Copper radionuclides for theranostic applications: towards standardisation of their nuclear data. A mini-review

Copper has several clinically relevant radioisotopes and versatile coordination chemistry, allowing attachment of its radionuclides to biological molecules. This characteristic makes it suitable for applications in molecular imaging or radionuclide targeted therapy. Of particular interest in nuclear medicine today is the theranostic approach. This brief review considers five radionuclides of copper. These are Cu-60, Cu-61, Cu-62, Cu-64, and Cu-67. The first four are positron emitters for imaging, and the last one Cu-67 is a β--emitting radionuclide suitable for targeted therapy. The emphasis here is on theory-aided evaluation of available experimental data with a view to establishing standardised cross-section database for production of the relevant radionuclide in high purity. Evaluated cross section data of the positron emitters have been already extensively reported; so here they are only briefly reviewed. More attention is given to the data of the 68Zn(p,2p)67Cu intermediate energy reaction which is rather commonly used for production of 67Cu.

Excitation functions of proton induced reactions on titanium and copper

Excitation functions of the Tnati(p,x)S43,47c, V48 and Cnatu(p,x)⁶⁴Cu, Z62,65n reactions were measured in the energy range of 8.8-18.4 MeV by using the stacked-foil activation technique and off-line gamma spectroscopy. The irradiation was carried out at the superconducting linac of the Institute of Modern Physics, Chinese Academy of Sciences. Besides, the reliability and effectiveness of theoretical data from the TALYS code, recommended data of the International Atomic Energy Agency (IAEA) and evaluated nuclear data of the ENDF/B-VIII.0, JENDL-4.0/HE and PADF-2007 libraries were evaluated and verified by comparing with experimental data. Our experimental results agree with most of the available literature data. TALYS-1.95 code could not reproduce, in most cases, the experimental data. Evaluated nuclear data from the ENDF/B-VIII.0, JENDL-4.0/HE and PADF-2007 libraries are able to reproduce, in most cases, the experimental data trend. Recommended data of the IAEA are in good consistent with our work and most of the available literature data.

Evaluation of production cross-sections for theranostic 67Cu radionuclide via proton-induced nuclear reaction on 68Zn target

Copper-67 (T_1/2 = 61.83 h, E_β-^mean=141 keV, I_β-^total=100%; E_γ = 184.577 keV, I_γ = 48.7%) is a promising radionuclide for theranostic applications especially in radio immunotherapy. However, one of the main drawbacks for its application is related to its limited availability. Various nuclear reaction routes investigated in the last years can result in ⁶⁷Cu production, although the use of proton beams is the method of choice taken into account in this work. The goal of this work is a revision of the cross-sections aimed at ⁶⁷Cu yield, which were evaluated for the ⁶⁸Zn(p,2p)⁶⁷Cu reaction route up to 80 MeV proton energy. A well-defined statistical procedure, i.e., the Simultaneous Evaluation on KALMAN (SOK), combined with the least-squares concept, was used to obtain the evaluated data together with the covariance matrix. The obtained evaluated data were also compared to predictions provided by the nuclear reaction model codes TALYS and EMPIRE, and a partial agreement among them has been found. These data may be useful for both existing and potential applications in nuclear medicine, to achieve an improvement and validation of the various nuclear reaction models, and may also find applications in other fields (e.g., activation analysis and thin layer activation).

Theoretical calculations of the reaction cross-sections for proton-induced reactions on natural copper using ALICE-IPPE code

A theoretical study of the nuclear-reaction cross sections for proton-induced reactions on (63)Cu and (65)Cu was performed in the proton energy range from threshold values up to 50MeV. The produced nuclei were different isotopes of Zn, Cu, Ni, Co and Mn, some of which have important applications. The reaction cross-section calculations were performed using the ALICE-IPPE code, which depends on the pre-equilibrium compound nucleus model. This code is suitable for the studied energy and isotopic mass ranges. Approximately 14 excitation functions for the different reactions have been constructed from the calculated cross-section values. The excitation function curves for the proton reactions with natural copper targets have been constructed from those for enriched targets using the natural abundance of the copper isotopes. Comparisons between the calculated excitation functions with those previously experimentally measured are given whenever the experimental values were available. Some statistical parameters were introduced to control the quality of the fitting between both the experimental and the theoretical calculated cross-section values.

Systematics of (p, n) reaction cross-section

Semi-empirical systematics of the (p, n) reaction cross-section was obtained at incident proton energies 7.5 MeV, 12.4 MeV and 24.8 MeV. Systematics is based on analytical formulas derived using the pre-equilibrium exciton model, evaporation model and semi-empirical mass formula Parameters of systematics were fitted to the data obtained from the analysis of available measured (p, n) reaction cross-section.

Systematics of (p,α) (p,nα), and (p,np) reaction cross-sections

Semi-empirical systematics of (p,alpha) (p,nalpha), and (p,np) reaction cross-sections were obtained at various incident proton energies from 17.9 to 28.5 MeV. Systematics are based on analytical formulas derived using the pre-equilibrium exciton model, evaporation model and semi-empirical mass formula. Parameters of systematics were fitted to the data obtained from the analysis of available measured cross-sections for (p,alpha) (p,nalpha), and (p,np) reactions.

