Production of the isotope copper-64 by using natural nickel target with proton energy 17 MeV and beam current 10 μA at cyclotron

A calculation method is developed for production of the copper-64 isotope from the 64Ni(p, n)64Cu nuclear reaction. The 64Cu radioisotope used in nuclear medicine is produced by irradiating a natural nickel target with a proton beam produced on a cyclotron. The conditions of the production were dictated by the capabilities of the cyclotron. The energy of the protons was 17 MeV (the beam current is 10 μॅ). As a result, the activity of copper-64 isotope for various irradiation times were obtained. The depth of proton penetration into the target material was studied.


Introduction
As known, nuclear medicine is based on the use of a variety radiopharmaceuticals, created on the basis of radioisotopes. Copper isotope 64 Cu is unique, since in the process of radioactive decay it can emit β + (0.65 MeV, 17.5%), β -(0.57 MeV, 38.5%) particles, and Auger electrons. Therefore, this isotope can be used both in positron emission tomography (PET) and for radionuclide therapy [1,2]. The great advantages of this isotope over other isotopes are not only its chemical properties, but also a long halflife (12.7 h), which makes it easier to obtain, transport and use radiopharmaceuticals labeled with it, compared to those widely used at present. 64 Cu has numerous advantages over the PET isotopes 18 F (t1/2= 109.8 min) and 11 C (t1/2= 20.4 min) currently used in clinics. Since the half-life of both 18 F and 11 C is relatively short, these isotopes are usually prepared on cyclotrons located near clinics. In addition, the preparation of radiopharmaceuticals requires the preliminary isolation of radioisotopes and their further attachment by a molecular carrier, which requires additional special equipment [3]. Isotope 64 Cu can be produced in nuclear reactors by the capture of either thermal neutrons 63 Cu(n,γ), or fast neutrons 64 Zn(n,p). Currently, for the production of 64 Cu there are two cyclotron methods. One is based on 64 Ni(p,n) and the other is based on 68 Zn(p,αn) [4,5].

Method of calculations
This report presents the results of calculation for 64 Cu production by using a proton beam energy 17 MeV (beam current 10 µA) to produce 64 Cu at the MGC-20 cyclotron of "SPbPU". The target is a natural mixture of nickel isotopes (the percentage of the 64 Ni isotope in natural nickel is 0.926%). The calculations take into account the loss of proton energy for excitation and ionization when passing through the target material [6].
Where dE/dx is the mean rate of energy loss (MeV/cm); x is the path traversed in the target material or the depth of the target (cm); Z is the atomic number of the target; A is the atomic mass (g/mol); ρ is the target density (g/cm 3 ); me is the electron mass (g); c is the speed of light (m/s); β = v/c is the ratio of the speed of the projectile to the speed of light and I is the mean excitation energy (eV). The production of 64 Cu is carried out due to the reaction 64 Ni(p,n) 64 Cu. The excitation function of this nuclear reaction has been measured in many experiments. In this paper, we used the result of combining the experimental data presented in the paper [7]. Using the solution of equation (1), we pass to the dependence of the cross section on the depth σ(x). The production of 64 Cu at different depths in the target will be determined by the equation:

(2)
Where NCu64 is the number of 64 Cu nuclei; J is the beam current (A); nNi64 is the concentration of 64 Ni nuclei in natural nickel (cm -3 ); λ is the decay constant of 64 Cu (s -1 ); e is the electron charge (C) and tirr is the irradiation time (s).
Integrating (2) from zero to the target thickness, we obtain the dependence of the 64 Cu production from zero to the target thickness τ: The solution of equation (1) is shown in 'figure 1' for protons energy of 17 MeV and natural nickel target. It can be seen that the optimal depth for stopping protons and losing all their energy is 0.056 cm.    (1) and (3) and the reaction cross sections given in [7], the activity of 64 Cu was determined using protons with an energy of 17 MeV, a current of 10 µA, and a natural nickel target.
In ' figure 4' shows the results of calculating the activity of produced 64 Cu, for various irradiation times.