Energy spectra of light charged particles emitted following muon nuclear capture on $^\mathrm{nat}$Si

Background: Charged-particle emission following muon nuclear capture (muNC) provides important information on the de-excitation dynamics of highly excited nuclei, particularly on the interplay between preequilibrium and evaporation processes. While proton emission has been relatively well studied, experimental data on composite charged particles remain limited, especially in the low-energy region for alpha particles. Purpose: This work aims to measure comprehensive energy spectra of charged particles emitted following muNC on silicon and to provide experimental constraints on theoretical models of charged-particle emission. Method: An experiment was performed at the RIKEN-RAL Muon Facility. Charged particles were identified using DeltaE-E telescopes and digital pulse-shape analysis with nTD-Si detectors. The initial energy spectra were reconstructed through an unfolding procedure and compared with calculations based on the microscopic and evaporation model (MEM) and the PHITS code with surface coalescence and meson-exchange-current extensions. Results: Energy spectra of protons, deuterons, tritons, and alpha particles were extracted over a broad energy range. In particular, the low-energy alpha-particle spectrum was measured for the first time. Proton spectra are reasonably reproduced by both MEM and PHITS. For alpha particles, the low-energy evaporation component is described by both models, while discrepancies remain at higher energies. For deuterons and tritons, MEM reproduces the spectral shapes well, whereas PHITS significantly underestimates the yields, especially at high energies. Conclusion: The results demonstrate clear particle-species-dependent differences in charged-particle emission following muNC. The measured energy spectra provide important constraints on preequilibrium and evaporation processes and indicate the need for improved modeling of composite-particle emission.