The radionuclide 64Cu (T1/2 = 12.7 h) is an important positron emitter, suitable for combining PET imaging and therapy. We evaluated four reactions, namely 64Ni( p, n)64Cu, 64Ni(d, 2n)64Cu, 68Zn( p, αn)64Cu and 64Zn(d, 2 p)64Cu.  Data analysis was generally limited up to about 30MeV using the nuclear model code TALYS-1.6. The result compared favourably with experimental as well as other theoretical works in literature. The integral yields calculated from those data are also given.  A critical comparison of the various production routes of 64Cu is presented. The   64Ni (p, n) 64Cu reaction, utilizing a highly enriched target, is the method of choice. Keywords: 6464Cu Production, Excitation Functions, Calculate Thick Target Yiel

Andam, Aba Bentil.

Banini, G. K.

Edusei, George

Fletcher, John J.

Tandoh, Joseph B.

English

International Institute for Science, Technology and Education (IISTE): E-Journals

Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.67, 2017          24  Simulation of Cross Section for the Production of Copper-64  George Edusei1*      Aba Bentil. Andam1      John J. Fletcher1      G. K. Banini2      Joseph B. Tandoh2 1.Graduate School of Nuclear and Allied Sciences, University of Ghana P.O. Box AE1, Atomic-Kwabenya,  Ghana 2.Ghana Atomic Energy Commission (GAEC), P.O. Box LG 80, Legon, Accra-Ghana  Abstract The radionuclide 64Cu (T1/2 = 12.7 h) is an important positron emitter, suitable for combining PET imaging and therapy. We evaluated four reactions, namely 64Ni( p, n)64Cu, 64Ni(d, 2n)64Cu, 68Zn( p, αn)64Cu and 64Zn(d, 2 p)64Cu.  Data analysis was generally limited up to about 30MeV using the nuclear model code TALYS-1.6. The result compared favourably with experimental as well as other theoretical works in literature. The integral yields calculated from those data are also given.  A critical comparison of the various production routes of 64Cu is presented. The   64Ni (p, n) 64Cu reaction, utilizing a highly enriched target, is the method of choice. Keywords: 6464Cu Production, Excitation Functions, Calculate Thick Target Yield  1. Introduction Copper-64 radioisotope (T1/2 = 12.7h) has a large application in radiotherapy. As this isotope is a positron emission radioisotope, it is known as a particularly effective radioisotope in Positron Emission Tomography (PET) imaging study, the utility of copper-64 depends on the chemical stability in water with proper energy and half-life as gamma emitters. The radioisotopes of copper have great potential for preparing metal-chelates for medical use (Blower et al, 1996). In particular the radionuclide 64Cu is very well suited: it has appropriate half-life, low β+ end-point energy of 0.65MeV, comparable to that of 18F (T1/2 = 110 min), the most commonly used positron emitter, and practically no γ-ray. These decay properties are almost ideal for imaging. The only drawback is the relatively low β+ abundance. On the other hand, its multiple decay modes (i.e., EC (43.8%), β+ (17.8%) and β− (38.4%)) renders it suitable for combining PET imaging and therapy (Sun, 1996 and Anderson et al, 1992). A pre-requisite of those studies, however, is the availability of 64Cu of very high purity and high specific activity. Our goal was to investigate cross section measurements on enriched zinc and nickel for various production routes of 64Cu and also to obtain the optimum production yield for the production of 64Cu and 67Cu on an enriched nickel and zinc target over a given range of proton-energy. In this study possible production routes of copper-64 are 64Ni (p, n) 64Cu, 64Ni(d, 2n)64Cu and 68Zn( p, αn)64Cu  were considered. The excitation functions of these reactions reported in the literature (Tarkanyi et al 2011 and Aslam, 2010) are in good agreement with this theoretical excitation function calculation of TALY-1.6 code.   1.1 Method   1.1.0 Taly’s Calculations Taly’s is a computer code system for analysis and prediction of nuclear reaction. The basic objective behind its construction is the simulation of nuclear reactions that involve neutrons, photons, deuterons, tritons, 3He- and alpha-particles, in the 1KeV-1GeV. The most important parameters involving nuclear theory, which were directly used in theoretical calculations of the excitation functions of reactions under consideration over a wide range of energy extending up to 30MeV. The default optical model potential (OMPs) of TALYs for protons and neutrons are from the local and global parameterization