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

TL;DR

This work measures comprehensive energy spectra of light charged particles emitted after muon-nuclear capture in natSi, including the first low-energy alpha spectrum. By comparing unfolded spectra with MEM and PHITS (with surface coalescence and MEC extensions), the study reveals proton spectra are reasonably captured by both models, while deuteron and triton yields are underpredicted by PHITS. Alpha-particle emission shows contrasting behavior: MEM matches evaporation-dominated low energies but overestimates high-energy preequilibrium contributions, whereas PHITS with SCM+MEC better describes the high-energy tail. The results provide crucial constraints on preequilibrium and evaporation processes in muNC and motivate more detailed coincidence measurements to unravel multi-particle emission dynamics. Overall, the data emphasize particle-species dependence in emission mechanisms and guide future refinements of microscopic and transport-model descriptions of muon-induced nuclear de-excitation.

Abstract

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.

Figures (15)

• Figure 1: Experimental setup around the Si target. (a) Schematic view of the detector arrangement around the target. Only the sensitive region of each detector is illustrated for simplicity. (b) Photograph of the actual setup installed in the vacuum chamber.
• Figure 2: Digitized waveform of the plastic scintillator from the photomultiplier tube obtained for the 21.5 MeV/$c$ muon beam run without the target. In this waveform, three muons reach the scintillator in the first beam bunch and two muons in the second beam bunch. Peaks observed around 1,425 ns and 2,415 ns are attributed to electrons originating from muon decay.
• Figure 3: Beam timing structure in the 21.5 MeV/$c$ beam run with the target removed. (a) Two-dimensional histogram of peak timing versus integrated waveform value obtained from the plastic scintillator. Two distinct loci corresponding to the first and second muon pulses are clearly visible. The applied threshold on the integrated value is indicated by the red dashed line. (b) Timing distribution of peaks with integrated values above 4,000 ch, projected from the top panel. The data were fitted with a composite function including Gaussian components for muon and electron peaks and an exponential background for decay electrons. The decay time constant extracted from the fit is also shown in the figure.
• Figure 4: Beam timing structure for the 21.5 MeV/$c$ run with the target in place. (a) Two-dimensional histogram of peak timing versus integrated waveform value. Due to energy loss in the target, the muon loci are less distinct than in the target-removed case. The applied threshold on the integrated value is indicated by the red dashed line. (b) Timing distribution of peaks after applying an integrated-value threshold of 300 ch. The distribution is fitted using the model described in Appendix \ref{['appendix:fit_function']}.
• Figure 5: Beam timing structure for the 18.0 MeV/$c$ run with the target removed. (a) Two-dimensional histogram of peak timing versus integrated waveform value. The applied threshold on the integrated value is indicated by the red dashed line. (b) Timing distribution of peaks after applying an integrated-value threshold of 500 ch. The distribution is fitted using the model described in Appendix \ref{['appendix:fit_function']}.