tc nuclear reactions were determined using 97.4 100 98 and 99.5% isotopic enrichment of Mo and Mo, respectively. The irradiations were performed on three different cyclotrons with overlapping data points from 6 to 65 100 99m MeV. The optimum energy range for the Mo (p,2n) Tc reaction was 22→12 MeV with a peak at ∼17 MeV and maximum cross section of ∼200 mb. Over this 99m energy range the production yield of Tc amounts to 11.2 mCi (415 MBq)/μA h or 102.8 mCi (3804 MBq)/μA at saturation. The study did not show any serious 99 radionuclide impurity problem and that, the production of Mo was not viable due to the low cross section (∼130 mb) over the proton energy range of 30 to 50 MeV. The 89 99m Mo(p,γ) Tc reaction was found to have a cross section of <0.2 mb over the proton energy range studied. The earlier assignment of this reaction channel as a potential 99m route for production of Tc with a medical cyclotron is refuted in this study. 99m 2.6.1 Production yield of Tc 100 According to Ibrahim et al. (2012), bombarding enriched Mo target with proton 99m beam, Tc can be produced directly in the (p,2n) reaction and also in the decay of 99 the parallel co-produced Mo. Production can be made by low energy, high intensity 100 commercial cyclotrons on an appropriate design of enriched Mo target. They observed that depending on the bombarding energy, the target thickness and the applied irradiation parameters beam current, irradiation time and cooling time, 99m different amounts of Tc would be available in the target for post irradiation processing. They said during a relatively short irradiation no considerable 99 99m contribution can arise from decay of Mo. Since the half-life of Tc (T1/2 = 6.01 h) 99 is much shorter than the half-life of its mother Mo (T1/2 = 66 h). The post irradiation 99m processes should be started as soon as possible in order not to lose activity of Tc 36 University of Ghana http://ugspace.ug.edu.gh 99 99m since the decay of Mo can compensate only fraction of the activity loss of Tc by applying longer cooling time (TRIUMF, 2012). 99m Alharbi et al (2011) reported that Tc is obtained from the decay of its parent 99 99 99m isotope Mo. It was discovered in 1937, and the first Mo/ Tc generator was invented at the Brookhaven National Laboratory in the U.S. in 1957. General usage of 99m Tc began in the early seventies when the Chalk River Laboratory established 99 routine production of Mo, its parent isotope (Tammemagi and Jackson, 2009; 99m Ullyett, 1997). Tc is versatile and can be used to produce some 20 different compounds of radiopharmaceuticals. In their work, it was realized that the three reactions contributing to the production of 99m 98 100 100 Tc by direct way are Mo(p,ɣ), Mo(p,2n), and indirect way by Mo(p,pn). 100 99m Possibly, the highest contribution is from the Mo(p,2n) Tc reaction (on the 100 99m 9.63% Mo present in the highly chemically pure Mo sample). Activity of Tc was measured in this work by detecting the gamma peak at energy 140.5 MeV after the resolution of this peak as described before. 99m 100 The production of Tc via the Mo(p,2n) reaction was evaluated, and the cross section data available were found to be consistent and in good agreement. 99m Extrapolating Tc yields obtained from this data, using the operational conditions of the existing 30 MeV accelerator technologies, suggest that large-scale (kCi) 99m production of Tc is possible (Glenn, et al., 1997). All the measured cross sections over the whole energy range were simulated using Talys code (Koning, et al., 2011), which is a computer program that integrates all types of nuclear reactions in the energy range of 1 keV-200 MeV. 37 University of Ghana http://ugspace.ug.edu.gh Celler et al, (2011) carried out some research work which investigated the various 100 99m parameters that lead to the production of technetium-99m through Mo(p,2n) Tc 99m reaction using a cyclotron. According to the authors, the production yields of Tc and various other radioactive and stable isotopes which would be created in the production process have been investigated, as these may affect the diagnostic outcome and radiation dosimetry in human studies. Besides, reaction conditions (beam and target characteristics, and irradiation and cooling times) needed to be investigated and 99m optimized in order to maximize the amount of Tc and minimize impurities. 99m They reported reaction yields for Tc and other radioactive isotopes created when natural and enriched molybdenum targets are irradiated by protons. They used a nuclear reaction computer program called the EMPIRE code for the determination of cross-sections for a proton energy range 6–30MeV for the various reaction channels created and subsequently drew excitation functions for analysis. They concluded that, although ultimately careful experimental verification of these optimized conditions must be performed, theoretical modeling can provide the initial guidance for the experiments as it allows for extensive investigation of experimental parameters at little cost to the user. In their conclusion, they stated that, although proton beam currents up to 1.2mA are possible, medical cyclotrons are typically designed to produce only about 200 μA beam currents (with possible upgrades to 500 μA). This means that a single 19 MeV cyclotron with a 200 μA proton beam could, in theory, produce about 430 to 440 GBq 99m of Tc in a 6 h bombardment. It may however be beneficial to perform shorter, 3 h, irradiations multiple times per day. They added that absolute production yields are 99m higher at proton energies of 19 MeV or even at 24MeV, the analysis of ratios of Tc to other reaction products indicate that proton energies closer to 16–19MeVmay 38 University of Ghana http://ugspace.ug.edu.gh 99m correspond to the most advantageous energy region, where the Tc production is high while the amount of contaminants is minimized. In summary, it is clear from the foregoing analysis of previous researches that, much 99m work has been done, as far as, the production of Tc is concerned both theoretically and experimentally. However, the theoretical work done so far in estimating the 99m optimum conditions for the production of Tc using the Talys computer program needs further investigation. For instance, Alharbi et al, (2006), in their work compared their experimentally measured excitation functions for each reaction channel leading to the production of each Technetium product (eg, Tc-96, Tc-94 etc.) with the excitation functions produced by the Taly code. However comparing the effects of excitation functions of the (p,n) and (p,2n) reactions of the other molybdenum 100 99m isotopes on the Mo(p,2n) Tc which is the main reaction channel leading to the 99m production of Tc was not considered. The current researcher will proceed to investigate the effects of (p,n) and (p,2n) reactions on other isotopes of Mo so that 99m the optimum energy range for the production of Tc can in the established. In Celler et al (2011), they theoretically determined the reaction yields for Tc-99m and other radioisotopes created when the natural and the enriched molybdenum targets were irradiated with protons. Besides, they used the computer program the EMPIRE for the calculations of the cross sections of the various reaction channels for the energy range 6-30MeV. Aside from the above intended investigations, the researcher intends to use the results that will be obtained during the research in estimating the optimum operating conditions for a cyclotron and compare it with the optimum conditions that were obtained by Celler et al (2011) in order to draw conclusions. 