Simulation Study on Irradiation Process for ²²⁵Ac Production via ²²⁶Ra(p,　xn) Reaction

²²⁵Ac is one of the most promising therapeutic radionuclides for targeted alpha therapy. Its decay chain emits multiple alpha particles with high linear energy transfer, which makes it suitable for the treatment of small tumors and metastatic lesions. However, the wider application of ²²⁵Ac radiopharmaceuticals is still limited by the shortage of stable and scalable production routes. Proton irradiation of ²²⁶Ra through the ²²⁶Ra(p,2n)²²⁵Ac reaction is one of the candidate accelerator production routes that has received attention in recent years, because it can be performed with low to medium energy cyclotrons and can avoid the long-lived ²²⁷Ac impurity commonly associated with high-energy thorium spallation. Nevertheless, the neighboring reactions ²²⁶Ra(p,n)²²⁶Ac and ²²⁶Ra(p,3n)²²⁴Ac can produce important radioactive impurities. These impurities affect the radionuclidic purity, cooling strategy, radiation field, and subsequent separation process. Therefore, in this work, the feasibility of ²²⁵Ac production through the ²²⁶Ra(p,xn) reaction is evaluated, and a reasonable irradiation process window is determined based on FLUKA simulations constrained by experimental cross-section data. In this study, a FLUKA Monte Carlo model was established for proton irradiation of a ²²⁶Ra target. Thin-target simulations were first performed to extract the partial cross sections of the ²²⁶Ra(p,2n)²²⁵Ac, ²²⁶Ra(p,n)²²⁶Ac, and ²²⁶Ra(p,3n)²²⁴Ac reactions. The calculated excitation functions were compared with available experimental data and recommended cross-section trends. The relative cross-section ratio σ(p,n)/σ(p,2n) was also analyzed to evaluate the ability of FLUKA to describe the competition between the main product channel and the impurity channel. On this basis, thick-target simulations were carried out for selected energy windows, irradiation times, and cooling times. The activities of ²²⁴Ac, ²²⁵Ac, and ²²⁶Ac were extracted, and the activity ratios of ²²⁴Ac/²²⁵Ac and ²²⁶Ac/²²⁵Ac were used as the main impurity indicators. The evolution of decay-chain nuclides during cooling was further analyzed to evaluate the total activity and the implications for separation and purification. The results show that FLUKA reproduces the general energy dependence of the main ²²⁶Ra(p,xn) reaction channels. Although the absolute calculated cross sections are higher than some experimental values, the calculated σ(p,n)/σ(p,2n) agrees well with experimental data in the key energy region. These results indicate that FLUKA can provide a reasonable description of the relative yields of ²²⁶Ac and ²²⁵Ac. The thick-target results show that the 13-14.8 MeV energy window is favorable for ²²⁵Ac production. In this region, ²²⁶Ra(p,2n)²²⁵Ac reaction is effectively used, while the high-energy side of the ²²⁶Ra(p,3n)²²⁴Ac reaction is suppressed. The simulation also shows that an irradiation time of 6-10 d improves the accumulation of ²²⁵Ac and reduces the relative contribution of ²²⁴Ac and ²²⁶Ac. For a ²²⁶RaCl₂ target irradiated by a 100 μA proton beam in the 13-14.8 MeV energy window, the calculated ²²⁵Ac activity reaches 1.34 Ci at the end of 10 d of irradiation. After 8 d of cooling, the activity of ²²⁵Ac and its decay daughters accounts for about 95.6% of the total activity, which shows that the later-stage radiation field is mainly governed by the ²²⁵Ac decay chain. The cooling analysis further shows that ²²⁴Ac and ²²⁶Ac behave differently. ²²⁴Ac is mainly controlled by the incident energy because it is produced through the high-energy ²²⁶Ra(p,3n) channel and has a short half-life. It decays rapidly during cooling and has limited influence on the final radionuclidic purity of ²²⁵Ac. In contrast, ²²⁶Ac is more sensitive to the cooling time. The activity ratio of ²²⁶Ac/²²⁵Ac decreases almost exponentially with cooling time. When activity ratio of ²²⁶Ac/²²⁵Ac is 10⁻³, it can be used as a reference criterion for high radionuclidic purity, a cooling time of about 8-10 d is needed, depending on the irradiation time. The results also show that the total activity does not decrease as fast as ²²⁴Ac alone, because ²²⁵Ac and its short-lived daughters, such as ²²¹Fr, ²¹⁷At, ²¹³Bi, ²¹³Po, and ²⁰⁹Pb, dominate the total activity after 8 d of cooling. The recommended process window is 13-14.8 MeV for the incident proton energy, 6-10 d for the irradiation time, and 8-10 d for the cooling time. This window offers a balanced condition between ²²⁵Ac yield and impurity control. The results also indicate that the separation and purification process should be arranged after sufficient cooling, and the continuous ingrowth of ²²⁵Ac decay daughters should be considered during product quality control. This study provides useful parameter references for the engineering development of accelerator-based ²²⁵Ac production using ²²⁶Ra targets.