by (Koning and Delaroche, 2003) whereas OMPs for deuterons, tritons, helion and alpha particles are based on the folding approach (Hauser and Feshbach, 1952). Depending on the structure of nuclei, calculation for direct reactions can be performed by coupled channel method, the distorted wave born approximation, weak- coupling model for giant resonance description. In all the calculation the default options for the direct reaction were used. The compound nucleus was treated within the frame–work of Hauser-Feshbach model along with the width fluctuation correction model of Moldauer, (1980) the pre- equilibrium reaction calculation were performed by exciton (Koning and Duijvestjin, 2004). 1.1.1 Generation of Nuclear Reaction Cross Section In the estimation of optimum energy range for the production of copper-64, cross section of the 64Ni (p, n) 64Cu 64Ni(d, 2n)64Cu, and  68Zn( p, αn)64Cu  which are function of their respective particle energies were generated using Taly’s code. This was done by feeding the code with input parameter 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 code to run. After processing, the cross section of the various reaction channels are grouped and displayed into the output of the code. Using theoretical cross section values, the thick target yields of copper-64 can be calculated using SRIM-2013 for the stopping power. The thick target yield(y) is calculated by using Simpson’s numerical integration.   Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.67, 2017          25    1  	     																																					 1 Where Na is the Avogadro number, M is the target atomic weight of the target element,  is the reaction cross section as a function of energy, λ is the decay constant of the product, t is the time of irradiation, I is the projectile current and S(E) is the target stopping power (SRIM, 2013) expressed in unit MeVcm2g-1 [13]. 1.1.2 Results and Discussion  1.1.2.1 Evaluation of Cross Sections of 64Ni (p, n) 64Cu Reaction The database for this reaction is fairly strong and 13 data sets reporting experimental cross section were found in literature. But out of the 13, three were consider namely (Tarkanyi 2010), (Aslam, 2009) and (Szelecsenyi et al, 1993) for 64Ni (p, n) 64Cu reaction within the energy range of 5-20MeV. From figure 1 it can be seen that the cross section values obtained by Tarkanyi are slightly higher but they are in good agreement with this work. Despite the difference in cross section values, the trend of shape formation for all the excitation functions is almost the same. Therefore it can be deduced that the optimum energy range for this reaction falls within 7-12Me   Figure 1 Comparison of excitation function for 64Ni (p, n) 64Cu reaction. 1.1.3 Evaluation of Cross Sections of 68Zn (p, αn) 64Cu Reaction Tarkanyi performed works to experimentally measure the production cross section of 68Zn (p, αn) 64Cu reaction for the production of 64Cu. The excitation function of his work and this current work are presented in figure 2. It can be observed that the maximum cross section is 51.4mb. Beside the trend of formation of the graph are almost the same. It can be deduced that the optimum energy range for the production of 64Cu is within 20-29MeV  Figure 2: Comparison of excitation function for 68Zn(p,αn)64Cu reaction. 5 10 15 200100200300400500600700800Energy (MeV)Cross section (mb)  This WorkTarkanyi 2011Szelecsenyi 1993Aslam 201014 16 18 20 22 24 26 28 300102030405060Energy (MeV)Cross section (mb)  This WorkAslam 2010Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.67, 2017          26  1.1.4 Evaluation of Cross Sections of 64Ni (d, 2n) 64Cu Reaction The amounts of experimental cross section data available for 64Ni (d, 2n) 64Cu is not large. In a recent experiment, Tarkanyi measured the cross section using enriched 64Ni as target and cross section values were also taken from Aslam. A comparison of excitation function of their work and this theoretical work are presented in figure 3. Analysis of the three graph show that there is variation of data point which may be due to unstable experimental conditions. It can also observed that result was fairly close to their work but deviation of peak were found in the energy range of 19-22MeV. The optimum energy range for the production is 10-18MeV.   