39 University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE METHODOLOGY 3.1 Materials and Methods The materials used for this research work were a laptop computer (G62-347CL Notebook), a nuclear reaction model code called the Talys code (TALYS-1.4): Talys is a computer code system for the analysis and prediction of nuclear reactions. The basic objective behind its construction is the simulation of nuclear reactions that 3 involve neutrons, photons, protons, deuterons, tritons, He- and alpha-particles, in the 1 keV - 200 MeV energy range and for target nuclides of mass 12amu and heavier. To achieve this, a suite of nuclear reaction models have been implemented into a single code system (Koning et al, 2011), and a computer software package called the SRIM (Stopping Power and Ranges of Ions in Materials) which calculates many features of the transport of ions in matter (Ziegler et al., 1989). The research was aimed at investigating parameters theoretically which are necessary for the estimation of optimum operational conditions for the production of Technetium-99m using a cyclotron. The procedures for determining the various parameters are outlined as follows: 3.1.1 Generation of Nuclear Reaction Cross Sections The nuclear reaction which leads to the direct production of Technitium-99-m is represented as: 100 99m Mo (p, 2n) Tc, (3.1) Where: 100 Mo is molybdenum-100 isotope which serves as the target in the cyclotron, 40 University of Ghana http://ugspace.ug.edu.gh p is the proton (Hydrogen particle) which is accelerated to bombard the target material, 2n represents two neutrons which are emitted during the bombardment 99m process and Tc is the Technitium-99m which is the desired radionuclide of interest. In the estimation of optimum energy range for the production of Technitium-99m 100 99m using a cyclotron, cross sections of the reaction Mo(p,2n) Tc which are functions of their respective particle energies were generated using the Talys code. This was done by feeding the code with input parameters such as the incident particle, the particle energy, the appropriate target, and the atomic mass of the target after which the data is submitted to the code to run. After processing, the cross sections of the various reaction channels are grouped and displayed into the output of the code. The figure below is the flow chart system of the Talys code. Start Input data: Projectile (p, n, de, etc) Manual Target element; Target mass; Target atomic mass  Optical model  Direct reaction model Output: Cross sections End Figure 3.1 Flow chart of the Talys code system. 41 University of Ghana http://ugspace.ug.edu.gh 100 99m The Mo (p,2n) Tc reaction channel excitation function was subsequently plotted from the cross sections generated for analysis. Besides, the excitation functions of the other competing reaction channels that led to the production of other technetium as well as non-Technetium products were equally plotted from their respective reaction cross sections generated by the code for analysis. Tables containing cross sections generated by the Talys code for the various nuclear reaction channels which led to the production of different products including Technitium-99m can be found in the next chapter. 3.1.2 Determination of Stopping Power Stopping power is defined as the average energy loss of the particle per unit path length, measured for example in MeV/cm. Stopping power is a necessary ingredient for many parts of basic science, for medical and for technological applications (ICRU 73, 2005). The average value of the distances (thickness) that a particle travels before coming to rest is called the "Range" (Gunasingha, 2008). A mathematical expression for stopping power is as follows: 144Zz2  2195E  S E   ln  (3.2a) AE  I  p  where S(E) is the stopping power, Z is the atomic number of the target, z is the atomic number of the projectile, E is the particle energy in MeV and Ip is the ionization potential of the target. In the estimation of thick target radionuclide production yield, the determination of stopping power values of the target for each particle‘s energy is highly necessary. This is because the stopping power of the target is an integral part of the thick target yield. 42 University of Ghana http://ugspace.ug.edu.gh In this work the stopping power values of the molybdenum-100 target for each proton energy were obtained by feeding into the SRIM software package the following input parameters: the appropriate particle to be accelerated, the particle energy range, the name of the target element and the state of the target. These parameters are now submitted to the software package and after processing the various stopping power values are displayed in the output of the software. The figure below is the graphical user interface of the SRIM software package. Figure 3.2 Graphical User Interface of the SRIM software package 43 University o.fP rGojhecatinlea- ( a thotmtpic :m//ausgs, satpoamcice n.uumgb.eer detuc.) Input .gh .Projectile energy range; .Target element- (atomic mass, atomic number, density etc.) Stopping power ,S. Processing/ interaction Range of particles in materials, R. Electronic stopping power, dE/dX. Nucleonic stopping power, dN/dX Output Figure 3.2.1 Flow chart system of SRIM software package Figure 3.1.1 is a flow chart system of the SRIM software package system. It presents the smooth flow or linkage of the various units in the package. 3.2 Determination of Saturated Thick Target Radionuclide Production Yield The yield of a nuclear reaction (Y) is a ratio of the number of the nucleus formed in a nuclear reaction to the number of the bombarding particles hitting the target (Szelecsenyi, 1997). Moreover, the yield for a target having any thickness can be defined as the ratio of the number of nuclei formed in the nuclear reaction to the number of particles incident on the target (Dmitriev, 1986). This particular work has focused on estimating the saturated thick target yield for the production of technetium-99m. Two methods were employed as follows: 3.2.1 Numerical method for the estimation of Saturated thick target radionuclide production yield (Simpson numerical integration) The thick target radionuclide production yield (Y) equation is given as: 44 University of Ghana http://ugspace.ug.edu.gh E N in  E  Y  6.241012  A   dE (3.2b) M S E E  out 12 Where the value 6.24 × 10 is the number of protons per second per μA, NA is the Avogadro number M is the target atomic mass, σ(E) is the reaction cross section as a function of energy is expressed in mb and S(E) is the target stopping power (SRIM 2 −1 2010) expressed in units MeV cm g (Celler et al, 2011). Now using the cross section values obtained (Table 4.1.1) by the Talys code for the 100 99m reaction Mo (p,2n) Tc for each of the particle energy and the corresponding stopping power values(Table 4.5) obtained by the SRIM package; and applying Simpson numerical integration method, the various radionuclide production yields were calculated using equation (3.2b) above. Finally, a graph of proton energy versus radionuclide production yield was plotted for analysis. This graph can be found in Figure 4.5. 3.2.2 Numerical estimation of saturated thick target radionuclide production yield using Newton forward difference formula The saturated thick target radioisotope production yield (Y) is given in equation (3.2b) above in section 3.2.1. The expression for the cross section [σ(E)] is given as σ(E)= 2.678*10-10 *NiA/ρtIx (3.3) and the expression of the stopping power S(E) is given in equation (3.2a). 45 University of Ghana http://ugspace.ug.edu.gh Where: N i = number of nuclei present in target during irradiation; A=atomic mass of target in (amu); ρ= density of target (Mo) in (amu); x= thickness of target in (μm); t= irradiation time in hours; I= beam current in (μA); Putting equation (3.3) and (3.2a) in (3.2b) implies b 12 N 2.67 10 10 ANi / txIY  6.2410 A   dE (3.5)M a 114Zz2 2195E   ln AE    I p  N 2 bA A Ni EY  11.57    M txIZz2  dE (3.6) a  2195E  ln   I p  L1  11.57, 2 L  N A22 A Ni / MIZz  b L Y  1  L2 E dE (3.7) tx  a 2195E ln I  p  where the limits b and a represents incident proton energy and exit proton energy respectively. L3 is the product of L1 and L2 b L3 EY   tx  dE (3.8) a ln 2195E     I p  and for Mo-100, I p  7.009 Let E f (E)  (3.9) ln 313.17E  46 University of Ghana http://ugspace.ug.edu.gh Now using Newton Forward Difference Formula below to expand equation (3.9) gives f E - E 2o   f E - Eo E - E1   3 f E - Eo E - E1 E - E2  f E   f (o)    h 2!h2 3!h3 4 f E - Eo E - E1 E - E2 E - E3   3.10 4!h4 where E0, E1, E2 etc. are first, second, third particle energies respectively; h is the 2 3 energy step size and Δ, Δ , Δ etc. are first, second and third differentials of the function. 