Self-energy correction to energy levels of highly charged ions in a path integral formalism

TL;DR

This paper develops a path integral approach to calculate self-energy corrections in highly charged ions, deriving the fermion propagator via Schwinger-Dyson equations and identifying observable Lamb shifts.

Contribution

It introduces a novel path integral formalism for self-energy calculations and applies it to highly charged ions, providing a new computational framework.

Findings

Derived the full fermion propagator using path integrals.

Calculated energy shifts from spectral function poles.

Identified ions with observable Lamb shifts.

Abstract

Self-energy corrections to the energy levels of bound electrons are calculated in the framework of path integrals. We arrive at the full fermion propagator, using methods of functional integrals, in the form of Schwinger-Dyson equation (SDE). From the full fermion SDE, the self-energy corrected propagator is identified and the energy shift is obtained from the poles of the spectral function. The numerical calculations are performed using complex contour integrals and the B-spline representation of basis functions. We identify ions with Lamb shifts observable via modern mass spectrometric methods.