Muon capture by3Henuclei followed by proton and deuteron production

Abstract

The paper describes an experiment aimed at studying muon capture by ${}^{3}\mathrm{He}$ nuclei in pure ${}^{3}\mathrm{He}$ and $\mathrm{D}_2 + {}^{3}\mathrm{He}$ mixtures at various densities. Energy distributions of protons and deuterons produced via $\mu^-+{}^{3}\mathrm{He}\to p+n+n + \nu_{\mu }$ and $\mu^-+{}^{3} \mathrm{He} \to d+n + \nu_{\mu}$ are measured for the energy intervals $10 - 49$ MeV and $13 - 31$ MeV, respectively. Muon capture rates, $\lambda_\mathrm{cap}^p (\Delta E_p)$ and $\lambda_\mathrm{cap}^d (\Delta E_d)$ are obtained using two different analysis methods. The least--squares methods gives $\lambda_\mathrm{cap}^p = (36.7\pm 1.2) {s}^{- 1}$, $\lambda_\mathrm{cap}^d = (21.3 \pm 1.6) {s}^{- 1}$. The Bayes theorem gives $\lambda_\mathrm{cap}^p = (36.8 \pm 0.8) {s}^{- 1}$, $\lambda_\mathrm{cap}^d = (21.9 \pm 0.6) {s}^{- 1}$. The experimental differential capture rates, $d\lambda_\mathrm{cap}^p (E_p) / dE_p $ and $ d\lambda_\mathrm{cap}^d (E_d) / dE_d$, are compared with theoretical calculations performed using the plane--wave impulse approximation (PWIA) with the realistic NN interaction Bonn B potential. Extrapolation to the full energy range yields total proton and deuteron capture rates in good agreement with former results.