47 University of Ghana http://ugspace.ug.edu.gh Table 3.1.1. Values of Δf as functions of particle energies. 2 3 4 5 E(Mev) f(E) Δf Δ f Δ f Δ f Δ f 8 1.023882 10 1.244316 0.220434 12 1.460056 0.215740 -0.0046945 14 1.672038 0.211982 -0.0037572 0.0009373 16 1.880905 0.208866 -0.0031161 0.0006411 -0.000300 18 2.087119 0.206215 -0.0026518 0.0004643 -0.000180 0.000119 20 2.291033 0.203913 -0.0023012 0.0003506 -0.000110 0.0000631 22 2.492918 0.201886 -0.0020276 0.0002736 -0.000077 0.0000367 24 2.692995 0.200077 -0.0018087 0.0002189 -0.000055 0.0000223 f E  ao  a1 E  Eo   a2 E  Eo E  E   a3 (E  Eo )E  E1 E  E1 2   a4 E  Eo E  E1 E  E2 E  E3  3.11 f 2 f 3 f Where a0, a1, a2, a3 represents f(0), , , etc. h h2 2! h3 3! After expanding equation (3.10), let K1  ao  a1Eo  a2Eo E1  a3Eo E1E2  a4Eo E1E2E3 (3.12) K2  a1  a2 Eo  E1   a3 Eo E1  Eo E2  E1E2   a4 Eo E1E2  Eo E1E3  Eo E2E3  E1E2E3  3.13 K3  a1  a3 Eo  E1  E2   a4 Eo E1  Eo E2  Eo E3  E1E2  E1E3  E2E3  3.14 K4  a3  a4 Eo  E1  E2  E3  and K5  a4 3.15 where K1 to K5 represents coefficients after expansion of equation (3.11). 48 University of Ghana http://ugspace.ug.edu.gh Therefore E f E   f  K1  K2 E  K E 2 3  K4 E 3  K 45E 3.16 ln 313.17E  Now integrating f(E); E Eot  K E2 K E 3 K E4 ot E K E 5  F E    f E dE  dE  K E  2  3  4 5  1   3.17ln 313.17E  2 3 4 5Ein  Ein K K3 K KLet: C1  K , C  2 1 2 ,C3  ,C4  4 ,C  5 5 2 3 4 5 E Eotot E F EdE   f E dE   dE  C1E C E 2 C E32 3 C4E 4 C E5 5 (3.18) ln313.17E E in Ein Inserting equation (3.18) back into equation (3.8) we get L E Y  3 in  C1E  C E 2 2  C 3 4 5  3E  C4 E  C5E  (3.19) tx Eot 11.54 * N 2a A Ni 13 But L3  L1 * L2   3.93*10 (3.20) M  IZz2 Substitute equation (3.20) into equation (3.19) gives 3.93*1013 Ein Y= * C E C E2 C 3 4 5  (3.21) 1 2 3E C4E C5Et * x Eot Now to find the values of: 1 a1, a2, a3, a4, a5 2 K1, K2 , K3, K 4 , K5 (3) C1, C2 , C3, C4 , C5 An excel program was used to determine the coefficients and put in the table below. 49 University of Ghana http://ugspace.ug.edu.gh Table3.1.2. Values of some variables and constants from equations (3.9) to (3.19) a0 a1 a2 a3 a4 1.023882 1.10217E-1 -5.9E-4 1.95271E-5 -7.7135E-7 E0 E1 E2 E3 E4 8 10 12 14 16 K1 K2 K3 K4 K5 7.5419E-2 1.3050E-1 -1.72E-3 5.3467E-5 -7.7135E-7 C1=K1 C2=K2/2 C3=K2/3 C4=K4/4 C5=K5/5 7.5419E-2 6.5248E-2 -5.7E-4 1.3367E-5 -1.5427E-7 Note, the energy step interval, h = 2MeV. For molybdenum-100, the following were used as shown in Table 3.1.2. Table3.1.3. Values of some constants in the radionuclide production yield equation (i.e. equation (3.1). Name of Constant Numerical Value Avogadro‘s Number, Na (particles) 6.02E+23 Atomic mass Mo-100 amu 1.00E+02 Number of nuclei present during 6.27E+21 irradiation ,Ni Atomic weight Mo, amu 9.60E+01 3 Density Mo, ρ (g/cm ) 10.28 Beam current, I (microamps) 2.00E+02 Atomic no of Mo, Z 42 Atomic no of H, z 1 Target thickness, X (µm) 223.49 Irradiation time , T (hrs) 6 50 University of Ghana http://ugspace.ug.edu.gh Substituting equations (3.18) and the ‗C‘ values in Table 3.1.2 back into equation (3.21), the final radioisotope production yield equation is written below as follows: 3.931013 Ein Y   0.075E  0.065E 2  5.7 1004 E3 1.337 1005 E4 1.541007 E5  (3.22)t  x Eot Now, to investigate the three operational parameters (i.e. proton energy (E), irradiation time (t), and target thickness (x)) of the cyclotron on the radioisotope production yield, using equation (3.22), various data tables are formed with respect to the parameters in next chapter and their respective graphs drawn against the production yield for analysis to be made. 51 University of Ghana http://ugspace.ug.edu.gh CHAPTER FOUR RESULTS AND DISCUSSION 4.0 Results This chapter entails all the results that were obtained by the different procedures carried out in chapter three. The various results are organized into tables and figures below. 4.1 Variation of Proton Energy with Reaction Cross Sections for different (p+Mo) Reaction Channels Table 4.1.1 gives particle energy in MeV and the reaction cross sections generated by the Talys code as described in chapter three for the different reaction channels leading to the production of different radio-nuclides. It can be observed from the table that when the charged particle (proton) was accelerated to interact with the molybdenum- 100 99m 100 99g 100 target, the reaction channels were as follows : Mo(p,2n) Tc, Mo(p,2n) Tc, 100 98 100 99 Mo(p,3n) Tc and Mo(p,pn) Mo. 100 99m Concerning the Mo (p, 2n) Tc channel which leads to the direct production of 99m Tc, reaction cross sections for particle energies ranging from 5-7MeV were zeros. The cross sections started rising at 8MeV, peaks between 11MeV to 18MeV after which they decreased slowly until 24MeV where they remain fairly constant with an 100 99g increase in energy. Cross sections values for the Mo(p,2n) Tc were also zeros from 5-7MeV, rose sharply to about 826mb at 17MeV after which cross section 100 98 values decreased sharply with an increase in particle energy. For the Mo(p,3n) Tc channel, reaction cross section values were zero from 5-16MeV, rose sharply to about 26MeV where the maximum cross section is 813mb and began to decrease 100 gradually with an increase in energy . Reactions cross sections for the Mo (p, pn) 99 Mo were zeros from 5-12MeV. However, the cross sections started rising sharply 52 University of Ghana http://ugspace.ug.edu.gh from 13MeVto 22MeV where it continues to rise gradually with energy. It can therefore be deduced from the table that the only reaction channel that seriously 100 99m 100 99g interferes with the Mo (p,2n) Tc channel is the Mo(p,2n) Tc channel whereby its reaction cross section values peak at almost the same energy range. However, the other channels though interfere but with little impact. 53 University of Ghana http://ugspace.ug.edu.gh Table 4.1.1. Particle Energy and Reaction Cross Sections for Different Radionuclide Products. Energy Reaction Cross sections(mb) (MeV) 100 99m 100 99g 100 98 100 99 Mo(p,2n) Tc Mo(p,2n) Tc Mo(p,3n) Tc Mo(p,pn) Mo 5 0 0 0 0 6 0 0 0 0 7 0 0 0 0 8 7 20 0 0 9 117 217 0 0 10 175 390 0 0 11 197 520 0 0 12 204 613 0 0 13 205 684 0 1 14 202 738 0 3 15 197 778 0 8 16 192 806 0 16 17 186 826 1 26 18 166 771 89 39 19 135 641 264 54 20 100 493 450 70 21 76 364 604 87 22 57 279 706 104 23 44 224 767 116 24 36 179 814 130 25 31 156 828 139 26 28 142 813 148 27 26 128 753 154 28 24 119 672 160 29 22 110 576 163 30 21 102 482 166 31 21 100 393 168 32 21 94 328 168 33 20 87 277 171 34 20 86 229 170 35 19 80 203 173 Graphs of particle energy versus nuclear reactions cross sections for the various nuclear reaction channels created when a proton bombards a molybdenum target is 54 University of Ghana http://ugspace.ug.edu.gh shown in Fig 4.1.1. It can be observed that the excitation function for 100 99m Mo(p,2n) Tc remains at the ground level up to approximately 6MeV, rising sharply to approximately 8-10MeV, peaks between 11a16MeV and then decrease with further increase in particle energy. It is clear that the only excitation function that poses a serious interference to the 99m 100 99g 100 98 production of Tc is the Mo(p,2n) Tc excitation function. The Mo(p,3n) Tc 100 99 and the Mo(p, pn) Mo excitation functions do not greatly affect or interfere with 100 99m the Mo(p,2n) Tc excitation function which leads to the direct production of 99m Tc up to 18MeV. 55 University of Ghana http://ugspace.ug.edu.gh 900 800 700 600 500 Mo100(p,2n)Tc99m 400 Mo100(p,2n)Tc99g Mo100(p,3n)Tc98 300 Mo100(p,pn)Mo99 200 100 0 0 5 10 15 20 25 30 35 40 -100 Energy/MeV 100 Fig 4.1.1: Graphs of particle energy versus nuclear reactions cross sections for Mo+p reaction products. 