Figure 3: Comparison of excitation function for 64Ni (d, 2n) 64Cu reaction 1.1.5 Calculation of Thick Target Yields for Copper-64 Analyzing the available theoretical information on the excitation functions for the reactions 64Ni (p, n) 64Cu, 64Ni (d, 2n) 64Cu and 68Zn(p, αn)64Cu. These data could now be used for calculation of production yield using SRIM code for stopping power of 64Cu via a given reaction over a certain energy range. Numerical valves of production yield in MBq/µA and particle energies in MeV were obtained from equation (1). We give the thick target yield from figure 4 to 6 From the figure below, it can be deduced that the production yield for 64Ni (p, n) 64Cu reaction increase with increase in proton energies. For these reaction four groups, namely (McCarthy et al, 1997), (Szelecsenyi et al, 1993), (Obata et al.2003) and Avila-Rodriguez et al, (2007) reported experimental 64Cu yields. Those values are appreciably lower than the theoretical values.  Figure 4: Calculated thick target yield for 64Ni (p, n) 64Cu, reaction 5 10 15 20 2501002003004005006007008009001000Energy (MeV)Cross section (mb)  This WorkAslam 2010Tarkankyi 20115 6 7 8 9 10 11 12 13 14 150100200300400500600Energy(MeV)Thick target yield (MBq/µA)Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.67, 2017          27   Figure 5: Calculated thick target yield for 64Ni (d, 2n) 64Cu reaction  Figure 6: Calculated thick target yield for 68Zn (p, αn) 64Cu reaction In the case of 64Ni (d, 2n) Hermanne et al, 2007) and (Daraban et al, 2009)  and also for 68Zn(p, αn)64Cu process (Boothe et al 1991) and (Smith et al 1996) reported experimental yields which are within the limits of the calculated yields and the values were considerably lower than the calculated yields. The reasons for low experimental yields are well known (loss of activity during irradiation and chemical processing, uncertainty in high beam current measurement, radiation damage, etc. The significance of the calculated yield is to define the ideal value which can be obtained via a given reaction. 1.1.6 Comparison of Production Yield of Copper-64 The nuclear reactions mention in this work are 64Ni (p, n) 64Cu, 64Ni (d, 2n) 64Cu and 68Zn (p, αn) 64Cu are the same as previously evaluated by previous researchers. For the 64Ni(p, n)64Cu, 64Ni (d, 2n) 64Cu and 68Zn(p,αn) 64Cu reactions, the cross sections and the thick target yield of this work are in good agreement with their work. But our values are higher than recommended values by the Tarkanyi and Aslam by 10–12%. Part of the difference arises possibly from the normalization of experimental cross section data to the new decay data of 64Cu.  1.1.7 Comparison of Production Routes of Copper-64 A comparison of the various nuclear processes evaluated in this work with regard to the production of 64Cu is given in Table 1. In each case the optimum energy range and the thick target yield are given below. 5 6 7 8 9 10 11 12 13 14 150100200300400500600700Thick target yield (MBq/µA)Energy (MeV)Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.67, 2017          28  Table1. Comparison of production routes of Copper-64 Nuclear process Optimum energy range (MeV) Thick Target yield (MBq/µA) 64Ni(p, n)64Cu 12→ 7 99-369 64Ni(d,2n)64Cu 18→10 182-664 68Zn(p, αn)64Cu. 29→20 169-568 1.1.8 Conclusion Copper-64 is a very important medical radioisotope. The study compared both experimental and theoretical data with the new version of Talys code 1.6 of which good agreement exit between them. Furthermore, the integral or thick target yields are estimated based on the measured excitation functions for all the investigated reactions of which the 64Ni(p, n)64Cu reaction is the method of choice for production of large quantities of high purity. The optimum energy range for this reaction is 12-7MeV and the thick target yield has been estimated with the same optimum energy of 99-369MBq/µAh. Finally, it is well known that for medical uses, enriched targets have to be used in the production to avoid the secondary produced unwanted impurities.  Acknowledgement The authors are much grateful to Mr. Yaw Nsuo Brobbey and School of Nuclear and Allied Sciences as well as members of Ghana Atomic Energy Commission for their assistance in the course of this research work.   References Blower P. J, Lewis J. S, and Zweit, J. (1996). 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Simulation of Cross Section for the Production of Copper-64

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Simulation of Cross Section for the Production of Copper-64

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