Calculations for the excitation functions of the 63Cu(p,n)63Zn, 63Cu(p, 2n)62Zn and 65Cu(p,n)65Zn reactions

Calculations for the excitation functions of 63Cu(p, n)63Zn, 63Cu(p, 2n)65Zn and 65Cu(p, n)65Zn reactions have been carried out in 3-30 MeV energy range using statistical and pre-equilibrium nuclear reaction models. The calculations have been compared with reported measurements and discussed.

Reactions of 88Sr with protons of energies7–85 MeV

Excitation functions for the (p,xn) (x = 1–5), (p,p3n), and (p,2pxn) (x = 1, 3, 4) reactions induced in 88Sr by protons of energy from 7 to 85 MeV have been measured by radiochemical methods. Cross sections for the individual isomeric species for the products of (p,2n), (p,3n), (p,4n), and (p,p3n) reactions are also presented.Excitation functions for each of the (p,2p3n) and (p,2p4n) reactions exhibit two peaks, the first of which is assigned to (p,α n) or (p,α 2n) reactions from threshold considerations. The experimental results are compared with Monte Carlo calculations using the codes of Chen et al. for the cascade stage and Dostrovsky et al. for the evaporation stage. The comparison suggests that the calculations of Chen et al. overestimate the extent of compound nucleus contribution at high energies.

NUCLEAR REACTIONS INDUCED IN TANTALUM BY PROTONS OF ENERGY UP TO 84 MEV

Nuclear reactions induced in tantalum by protons of energy up to 84 Mev have been studied and excitation functions obtained for products formed by (p,xn), (p,pxn), (p,2pxn), and (p,3pxn) reactions. Radiation characteristics of the products were redetermined. Previously unreported γ-rays with energies 90 to 1050 kev have been found for W176, and 113 kev for W177. A new half-life of 2.7 ± 0.1 hr for W176 is reported. The cross sections for the (p,xn) reactions were compared with the values predicted by Jackson's schematic model and found to be in reasonable agreement. More complex reactions are discussed in the light of current nuclear theories.

THE SPALLATION OF IRIDIUM WITH PROTONS OF ENERGIES 9–87 MEV

Iridium metal has been bombarded with protons varying in energy from 8 to 87 Mev. The spallation products were radiochemically separated and decay characteristics and formation cross sections were determined. It was confirmed that both Pt187 and Pt186 have half-lives of about 3 hr, and a half-life of 13.3 ± 0.2 days was found for Ir189. An isomeric state of Ir186 with half-life 2.0 ± 0.5 hr has been found. Fair agreement was obtained between excitation functions for (p,xn) reactions determined experimentally and those predicted by the Jackson model. The (p,pn) yield at 84 Mev has been compared with that calculated from Monte Carlo cascade data combined with evaporation theory and found to be too high by a factor of 4.

REACTIONS PRODUCED ON ERBIUM BY PROTONS OF ENERGIES BETWEEN 6 AND 87 MEV

Erbium was bombarded with protons of energies varying between 6 and 87 Mev. Nuclear characteristics and excitation functions were studied for isotopes of Tm, Er, Ho, and Dy, formed by various (p,xn) and (p,xpxn) reactions. Bombardment of enriched Er isotopes helped elucidate some of the excitation functions. A comparison has been made of the experimental (p,xn) cross sections with those predicted by the Jackson model and reasonable agreement has been found. Holmium was bombarded with α-particles to produce the compound nucleus Tm169* and the ratios σ (p,n): σ (p,2n) = σ (α,n): σ(α,2n) were found to hold.

INTERACTION OF VANADIUM WITH PROTONS OF ENERGIES UP TO 84 MEV

Radiochemical techniques have been used to determine absolute excitation functions for 17 nuclides formed as spallation products from the irradiation of vanadium by protons of energy up to 84 Mev. The shape of the excitation functions and classical threshold calculations showed evidence of contribution of heavy-particle emission in the reactions of the type (p,3pxn), (p,5pxn), and (p,7pxn). The Barr method for analysis of the cross-section distribution was modified and applied at 60 and 80 Mev bombarding energies. The experimentally measured cross sections for 16 nuclides at 60 and 80 Mev bombarding energies were fitted to the four-parameter Rudstam equation σ (A,Z) = exp [PA−Q−R(Z−SA)2]. Comparison of the results obtained at 8 Mev bombarding energy with the predictions of the weak and strong absorption models showed better agreement with the predictions obtained by using the surface absorption Fernbach–Bjorklund potential.

DISTRIBUTION OF NUCLEAR CHARGE IN THE PROTON-INDUCED FISSION OF Th232

The cross sections for the independent formation of I130, I131, Te131, I132, and I134 and for the cumulative formation of Te132, I133, and I135 in the proton-induced fission of Th232 have been measured at nine proton energies between 8 and 87 Mev. From these data and from published total chain yield data, charge distribution curves have been obtained. These are compared with published charge distribution curves for uranium fission at energies up to 480 Mev and together they show a shift of the most probable fission product charge toward stability and a widening of the distribution with increasing bombarding energy. These phenomena are interpreted in terms of current models for nuclear reactions.