56 Cross sections/mb University of Ghana http://ugspace.ug.edu.gh 4.2 Variation of Proton Energy with Reaction Cross Section for Different Molybdenum Targets through (p, n) Reactions. The (p,n) reactions usually lead to the production of other technetium products that 99m serves as interferences(impurities) to the production of Tc. The table below therefore displays the cross sections the competing reactions on other molybdenum 100 99m isotopes and cross sections of Mo(p,2n) Tc reaction. From the table it can be observed that the reaction cross sections which led to the direct production of the 98g 97g 97m 96m contaminants (i.e. Tc, Tc, Tc, Tc etc) through the (p,n) reactions are higher with lower proton energies, 5-13Mev, after which the cross sections begin to decrease in proton energies. This means that using an impure molybdenum-100 target for irradiation, the proton energy should be chosen in such a way that excitation functions of contaminants through (p,n) reactions should be excluded. 57 University of Ghana http://ugspace.ug.edu.gh Table 4.2.1. Particle energy and cross sections for (p,n) reactions leading to different technetium products. Desired Product Interference Product 100 99m Mo(p,2n) Tc cross sections/mb for Mo(p,n)Tc 99m 98g 97g 96g 97m 96m 95g 95mE/MeV Tc Tc Tc Tc Tc Tc Tc Tc 5 0 57.12 0.05 23.46 0.05 27.69 33.15 15.46 6 0 176.10 0.12 76.09 0.09 83.96 104.95 46.29 7 0 335.25 0.22 160.45 0.15 156.64 211.54 91.62 8 7.32 480.87 0.32 249.95 0.19 217.85 319.62 132.65 9 116.86 600.22 0.39 327.66 0.22 263.92 414.23 160.45 10 174.90 675.86 0.46 388.81 0.24 297.66 490.67 172.97 11 196.98 415.00 0.57 438.50 0.29 322.65 538.81 157.78 12 204.44 232.65 0.65 449.51 0.31 318.46 530.23 117.72 13 204.77 137.68 0.74 287.31 0.33 190.13 422.70 74.82 14 201.80 95.81 0.82 177.57 0.33 110.42 257.51 42.60 15 196.99 75.08 0.88 106.87 0.32 62.67 155.90 25.62 16 191.76 63.09 0.92 70.66 0.30 39.59 102.82 17.49 17 186.23 58.29 0.97 54.71 0.29 29.49 76.07 13.51 18 166.07 52.60 0.95 48.18 0.26 25.32 62.79 11.37 19 134.85 49.84 0.85 41.98 0.22 21.33 55.41 10.07 20 100.20 47.62 0.79 39.78 0.20 19.77 50.72 9.25 21 75.52 45.50 0.63 38.08 0.16 18.49 47.44 8.57 22 57.22 43.80 0.58 36.47 0.14 17.26 45.31 8.02 23 44.36 43.40 0.48 35.09 0.12 16.19 43.52 7.55 24 35.96 40.78 0.45 33.58 0.11 15.06 41.73 7.08 25 31.06 38.96 0.39 32.37 0.09 14.11 40.36 6.72 26 28.27 37.82 0.37 32.46 0.09 13.95 39.92 6.36 27 25.57 35.44 0.35 30.66 0.08 12.85 37.85 5.99 28 23.97 34.31 0.32 28.94 0.07 11.84 35.89 5.66 29 22.36 32.41 0.31 28.29 0.07 11.37 35.40 5.36 30 20.93 30.67 0.31 26.52 0.07 10.46 33.02 5.04 31 21.08 30.45 0.27 25.90 0.06 10.04 32.65 4.79 32 20.85 27.70 0.27 25.38 0.06 9.88 30.19 4.50 33 19.61 26.65 0.26 23.54 0.06 8.82 29.77 4.30 34 19.56 26.60 0.26 22.84 0.06 8.56 27.89 4.10 35 18.56 24.54 0.23 22.31 0.05 8.31 27.03 3.88 58 University of Ghana http://ugspace.ug.edu.gh 800.00 A GRAPH OF PARTICLE ENERGY VS REACTION CROSS 700.00 SECTIONS Mo100(p,2n)Tc99m 600.00 Mo98(p,n)Tc99g Mo97(p,n)Tc97g 500.00 Mo97(p,n)Tc97m 400.00 Mo96(p,n)Tc96g 300.00 "Mo96(p,n)Tc96m 200.00 "Mo95(p,n)Tc95g" Mo95(p,n)Tc95m 100.00 0.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 -100.00 Energy/MeV 100 99m Fig4.2.1: Comparison of the Mo (p,n) Tc excitation function to the six other technetium isotopes which are produced through the (p,n) reaction. 59 cross sections/mb University of Ghana http://ugspace.ug.edu.gh Figure 4.2.1 in the previous page contains the excitation functions of the desired 100 99m 99m reaction Mo(p,2n) Tc that leads to the direct production of Tc as well as (p,n) reactions which lead to the production of other interferering technetium products. It can be seen from the figure that the interferences of contaminants though the (p,n) 99m reactions really occur at lower energy proton energies during the production of Tc. 4.3 Variation of reaction cross sections with proton energies for different molybdenum isotopic targets through (p, 2n) reactions. 100 99m The (p, 2n) reactions do not only produce the desired reaction Mo (p, 2n) Tc but can result in the production of other Technetium products which are usually considered as interferences. Table 4.3.1 below displays how the reaction cross sections of these contaminants vary with particle energy. It can be seen that most of the reaction cross section values for these contaminants peaks around 15MeV to 22MeV energy range. Besides, the reaction cross sections values of the desired 100 99m reaction ( Mo (p,2n) Tc) also peak around 10-20MeV. This implies that to 99m optimize the production of Tc the Mo-100 target must be appropriately enriched to suppress these competing reactions to a minimum. 60 University of Ghana http://ugspace.ug.edu.gh Table 4.3.1 Particle energy and reaction cross sections of (p,2n) reactions leading to the production of different technetium products. 100 Energy Cross sections/mb for Mo(p,2n)Tc 99m 99g 97g 97m 96g 96m 95g 95m E/MeV Tc Tc Tc Tc Tc Tc Tc Tc 5 0 0 0 0 23.46 27.69 0 0 6 0 0 0 0 76.09 83.96 0 0 7 0 0 0 0 160.45 156.64 0 0 8 7.32 19.58 0 0 249.95 217.85 0 0 9 116.86 217.32 0 0 327.66 263.92 0 0 10 174.90 389.81 10.16 8.76 388.81 297.66 0 0 11 196.98 520.36 249.44 109.12 438.50 322.65 0 0.00 12 204.44 613.23 448.70 162.30 449.51 318.46 41.56 13.34 13 204.77 684.17 582.74 183.81 287.31 190.13 274.08 127.91 14 201.80 738.43 666.54 189.42 177.57 110.42 445.58 191.01 15 196.99 777.69 724.22 186.04 106.87 62.67 566.69 219.65 16 191.76 806.04 764.28 179.28 70.66 39.59 639.91 223.58 17 186.23 826.41 789.86 170.18 54.71 29.49 679.43 215.98 18 166.07 771.36 812.43 160.93 48.18 25.32 701.59 205.02 19 134.85 640.75 829.45 151.90 41.98 21.33 719.69 193.37 20 100.20 493.31 823.61 138.46 39.78 19.77 731.17 180.04 21 75.52 364.21 736.52 114.79 38.08 18.49 731.24 160.41 22 57.22 279.22 596.96 86.89 36.47 17.26 705.92 133.74 23 44.36 224.04 448.55 61.55 35.09 16.19 629.19 104.30 24 35.96 179.41 347.74 45.34 33.58 15.06 519.33 77.76 25 31.06 156.33 269.02 33.33 32.37 14.11 404.57 57.23 26 28.27 141.64 216.40 26.55 32.46 13.95 314.79 42.58 27 25.57 127.89 184.00 21.47 30.66 12.85 248.74 33.19 28 23.97 119.37 162.82 18.63 28.94 11.84 202.94 26.79 29 22.36 110.16 147.73 16.17 28.29 11.37 172.30 22.59 30 20.93 101.96 135.45 14.85 26.52 10.46 150.90 19.62 31 21.08 99.86 124.70 13.21 25.90 10.04 134.51 17.72 32 20.85 93.68 117.62 12.34 25.38 9.88 122.89 15.84 33 19.61 86.63 110.32 11.32 23.54 8.82 115.88 14.98 34 19.56 85.85 108.14 10.73 22.84 8.56 110.24 13.76 35 18.56 79.82 102.26 9.90 22.31 8.31 104.23 12.71 61 University of Ghana http://ugspace.ug.edu.gh Figure 4.3.1 in the next page comprised of an excitation function of the desired 100 99m reaction Mo(p,2n) Tc as well as excitations functions of (p,2n) reactions which led to the production of other interfering technetium products. Analyzing the figure it is clear that, the excitations of the competing reactions for the production of the 97g 97m 96m 96g contaminants (e.g. Tc, Tc, Tc, Tc etc) are strongly interfering with the 100 99m excitation function of the Mo (p,2n) Tc reaction which leads to the production of 99mTc within almost the same proton energy range. 62 University of Ghana http://ugspace.ug.edu.gh 900.00 A GRAPH OF PARTICLE ENERGY VS REACTION CROSS SECTIONS 800.00 700.00 600.00 Mo100(p,2n)Tc99m 500.00 Mo100(p,2n)Tc99g Mo98(p,2n)Tc97g 400.00 Mo98(p,2n)Tc97m Mo97(p,2n)Tc96g 300.00 Mo97(p,2n)Tc96m Mo96(p,2n)Tc95g 200.00 Mo969p,2n)Tc95m 100.00 0.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 -100.00 Energy/MeV 100 99m Fig4.3.1: Comparison of the Mo (p, 2n) Tc excitation function to the other isotopes which are produced through the (p,2n) reaction. 