Elastic scattering of positive muons from He3 and He4

Abstract

The study of positive muon ${\ensuremath{\mu}}^{+}$-He scattering plays an important role in precision experiments involving positive muons. In this paper, we employed the confined variational method to investigate $S$-wave ${\ensuremath{\mu}}^{+}$-He scattering with scattering momenta below $0.1{a}_{0}^{\ensuremath{-}1}$, where ${a}_{0}$ denotes the Bohr radius. Our approach yielded accurate $S$-wave phase shifts and scattering lengths. By utilizing the modified effective range formula, we determined the $S$-wave scattering lengths to be $\ensuremath{-}12.3{a}_{0}$ and $\ensuremath{-}10.6{a}_{0}$ for ${\ensuremath{\mu}}^{+}\text{\ensuremath{-}}^{4}\mathrm{He}$ and ${\ensuremath{\mu}}^{+}\text{\ensuremath{-}}^{3}\mathrm{He}$ scattering, respectively. Furthermore, we examined the distortion effects on helium induced by ${\ensuremath{\mu}}^{+}$.