The study of positive muon ${\mu }^{+}$-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 ${\mu }^{+}$-He scattering with scattering momenta below $0.1a_0^{-1}$, 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 $-12.3a_0$ and $-10.6a_0$ for ${\mu }^{+}\text{−}{}^4\mathrm{He}$ and ${\mu }^{+}\text{−}{}^3\mathrm{He}$ scattering, respectively. Furthermore, we examined the distortion effects on helium induced by ${\mu }^{+}$.

• Received 21 March 2023
• Accepted 17 April 2023

DOI:https://doi.org/10.1103/PhysRevA.107.042815