63 cross sections/mb University of Ghana http://ugspace.ug.edu.gh 4.4 Comparison of Excitation Functions of this Work and Works Done by Previous Researchers [Levkovskij (1991), Scholten et al (1999), Celler et al. (2011), Takacs et al. (2003)] performed various experimental and theoretical measurements of reaction cross 100 99m section for Mo(p,2n) Tc reaction respectively . These cross sections data was included in the EXFOR data at the National Nuclear Data Center (NNDC) at the IAEA website, except, the theoretical data obtained by Celler et al. (2011). The table below contains particle energy in (MeV), reaction cross sections (in mb) generated by 100 99m this work using Talys code for the reaction Mo (p,2n) Tc as well as EXFOR data of reaction cross sections obtained by the above researchers for the same reaction. From the table it can be observed that reaction cross section values for this work remain zeros for the 5-7MeV energy range. This trend is experienced by Levkovskij (1991), and Celler et al (2011). Reaction cross sections values obtained by Schloten (1999) and Takacs et al (2003) within the same energy range are however very low. Moreover, reaction cross section values obtained for this work increased sharply from 9MeV to 14MeV after which they decreased very gradually until 20MeV. From the 20MeV, the cross section values began decreasing sharply until 35MeV where they remain almost constant with an increase in energy. Analysis of reaction cross sections values obtained by the previous researchers in the table indicates that they follow the same trend as pertained in this current work with an increase in energy. 64 University of Ghana http://ugspace.ug.edu.gh Table 4.4.1 Particle energy, cross sections by Talys code and cross sections from 100 99m EXFOR data for Mo (p,2n) Tc reaction by (Levkovskij ,1991, Scholten et al 1999, Celler et al, 2011; Takacks et al, 2003; ) Cross sections (in mb) ENERGY Levlovskij Scholten Takacs et Celler et al This Work 1 2 (MeV) (1991) E et al al (2011) E (2013) T (1999) E (2003) E 5 0 0 0 0 0 6 0 1 5 0 0 7 0 2 12 0 0 8 0 31 21 7 7 9 121 83 31 80 117 10 189 118 81 150 175 11 231 136 141 180 197 12 269 149 182 200 204 13 289 166 197 210 205 14 306 193 209 220 202 15 306 193 210 220 197 16 288 180 211 220 192 17 276 185 211 210 186 18 257 191 206 200 166 19 263 189 184 180 135 20 209 163 161 150 100 21 155 136 138 120 76 22 121 95 113 110 57 23 97 61 92 80 44 24 77 36 60 70 36 25 62 33 45 50 31 26 53 29 37 40 28 27 39 24 24 NA 26 28 39 23 15 NA 24 29 39 22 16 NA 22 30 37 20 16 NA 21 31 NA 19 14 NA 21 32 NA 20 16 NA 21 33 NA 18 17 NA 20 34 NA 20 16 NA 20 35 NA 20 17 NA 19 1 2 NA – data not available; E–Experimental; E – Empire code; T–Talys Code 65 University of Ghana http://ugspace.ug.edu.gh The figure 4.4.1 below compares the excitation function obtained by this work (2013) using the Talys code and the excitation function obtained by (Takacks, 2003) for 100 99m Mo (p,2n) Tc reaction. In the figure excitation functions for this work and that of Takacs et al 2003 rose sharply from 8MeV to their maximum cross section values (205mb) at 14MeV and (210mb) at 16MeV respectively. The excitation functions of both works then decrease exponentially until about 25MeV where they remain fairly constant with an increase in energy. Although there is a shift in their peaks the trend of formation of shapes of both excitation functions are the same. 250 A GRAPH OF CROSS SECTIONS VS PARTICLE ENERGY 200 150 100 100Mo(p,2n)99mTc Takacs(2003) 50 0 0 10 20 30 40 -50 Energt/MeV Figure4.4.1 comparison of excitation functions obtained by this work and by 100 99m (Takacs et al, 2003) for the Mo (p,2n) Tc reaction. 66 cross section/mb University of Ghana http://ugspace.ug.edu.gh 100 An excitation function obtained by this work using the Talys code (2013) for 99m Mo(p,2n) Tc reaction and the excitation function obtained by (Schoten, 1999) by the experimental measurement of cross sections for the same reaction are shown in the figure 4.4.2 below. It is clear from the figure that the excitation functions of both works raised sharply from 8MeV until about 10MeV when there is a deviation of Scholten‘s graph to peak at a cross section value of (193mb) at 25MeV, while this work peaks at a cross section value of (205mb) at 14MeV. Analyzing the figure it is clear that, the excitations of the competing reactions for the production of the 97g 97m 96m 96g contaminants (e.g. Tc, Tc, Tc, Tc etc) are strongly interfering with the 100 99m excitation function of the Mo (p,2n) Tc reaction which leads to the production of 99m Tc within almost the same proton energy range. At their maximum peak values both excitation functions decrease exponentially to about 25MeV where they remain fairly constant with an increase with proton energy. 350 300 250 200 This Work(2013) 150 Levkovskij(1991) 100 50 0 0 5 10 15 20 25 30 35 40 -50 Energy/MeV Figure 4.4.2 Comparison of excitation functions (cross sections vrs energy) obtained 100 99m by this work and by Levkovskij (1991) for the Mo (p,2n) Tc reaction. 67 cross section/mb University of Ghana http://ugspace.ug.edu.gh Figure 4.4.3 below consists of excitation functions obtained by this work (2013) using 100 99m the Talys code for Mo (p, 2n) Tc reaction and the excitation function obtained by (Levkovskij, 1991) by experimentally measuring the reaction cross sections for the same reaction. It is observed that the trend of formation of the shapes of the two excitation functions is the same. For instance, they both peak within the 10-20MeV energy range. However the reaction cross measured experimentally by Levkovskij are 100 99m higher than those obtained theoretically by this work for the Mo(p,2n) Tc reaction within the same energy range as can be seen in the figure. 250 200 150 This Work(2013) Scholten(1999) 100 50 0 0 10 20 30 40 50 60 70 -50 Energy/MeV Figure 4.4.3 Comparison of excitation functions (cross sections vrs energy) obtained 100 99m by this work and by Scholten et al (1999) for the Mo (p,2n) Tc reaction. 68 Cross section/mb University of Ghana http://ugspace.ug.edu.gh Celler et al, 2011 performed a theoretical measurement of nuclear reaction cross 100 99m sections for Mo(p,2n) Tc reaction using an EMPIRE code, another nuclear reaction model code for the generation of nuclear reaction cross sections. This work also focused on the theoretical measurement of nuclear reaction cross sections for the same reaction using Talys code. Figure 4.4.4 compares the excitation functions obtained by this work using the Talys code (2013) and the excitation function 100 99m obtained by (Celler et al, 2011) for (p, 2n) Tc reaction using the EMPIRE code. Analyzing the figure one could see that the excitation functions for both research works increased sharply from 8MeV and peak art cross values of (205mb) at 14MeV and (210mb) at 15MeV respectively. The excitation functions then decreased exponentially until 22MeV when they remain almost constant with an increase in energy. 250 200 150 A. Celler et al(2011) 100 this work-Mo100(p,2n)Tc99m 50 0 0 10 20 30 40 -50 Energy/MeV Figure 4.4.4 Comparison of excitation functions obtained by this work and by Celler 100 99m et al (2011) for the Mo (p,2n) Tc reaction. 69 cross sections/mb University of Ghana http://ugspace.ug.edu.gh 4.5 Variation of Saturated Thick Target Yield with Operational Parameters of a Cyclotron To estimate the thick target reaction yield for radionuclide production, values for the 100 99m reaction cross sections, σ(E), as functions of energies, for the Mo(p,2n) Tc reaction and values of the stopping power, S(E), for the target material (molybdenum- 100) target for the various projectile energies as well as values of the quotient of cross sections and stopping power, σ(E)/ S(E) must be calculated. These values are usually substituted into the radionuclide production yield equation in chapter three so that the yield can be obtained. These values are contained in the table 4.5 below. From the table it can be noticed that stopping power values of the target (Mo-100) started decreasing from 5MeV to about 13MeV. Between 14MeV to about 16MeV, stopping power values fluctuated after which the values decreased exponentially with an increase in energy. The ratio of the cross section values, σ(E), to the stopping power values, S(E), also fluctuated in the same order as happened with the stopping power values with an increase in proton energies. 