Perturbative hydrogenic Lamb shifts and radiative decay rates -- an so(4,2)-based algebraic approach

TL;DR

This paper introduces an algebraic method based on the so(4,2) Lie algebra to efficiently compute Lamb shifts and radiative decay rates in hydrogenic systems, extending previous approaches.

Contribution

It develops a systematic algebraic framework using so(4,2) symmetry to evaluate energy shifts and decay rates, including beyond the dipole approximation.

Findings

Derived integral representations for energy shifts and decay rates.

Numerical results demonstrate the method's applicability beyond dipole approximation.

Abstract

It is shown that algebraic techniques based on the Lie algebra so(4,2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay. In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case.