# Investigating the Secondary Thermal Neutron Intensity of Neutron Capture-Enhanced Proton Therapy
## 1 Introduction  
Proton-beam therapy (PBT), first proposed by [PERSON], is used to treat various diseases [1]. Charged particles, such as protons, have a unique physical property wherethe energy lost is inversely proportional to the square of their velocity, resulting in a peak energy release called the Bragg peak immediately before cessation [2]. This property enables a high dose to be focused on the tumor while minimizing the integral dose to the surrounding healthy tissues compared with conventional radiation therapy. However, this property also makes PBT more susceptible to anatomical variations between and within the treatment fractions than photon-based radiation therapy [3]. PBT is characterized by radiation with relatively high linear energy transfer (LET); however, its effectiveness against radioresistant tumors may be limited compared with that of high-LET radiation, which is effective in destroying such tumors [4]. To address this, neutron capture-enhanced particle therapy (NCEPT) has been developed. NCEPT is a therapeutic approach that utilizes alpha particles produced from nuclear interactions between thermal neutrons generated by PBT and tumor-specific agents for dose enhancement and is expected to increase the biological dose contrast between tumors and normal tissues [5; 6; 7].  
In PBT, the energy of the neutrons generated in the body is typically \(<\)1 MeV, and most are thermal neutrons [8; 9]. When thermal neutrons interact with water, they mainly capture hydrogen and emit high-energy gamma rays. However, their interaction with 10B, which has a large cross-section for neutrons (3840 barns), produces high-energy charged particles (alpha particles and recoiling lithium 7 nuclei) [10]. In NCEPT, a drug containing 10B is administered to the patient before PBT, and the target dose is increased by the 10B(n,\(\alpha\))7 Li capture reaction (boron neutron capture reactions: BNCRs) induced by the thermal neutrons generated during PBT. The ranges of the alpha particles and recoiled lithium 7 nuclei emitted by the BNCRs range between approximately 9 \(\upmu\)m and 4 \(\upmu\)m, respectively, corresponding to the size of a single cell. Theoretically, this enables the selective destruction of cancer cells that have taken up 10B, sparing the surrounding healthy cells.  
This allows NCEPT to enhance the dose via BNCRs in tumor cells in addition to the dose from PBT. Compared to PBT alone, this approach offers geometric and biochemical advantages, potentially enabling more precise cancer control. Moreover, while the secondary neutrons produced by PBT may generally induce adverse effects such as secondary cancers [11], NCEPT offers the potential benefit of repurposing these effects to enhance therapeutic outcomes.  
However, to achieve sufficient dose enhancement, appropriate intracellular boron concentrations and thermal neutron fields are required to induce the BNCR [12]. Research on these matters remains insufficient. Therefore, this study aimed to elucidate, using Monte Carlo simulations (MCSs), the relationship between the proton-beam energy and the fluence distribution of secondary thermal neutrons generated within the target under clinically relevant conditions to promote the clinical application of NCEPT.