70 University of Ghana http://ugspace.ug.edu.gh 100 99m Table 4.5 Particle energy, values of reaction cross section for Mo(p,2n) Tc , values of stopping power for Mo target and values of the quotient cross sections and stopping power(σ(E)/S(E). Energy Cross Sectionsσ(E) Stopping Power S(E) RATIO 100 99m (MeV) (for Mo(p,2n) Tc) (MeV/cm2/mg) σ(E)/S(E) (mb) 5 0 0.3846 0 6 0 0.0341 0 7 0 0.0307 0 8 7 0.0281 249.43 9 117 0.0259 4523.84 10 175 0.0240 7282.00 11 197 0.0225 8766.89 12 204 0.0211 9659.04 13 205 0.0199 10281.13 14 202 0.1890 1068.73 15 197 0.0180 10951.55 16 192 0.1716 1118.83 17 186 0.0164 11322.51 18 166 0.0158 10534.94 19 135 0.0152 8901.04 20 100 0.0146 6855.67 21 76 0.0141 5391.53 22 57 0.0134 4264.61 23 44 0.0132 3342.01 24 36 0.0128 2820.10 25 31 0.1236 250.80 26 28 0.0120 2328.46 27 26 0.0115 2255.99 28 24 0.0114 2109.93 29 22 0.0111 1984.73 30 21 0.0108 1945.43 31 21 0.0105 1991.58 32 21 0.0102 2064.04 33 20 0.0101 1987.25 34 20 0.0984 203.22 35 19 0.0962 197.46 71 University of Ghana http://ugspace.ug.edu.gh 4.5.1 Variation of Saturated Thick Target Yield with Proton Energy Results of various particle energies in MeV and values of radionuclide production yields in MBq/µA obtained from equation (1) in chapter three through Simpson Numerical Integration method is displayed in the table below. It can be deduced from the table that thick target yields for radionuclide production increased with an increase in proton energies. Table 4.5.1(a). Particle Energies and Corresponding saturated thick target Radionuclide Production Yields at different times of irradiation (Simpson‘s Rule) E/MeV E/MeV Saturated Yield/(MBq/μAh) 8 0 0.5 11 8 90.67 15 8 309.17 18 8 505.17 20 8 620.00 22 8 691.67 In order to analyze the effect of particle energy on radionuclide production yield, a graph of thick target radionuclide production yield versus proton (projectile) energy would have to be plotted. The said graph can be seen in the figure 4.5 below. Analyzing the figure below, one can conclude that radionuclide production yields in thick targets increases exponentially with proton energies. 72 University of Ghana http://ugspace.ug.edu.gh 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0 5 10 15 20 25 Energy/MeV Figure 4.5 A graph of saturated thick target radionuclide production yield versus particle energy. An alternative method for estimating the radionuclide production thick target yield was to numerically solve the radionuclide production yield equation (i.e. equation (1) see Appendix A using Newton‘s Forward Difference Formula) and then put in the appropriate apportioned energy ranges as well as other parameters. Below is a table that contains the apportioned energy ranges and the corresponding radionuclide production yields calculated from the numerically solved equation. It is very obvious from table that thick target yields increases with an increase in proton energies. 73 saturated Yield/(MBq/μAh) University of Ghana http://ugspace.ug.edu.gh Table 4.5.1(b) A table of Particle Energy Ranges and Corresponding Radionuclide Production Yields(Newton‘s Formula). Ein/MeV Eout/MeV Saturated Yield/(MBq/μAh) 11 8 127 15 8 245 18 8 316 20 8 358 22 8 395 24 8 432 To be able to investigate the effects of proton energy on the radionuclide production yield, the figure below was plotting (i.e., the yield against the projectile energy) to aid in the analysis. The figure 4.5.1 depicts a similar trend whereby a thick target yield of radionuclide production increases almost proportionally with thick target yield as stated earlier. 500 450 400 350 300 250 200 150 100 50 0 10 15 20 25 Energy(MeV) Fig 4.5.1. Saturated thick target Radionuclide Production Yield Versus Particle Energy. 74 saturated Yield/(MBq/μAh University of Ghana http://ugspace.ug.edu.gh 4.5.2 Comparison of saturated yields obtained by Newton’s Forward Difference (N.F.D) formula and Simpson Numerical Integration (S.N.I) method. Table 4.5.2 Particle energy ranges and saturated yield values for N.F.D and S.N.I Enery Saturated Yield(MBq/µA) (MeV ) S.N.I2/ Ein Eout N.D.F1 S.N.I1 N.D.F2 S.N.I2 N.D.F2 11 8 127 91 92.28 146.73 1.59007 15 8 245 309 215.2 342.30 1.59061 18 8 316 505 309.39 488.98 1.59073 20 8 358 620 368.85 586.76 1.59078 22 8 395 692 430.31 684.44 1.59082 In order to establish a relationship betweein the saturated yield obtained by N.F.D method and S.N.I method, values of the saturated yield within the same particle energy ranges for the production of Tc-99m are tabulated in table 4.4.2 above. It can be observed in the table that, saturated yield values in both methods incresses with an increase in particle energy, however, it can be realised that the saturate yield values within the same energy range for botn methods are not the same. Therefore through the process of curve fitting and minimisation of the plotted data (saturated yield against particle energy) which was meant to cause both graphs to start at 8MeV on the X-axis when the saturated yield is zero on the Y-axis as shown in figure 4.2.2 below, trend line equation for the curve of best fit was obtained for each method. 75 University of Ghana http://ugspace.ug.edu.gh Subsequently, respective particle energies were substituted into these trend line equations (see Figure 4.2.2) and the corresponding new S.N.I2 and N.F.D2 values obtaind as shown in Table 4.2.2. A constant factor of 1.59 has been established as a ratio of S.N.I2 to N.F.D2 values for each of the energy range considered in the table. In Figure 4.2.2, it can be clearly seen that the graph obtained by the N.F.D method underestimates the saturated yield values as compared to the values obtaind by the S.N.I method. This implies that in the absence of appropriate nuclear reaction model code and the SRIM software package to generate cross section values and stopping power values respectively that demands the usage of the S.N.I method (which is a standard method) for the calculation of saturate yield, one can employ the N.F.D. method and always multiply the value gotten by a factor of1.59 to obtain almost the same values which would have been obtained by the S.N.I method. 800 700 600 500 N.D.F 400 y = 48.892x - 391.08 R² = 0.9763 S.N.I 300 Linear (N.D.F) Linear (S.N.I) 200 y = 30.73x - 245.75 R² = 0.9237 100 0 0 5 10 15 20 25 Energy/MeV Figure 4.5.2 Graphs of particle energy against saturated yields for N.F.D and S.N.I 76 Saturated Yield/(MBq/µAh) University of Ghana http://ugspace.ug.edu.gh 4.5.3 Variation of Saturated Thick Target Yield with Irradiation Time. It is equally important to investigate the effects irradiation time on the radionuclide production yield. Table 4.5.3 below contains different irradiation times and the corresponding radionuclide production yields. It can be observed that saturated thick target radionuclide production yields decreases with an increase in irradiation time. This is further elaborated by the graph in figure 4.5.3 where it is clear that saturated thick target yields for radionuclide production decreases exponentially with an increase in irradiation time. Table 4.5.3: Saturated Thick Target Yields for Different Irradiation Time in Hours. Irradiation time Yield (hrs) (MBq/μAh) 1 2591.07 2 1295.54 3 863.69 4 647.77 5 518.21 6 431.85 3000 2500 2000 1500 1000 500 0 0 1 2 3 4 5 6 7 Irradiation Time (h) Figure 4.5.3: A graph of saturated thick target radionuclide production yield against irradiation time. 77 saturated Yield (MBq/μAh) University of Ghana http://ugspace.ug.edu.gh 4.5.4 Variation of Saturated Thick Target Yield with Target Thickness. In order to assess the effects of target thickness on the radionuclide yield, it is necessary to vary the target thickness and calculate the corresponding target production yields. Table4.5.4 below contains different target thicknesses and their respective target production yields. From the table one can clear see that thick target yields for radionuclide production decreases exponentially with target thickness. A plot of radionuclide production yield against different target thicknesses is shown in Figure 4.5.4. Table 4.5.4 : Values of radionuclide production yield and that of various thicknesses of the target material. Target thickness,X (µm) Yield(MBq/μAh) 223.49 1091.33 312.15 781.36 388.04 628.55 442.94 550.64 503.62 484.30 564.79 431.85 78 University of Ghana http://ugspace.ug.edu.gh 1200 1000 800 600 400 200 0 220 270 320 370 420 470 520 570 620 Thickness(μm) Figure 4.5.4: A graph of radionuclide production yield versus various thickness of the target. 