1 Introduction

Nuclear medicine uses radiation to provide information about the morphology and functioning of a person’s specific organs, but also to direct highly destructive charged particles to pathological sites/processes with the aim of palliative or curative effects. In nuclear medicine, radioisotopes are of paramount importance to medical diagnosis and therapy [1]. Currently, thermal neutron-induced fission and charged-particle reactions with protons are the main production routes for medical radioisotopes. The increasing demand for medical radioisotopes requires more production facilities [2], along with the investigation of new ways to produce and apply application of new radioisotopes in both diagnosis and therapy.

Photon-induced reactions can provide an opportunity for the production of neutron-deficient isotopes, but conventional bremsstrahlung photon beam sources do not have a flux density sufficiently high to produce radioisotopes with high enough specific activities [3]. In contrast to conventional bremsstrahlung photon beam sources, Compton backscattering (CBS) γ-beam sources provide the capability to selectively tune photons to energies of interest [4-6]. This feature, coupled with the ubiquitous giant dipole resonance excitations of atomic nuclei, promises a fertile method of medical radioisotope production.

The large scale facility, Extreme Light Infrastructure - Nuclear Physics (ELI-NP) [7], which is currently under development, is one of the three pillars of the Extreme Light Infrastructure Pan-European initiative, which is dedicated to nuclear physics with extreme electromagnetic fields. Two 10 PW lasers and one very brilliant γ-beam facility will be installed at ELI-NP. The γ-beam facility will produce highly polarized (>99%), CBS-based tunable γ-ray beams with a spectral density of 10⁴ photons/s/eV in the range from 200 keV to 19.5 MeV with a bandwidth of ≤0.5%. This will likely allow for the production of certain radioisotopes useful for medical diagnostics and radiotherapy.

Copper-64 (T_1/2=12.7 h; β⁺ with 278 keV mean energy [17.6%]; β^- with 191 keV mean energy [38.5%]) has decay characteristics that allow for various applications in nuclear medicine, including positron emission tomography (PET) imaging and targeted radiotherapy of cancer [8]. Currently ⁶⁴Cu is regarded as a cyclotron radioisotope and is mainly produced by ⁶⁴Ni(p,n) reactions. However, it requires the rare and expensive ⁶⁴Ni target and the chemical separation step. An alternative production of ⁶⁴Cu with intense γ-beam was proposed and investigated by using ⁶⁵Cu(γ,n) reaction, as discussed later. Compared to ⁶⁴Ni with a natural abundance of 0.93%, ⁶⁵Cu has a relatively high natural abundance of 30.85% and the resulting production route further saves the chemical separation step. In this work, we present the results of simulations of the production of the medical radioisotope ⁶⁴Cu by (γ,n) using the ELI-NP γ-beam.

2 Methods

Several simulation codes have been designed to predict the beam characteristics of laser Compton sources [9-12]. Combining with the Geant4 toolkit [13], a complex simulation code of the CBS between laser photons and relativistic electrons was developed, considering the electron beam size and emittance [14, 15]. The code was benchmarked against experimental data produced at the γ-ray beam line at the synchrotron radiation facility, NewSUBARU [15]. We used this code to diagnose the beam characteristics when the CBS γ-rays arrive at the surface of the irradiated target. A realistic model of the γ-ray beam collimation system, which will be installed at ELI-NP, and also the geometry of the thin cylindrical target with a flexible radius placed in the beam for the production of the radioisotopes of interest, has been implemented in the combined code.

In order to calculate the photonuclear reaction yield and then to obtain the specific activity of medical radioisotopes, a data-based Monte Carlo simulation program has been developed [16]. We used the spectral and transversal spatial distributions of the γ-ray beam, predicted from the above CBS simulation code, as input. We also took into account the reliable photonuclear cross-section and the attenuation effect of the γ-rays interacting with the target isotope. Generally, the reaction cross-section required for the calculation of the activity of the isotopes are taken from the EXFOR database [17], from the EMPIRE calculation [18] or TENDL evaluation [19]. The data-based simulation program was tested against experimental data in the region of incident photon energy Eγ≤∼30 MeV and the analysis along, with a complete description of the program, will be included in [16].

