Study of atomic effects on electron spectrum in bound-muon decay process

TL;DR

This paper investigates how atomic effects influence the electron spectrum in bound-muon decay near the endpoint, incorporating various corrections to improve the accuracy for upcoming experiments on muon-to-electron conversion.

Contribution

It provides a comprehensive, self-consistent analysis of atomic effects on the electron spectrum in bound-muon decay, including nuclear and quantum corrections, relevant for experimental searches.

Findings

Atomic effects significantly alter the electron spectrum near the endpoint.

Corrections such as finite-nuclear-size and vacuum polarization are essential for precise predictions.

Results are applicable to isotopes C, Al, and Si for upcoming experimental searches.

Abstract

For the bound-muon decay process, the study of atomic effects on the electron spectrum near its endpoint is performed within the framework of the Fermi effective theory. The analysis takes into account for corrections due to finite-nuclear-size, nuclear-deformation, electron-screening, and vacuum-polarization effects, all of which are incorporated self-consistently into the Dirac equation. Furthermore, the nuclear-recoil correction to the muon binding energy is included. Calculations are carried out for the isotopes of C, Al, and Si, which are of a particular importance for forthcoming experiments aimed at search for the charged-lepton flavor-violating process of muon-to-electron conversion in a nuclear field.