Existence and Construction of Resonances for Atoms Coupled to the Quantized Radiation Field

TL;DR

This paper develops an iterative scheme to construct and analyze resonances in nonrelativistic atoms coupled to quantized radiation, allowing precise calculation of resonance properties without infrared cutoff.

Contribution

It introduces a convergent iterative method inspired by prior works to construct and compute atomic resonances to arbitrary order in the fine-structure constant.

Findings

Successfully constructs resonances from excited states.

Provides a convergent algorithm for resonance eigenvalues and states.

Offers an alternative proof to existing results.

Abstract

For a nonrelativistic atom, which is minimally coupled to the quantized radiation field, resonances emerging from excited atomic eigenstates are constructed by an iteration scheme inspired by \cite{Pizzo2003} and \cite{BachFrohlichPizzo2006}. This scheme successively removes an infrared cut off in momentum space and yields a convergent algorithm enabling us to calculate the resonance eigenvalues and eigenstates, to arbitrary order in the feinstructure constant $\alpha \sim 1/137$, and is thus an alternative method of proof of a similar result obtained in \cite{Sigal2010}.