3 Results and discussions

We simulated the CBS process to produce the γ-beam with the most appropriate parameters, its transport and delivery to the isotopic target for irradiation, and the subsequent isotope production. A layout example for simulation of ELI-NP γ-beam transport and irradiation on the target is shown in Fig. 1. In these simulations, we considered a cylindrical target of ⁶⁵Cu with a density of 8.96 g/cm³ and a γ-beam flux of 10¹¹ s^-1, which is a conservative value for the ELI-NP. We optimized the isotopic target dimensions and the beam parameters at a defined irradiation time interval in order to maximize the activity of the radioisotope.

Fig. 1.Full-screen View

A layout example for ELI-NP γ-beam transport and irradiating on the target isotope. After producing at the IP (see red pentagram displayed in the bottom left corner), the CBS γ-rays pass through the concrete wall and the collimation system of ELI-NP, and then arrive at the surface of the isotopic target. The collimator’s role is to stop the low-energy scattered γ-rays that cannot trigger a photonuclear reaction. Due to a strong penetrating power, only partial γ-rays interact with the target isotope, especially for a thin cylinder target, and the rest of them could be delivered to the experimental hall downstream for further nuclear physics experiments in parallel.

During the Compton scattering process, the energy of the scattered photons depended on the energy of the electrons, E_e, the energy of the laser photons, E_L, and the laser incident angle, θ_L, and the scattering polar angle of the scattered photons, θ, with respect to the electron direction of propagation. Choosing a scattering polar angle of zero, the scattered photons have the end-point (i.e. on-axis) energy:

where γ is the Lorentz factor of the relativistic e-beam. In the presence of a 515 nm laser colliding at θ_L = 172.5° with a relativistic e-beam, the on-axis energy of the scattered γ-rays as a function of the e-beam energy is shown in Fig. 2. The on-axis γ-ray energy from the simulation is in good agreement with that from Eq. (1).

Fig. 2.Full-screen View

The on-axis energy of the scattered γ-rays as a function of the e-beam energy.

Existing measurements of the ⁶⁵Cu(γ,n) reaction cross-section is presented in Fig. 3, together with the corresponding EMPIRE calculations [18]. The reaction cross-section from the EMPIRE calculations (75 mb) underestimates the experimental cross-section (90.5 ± 2.8 mb) by a factor of 1.2, but keeps almost the same shape distribution. The experimental data was chosen for our induced activity calculation.

Fig. 3.Full-screen View

Existing measurements of (γ,n) cross-sections for ⁶⁵Cu retrieved from the EXFOR database [17] together with corresponding EMPIRE calculations [18]. Experimental points in the figure are taken from [20].

Concerning the radioisotopes obtained by photonuclear reactions using a CBS γ-beam, its specific activity (A/m) is closely related to the production of the reaction cross-section, (Eγ), and the γ-ray flux density, and can be written as

Here, ρ and M are the density and molar mass (g/mol) of the irradiated target isotope, μ is the linear attenuation coefficient of the γ-beam inside the isotopic target with a mass, m, thickness, L, and radius, R. λ₁ = ln(2)/T_1/2 is the decay constant of the product isotope with a half-life of T_1/2, t_irr is the irradiation time, E_th is the threshold energy of the photonuclear reaction, E_max is the end-point energy of the photons, I(Eγ, r) is the γ-ray linear flux density at the surface of the isotopic target after the polar-angle integration, and N_A = 6.02 × 10²³ represents Avogadro’s constant. From Eq. (2), one can see that a good convolution of the γ-ray flux density and the reaction cross-section is helpful for the optimization of the specific activity of the product isotope.

