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

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.