Rydberg states of muonic helium in quantum electrodynamics

TL;DR

This paper employs a variational method with Gaussian wave functions to calculate energy levels of Rydberg muonic helium, including corrections, providing results suitable for experimental verification.

Contribution

It introduces a detailed variational approach to compute muonic helium Rydberg states with analytical matrix elements and correction terms.

Findings

Calculated a series of muonic helium Rydberg energy levels.

Included vacuum polarization and relativistic corrections.

Provided results that can be tested experimentally.

Abstract

The variational method is used to study the energy levels of muonic helium $(\mu^{-} \, e^{-} \, He)$ with an electron in the ground state and a muon in an excited state with principal and orbital quantum numbers $n \sim l+1 \sim 14$. The variational wave functions are chosen in the Gaussian form. The matrix elements of the Hamiltonian in the nonrelativistic approximation, as well as corrections for the vacuum polarization and relativism, are calculated analytically. A series of energies of the Rydberg muon states is obtained, which can be studied experimentally.