Figure 4 shows the saturation specific activity of ⁶⁴Cu radioisotopes as a function of the target radius. For each e-beam energy, the curve of the specific activity has an inflection point, where the highest specific activity was achieved. The inflection point demonstrates the best convolution between the γ-ray spectrum and the shape of the reaction cross-section, and, hence, its position is flexible for different γ-beam energies. Note that at the target radius, r=0.5 mm, the value of the specific activity for the 700 MeV e-beam case is about 10% larger than that for the 710 MeV case. This is mainly due to the dipped curve of the experimental cross-section on ⁶⁵Cu(γ,n) at ∼17.8 MeV, as shown in Fig. 3. The 700 MeV and 710 MeV electron beams could provide CBS γ-beams with an end-point energy of 17.6 MeV and 18.2 MeV, respectivley. Hence, while the latter (18.2 MeV) covered exactly the experimental data dip at ∼17.8 MeV, the former (17.6 MeV) did not reach it. It is also shown that for ≤17.6 MeV γ-ray beams (i.e. ≤700 MeV e-beams), the specific activity increased as the target radius decreased.

Fig. 4.Full-screen View

Saturation specific activity of ⁶⁴Cu radioisotope as a function of the target radius for different e-beam energy. The isotopic target with thickness of 1.0 cm was used.

Figure 5 shows the saturation specific activity of ⁶⁴Cu radioisotopes as a function of the target thickness for different e-beam energy as input. The 700 MeV e-beam (corresponding to the end-point energy Eγ of 17.6 MeV) provided the highest specific activity compared to other e-beam conditions. This was mainly caused by the fact that the CBS γ-beam spectrum covers the energy, 17 MeV, that leads to a peaked GDR cross-section in ⁶⁵Cu(γ,n) reactions. The calculations showed that the highest specific activity of approximately 1.6 mCi/g can be achieved for a thin target (radius ≤2.0 mm and thickness 1.0 cm). It is also shown in Fig. 5 that the thinner the isotopic target, the higher the specific activity was.

Fig. 5.Full-screen View

Saturation specific activity of ⁶⁴Cu radioisotope as a function of the target thickness for different e-beam energy. The isotopic target with radius of 2.0 mm was used.

Fig. 6 shows the specific activities of ⁶⁴Cu isotopes as a function of the irradiation time. Using an optimal e-beam energy (700 MeV) and a thin target (radius 1-2 mm, thickness 1 cm), the specific activities of the ⁶⁴Cu isotope reached 1.2 mCi/g after one day irradiation, while their saturation specific activities exceeded 1.5 mCi/g after more than 5-6 times the half-life irradiation interval. According the current simulations, the achievable specific activity for ⁶⁴Cu isotopes is of the order of 1-2 mCi/g, using a conservative γ-beam flux of 10¹¹ s^-1 at ELI-NP. Note that such radioactivity may not be applied directly for clinical use, but suitable for research and development purposes to evaluate this novel production method with high-intensity and energetic γ-beams and, thus, paves the way towards possible future production facilities for clinical use.

Fig. 6.Full-screen View

Specific activity of ⁶⁴Cu as a function of irradiation time integral. The input parameters for the isotopic target were 2.0 mm radius, and 1.0 cm thickness.

4 Conclusion

We have shown in this paper that production through photonuclear reactions of ⁶⁴Cu radioisotopes (taken as an example) at ELI-NP is possible for optimized γ-beam energy and target geometry. Using Monte Carlo simulations, we estimated that after 5-6 times the half-life irradiation interval, a specific activity of the order of 1-2 mCi/g can be achieved for a thin target (radius 1-2 mm, thickness 1 cm), considering a γ-beam flux of 10¹¹ photons/s. We expect that the upcoming ELI-NP would provide an unprecedented possibility for the production of some key radioisotopes, such as ^64,67Cu, ²²⁵Ra/²²⁵Ac, and ¹⁸⁶Re for nuclear medicine research.