4.6 DISCUSSION 4.6.1 Excitation Functions Excitation functions are plots of nuclear reaction cross sections against incident particle energies. Considering Fig 4.1.1 in chapter four, when a proton particle is accelerated at different energies to interact with Mo-100 target, different nuclear reaction channels are created. The desired reaction channel that leads to the direct 100 99m production of technetium-99m is the Mo (p, 2n) Tc reaction. However, the rest are competing reaction channels that lead to the production of contaminants. Looking 100 99m 99m at the excitation function of the Mo (p, 2n) Tc reaction, Tc can best be produced within the 10-19 MeV energy range. 79 saturated Yield (MBq/μAh) University of Ghana http://ugspace.ug.edu.gh 100 99m Figure 4.2.1 compares the excitation function of Mo (p, 2n) Tc reaction for the 99m production of Tc to the excitation functions of (p, n) reactions which led to the production of six other technetium products. The fact is that, it may not be possible for a target to be100% pure molybdenum-100. There might be other isotopes of molybdenum which would go through (p, n) reactions. It can therefore be seen clearly in the figure that those reactions peak at lower energy particle energies. Moreover, 100 99m Figure 4.3.1 compares the excitation function of Mo (p, 2n) Tc reaction with other technetium products which are produced through the (p, 2n) reactions. It can also be observed that the excitation functions of these reactions really peak at higher particle energy values. Therefore it can be deduced that the optimum energy range for 99m the production of Tc falls within 10-19MeV. Finally, the analyses of all the excitation functions of all the figures above indicated that in the investigated energy range the (p, n) and (p, 2n) reactions are responsible for the creation of the majority of these contaminants. 4.6.2 Comparisons with Experimental Data Figure 4.4.3 shows the excitation function obtained in this work whereby Talys code 100 99m was used to generate cross sections for Mo(p,2n) Tc reaction and that obtained by Levkovskij (1991) whereby cross sections were experimentally measured for the same reaction within the energy range 5-35MeV. It can be seen that the cross sections values obtained by Levkovskij (1991) are higher than that obtained by this work. This 99m may be due to the fact that the elevated Tc cross-sections of their work may 99 perhaps be attributed to the incomplete subtraction of the Mo 140 keV peak 99 contributions due to the underestimated Mo cross-sections observed in Fig.4.1.1. Although Levkovskij (1991) mention that they have corrected for the growth and decay of the metastable and ground states, since decay data and cross section 80 University of Ghana http://ugspace.ug.edu.gh 99 information is not provided for Mo, it is unclear if corrections were performed to 99 99 99m account for interfering Mo 140 keV γ-rays or Mo→ Tc contributions post-EOB. 99m The absence of such corrections would similarly explain the elevated Tc cross- sections. Despite the difference in cross section values, the trend of shape formation of the two excitation functions is almost the same. Analysis from the two excitation 99m functions indicates that the optimum energy range for the production of Tc is from 10-20MeV. Scholten et al, (1999) performed further works to experimentally measure the 100 99m 99m production cross sections of Mo (p,2n) Tc reaction for the production of Tc. The excitation function of their work and this current work are presented in figure 4.4.2. It can be observed that the maximum production cross section for each work is around 200mb. Besides the trend of formation of the graphs are almost the same except one data point towards the peak. This variation of data point may be due to unstable experimental conditions. It can be deduced that the optimum energy range 99m for the production of Tc is within 10-20MeV. Furthermore, Takacs et al, (2003) undertook an experimental research to optimize the 99m production of Tc. In their work they carried out nuclear reaction cross section 100 99m 99m measurement for Mo (p,2n) Tc reaction which leads to the production of Tc for the energy range 5.7-37.9MeV. A comparison of excitation functions of their work and this theoretical work are presented in figure 4.4.1 Analysis of the two graphs show that the cross sections calculated in this work using the Talys code are in good agreement with the cross sections obtained by Takacs et al. It can also be observed that the trend of shape of the two graphs is the same and they both peak around 200mb. Moreover, deducing from both excitation functions the optimum energy range 99m for the production of Tc is 10-20MeV. 81 University of Ghana http://ugspace.ug.edu.gh Finally, Celler et al (2011), carried out a theoretical measurement of nuclear reaction 100 99m 99m cross section for Mo(p,2n) Tc reaction for the optimum production of Tc using the empire code, another nuclear reaction model code. The excitation functions of their work and this current work (using the Talys code) are presented in Fig. 4.4.4 Analyzing the two excitation functions it is realized that the nuclear reaction cross sections generated by the two codes within the 5-35MeV energy range are in good agreement with each other except at the peak where the maximum cross section of their work is 220mb and that of this work is around 210mb which gives a relative error of only ±0.045. Besides, the trend of shape formation of the excitation functions is the same and the optimum energy range for each is 10-20MeV. 4.6.3 Radionuclide Production Yield 99m In order to optimize the production of Tc, there is the need to estimate the radionuclide production yield within the optimum energy range. In this work and from the nuclear reaction cross section analysis above, the optimum energy range for 99m the production of Tc using the Talys code is 20-11MeV. Applying the saturated thick target radionuclide production yield equation (i.e equation 1) in Chapter three, Celler et al, (2011) and Simpson numerical integration method, the estimated radionuclide production yield within the optimum energy range (20-11)MeV is 565MBq/µAh. This yield value is in good agreement with the value estimated by Celler et al, (2011) who in their work estimated the saturated thick target yield within 19-10MeV to be 705.83MBq/µAh. 99m According to Gagnon et al, (2011) the thick target production yield of Tc through 100 99m Mo (p,2n) Tc reaction within the 22-10MeV energy range was calculated in their work to be 712MBq/µAh. Their value is in good agreement with the yield estimated 82 University of Ghana http://ugspace.ug.edu.gh in this work whereby the yield estimated in 20-11MeV energy range yielded 601MBq/µAh. They also reported that their estimated yield value was however higher than the values obtained by Scholten et al, (1999) which was measured to be 414MBq/µAh within 22-12MeV energy range; and Takacs et al, (2003) which was 629MBq/µAh within 25-5MeV energy range. It can therefore be deduced that the respective yield calculations done by the previous researchers are in good agreement with this current work. Figure 4.5 presents a graph of saturated radionuclide production yield against particle energy. It can be observed that the yield increases steadily with particle energy until up to 18MeV where it begins to increase slowly till saturation was reached. This trend of the yield versus energy graph is in good agreement with similar graphs presented in literature. 