Precision study of structural and elastic electron scattering properties of muonic helium systems

In this study, we investigate the structural properties of the three-body system $\textmu{}{\text{He}}^{+}$ and the four-body system $\textmu{}\text{He}$ using explicitly correlated Gaussian basis functions with global vectors. Our results quantitatively demonstrate the pronounced shielding effect of the muon on the nucleus and reveal structural characteristics of $\textmu{}{\text{He}}^{+}$ and $\textmu{}\text{He}$, analogous to those of H and ${\mathrm{H}}^{\ensuremath{-}}$, respectively. Using the confined variational method, we examine $s$-wave electron scattering from $\textmu{}{\text{He}}^{+}$ at incident energies below 8.7 eV, considering both $^{1}S$ and $^{3}S$ symmetries of the two electrons. By fitting near-threshold phase shifts to the modified effective range theory, we determine the scattering lengths to be 5.95 ${a}_{0}$ for $^{1}S$ symmetry and 1.76 ${a}_{0}$ for $^{3}S$ symmetry. Finally, we explore the distortion effects on $\textmu{}{\text{He}}^{+}$ induced by electron impact.