4.6.4 Investigation of the effects of some operational parameters on saturated thick target radionuclide production yield. Important operational parameters such as particle energy, target thickness, and irradiation time were investigated in this work to determine their effects on saturated thick target radio nuclide production yield. Using the derived saturated thick target radionuclide production yield equation in chapter three (Equation 3.21) and assuming some constant values for the irradiation time and the target thickness, the appropriate radionuclide production yield values were calculated at different particle energies. Figure 4.5.1 presents a graph of saturated thick target yields against particle energies. It can clearly be seen that as the particle energy increases the saturated thick target yield also increases accordingly but very slowly. Figure 4.5.3 shows a graph of saturated thick target yield versus irradiation time. The graph indicates that when values of particle energy and target thickness values are constant then, an increase in irradiation time leads to an exponential decrease in 83 University of Ghana http://ugspace.ug.edu.gh saturated thick target yield. Finally it is also clear in figure 4.5.4 that an increase in target thickness decreases exponentially with saturated thick target yield. 84 University of Ghana http://ugspace.ug.edu.gh CHAPTER FIVE CONCLUSION AND RECOMMENDATIONS 5.1 Conclusion 100 99mTc The study presents a theoretical evaluation of Mo (p, 2n) excitation function in the 5-35MeV energy range. From page 33, analysis of the cross sections generated by the Talys code for the various reaction channels when a proton particle interacts with a molybdenum-100 target indicates that the optimum energy range for the production 99m of Tc is in the 10-20MeV energy range. It is also interesting to note that trend of reaction cross section values and hence the formation of the shapes of excitation functions of this work is in the same pattern and trend with cross section values obtained by previous researchers over the same energy range for the same reaction 100 99mTc 99m channel, Mo (p, 2n) for the direct production of Tc. Though there are little deviations between this theoretical work and the previous experimental works, which might be due to unstable experimental conditions (e.g. beam current, proton flux etc.), these deviations were within the limits of experimental errors and therefore could not affect the significance of the study. Besides the results of Celler et al (2011) which were obtained theoretically are also in good agreement with the results of this work in terms in reaction cross sections and trend of formation shapes of excitation functions. Thick target radionuclide production yield has been estimated within the optimum energy range 20-10MeV to be 565MBq/µAh. Gagnon (2012) , in addition to 100 99m 100 99 evaluating the Mo(p,2n) Tc and Mo(p,x) Mo reactions, presented the first 100 99g experimental evaluation of the Mo(p,2n) Tc excitation function in the range of 8– 18 MeV. Thick target calculations in his work suggested that large quantities of 99m cyclotron-produced Tc may be possible. For example, a 6 hr irradiation at 500 μA 99m with an energy window of 18-10 MeV is expected to yield 1.15 TBq of Tc. 85 University of Ghana http://ugspace.ug.edu.gh This work has further demonstrated the effect of particle energy on thick target yield, the effect of irradiation time on saturated thick target yield and finally the effect of target thickness on the saturated thick target radionuclide production yield. These 99m findings suggest that the cyclotron production of Tc may be a feasible alternative to the reactor based production strategy. 5.2 Recommendation The main challenge of this work has being the installation and the usage of the nuclear reaction model code (Talys Code) which only works on Linux platforms. The fact of the matter is that the installation procedures given in the code‘s user manual are not straight forward. The following recommendations are therefore being made to improve upon the radionuclide production in general: i. Workshops on nuclear reaction model codes installation and usage should be organized occasionally to train students in the discipline who might want to conduct theoretical studies on radionuclide production. ii. An experimental verification of the results so far obtained in this theoretical research should be done. iii. Exploration works should be carried out in Ghana to uncover the possible deposits of molybdenum resources which serves as the major raw material for 99m the production of Tc in cyclotrons. iv. A research work should be done on how to write a code in MATLAB for the numerical solution obtained in this work. v. 99m Government should try and acquire cyclotrons for the production of Tc for 99 99m distribution to hospitals in the country instead of the Mo/ Tc generators which are unreliable, expensive and eventually causes delays in medical appointments with patients 86 University of Ghana http://ugspace.ug.edu.gh REFERENCES Alharbi A., Azzam A. , McCleskey M., Roeder B., Spiridon A., Simmons E., Goldberg V.Z. , Banu A., Trache L. and Tribble R. E. (2011). 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(2012) Accelerator Based Alternatives to Non-HEU Production of 99 99m Mo/ Tc In: Report on First Coordination Meeting, 16-20 April, 2012, TRIUMF, Vacouver, Canada. Schmor P. W. (2010). Review of Cyclotrons Used In the Production f Radioisotopes for Biomedical Applications, AAPS Inc., TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada Shotens B., Lambrech R. M., Cogneau M., Ruiz H. V. and Qaim S. M. (1999). 99m 99 Excitation functions for the cyclotron production of Tc and Mo: Elsevier Science Ltd. Science Media Centre of Canada (2012). Mastering Production of Medical Isotopes www.Sciencemedia.Ca | Twitter: @Smccanada. 99m Suzanne E. L., Michael J. W. (2012). Cyclotron Production of Tc. In: Report on the 1st Research Coordination Meeting on ―Accelerator-based Alternatives to Non-HEU Production of 99Mo/99mTc‖, TRIUMF, Vancouver, Canada 92 University of Ghana http://ugspace.ug.edu.gh Szelecsenyi F. (1997). Measurement of Cross Sections of Proton Induced Nuclear Reactions on Ti, Zn, Cd, and Au up to 30mev and their Applications in Radioisotope Production, Lajos Kssuth University, Debrecen, Hungary. Takacs S., Szucs Z., Tarkanyi F. Hermanne A. and Sonck M. (2003). Evaluation of 100 99m proton induced reactions on Mo: New cross sections for production of Tc 99 and Mo Journal of Radioanalytical & Nuclear Chemistry;Jul. 2003, Vol. 257 Issue 1, p195. TRIUMF (2012). Report on First Research Coordination Meeting (2012). ―Accelerator-Based Alternatives to Non-HEU Production of 99Mo/99mTc‖ Vancouver, Canada. Tammemagi, Hans., David Jackson (2009). Half-Lives - A Guide to NuclearTechnology in Canada, Oxford University Press, p.11-13, 156. Ullyett, B., (1997). Chapter Five - Canada Enters the Nuclear Age, published for Atomic Energy of Canada Limited by McGill-Queen's University Press US-DOE (2010). ―Molybdenum-99‖, Solicitation DE-FOA- 0000323, March 26. Van Gelder Jan Willem And Herder Anniek (2010). Alternatives for the Production of Medical Isotopes: A Research Paper Prepared for Greenpeace Netherlands, ProfundoRadarweg 60 1043 NT Amsterdam, the Netherlands. Ziegler J. F. and Manoyan J. M., Nuclear Inst. and Meth., B35, 215-28 (1989). 93 University of Ghana http://ugspace.ug.edu.gh APPENDIX Table: List of current manufactures of cyclotrons used in radioisotope production for medical applications, their cyclotron models, and compares some key cyclotron specifications. (Schmor, 2010) 94