Strong-Field S-Matrix Theory With Coulomb-Volkov Final State in All Orders

TL;DR

This paper develops a systematic strong-field S-matrix theory incorporating Coulomb-Volkov final states, enabling accurate analysis of ionization processes in intense laser fields with Coulomb interactions.

Contribution

It introduces a complete S-matrix expansion with Coulomb-Volkov final states, resolving a long-standing theoretical gap in strong-field physics.

Findings

Derived the Coulomb-Volkov Hamiltonian and propagator.

Constructed the full S-matrix series in all orders.

Provided gauge-independent formulation of the theory.

Abstract

Despite its long standing usefulness for the analysis of various processes in intense laser fields, it is well-known that the so-called strong-field KFR or SFA ansatz does not account for the final-state Coulomb interaction. Due to its importance for the ubiquitous ionisation process, numerous heuristic attempts have been made during the last several decades to account for the final state Coulomb interaction with in the SFA. Also to this end an ad hoc model with the so-called Coulomb-Volkov final state was introduced a long time ago. However, till now, no systematic strong-field S-matrix expansion using the Coulomb-Volkov final state could be found. Here we solve this long standing problem by determining the Coulomb-Volkov Hamiltonian, identifying the rest-interaction in the final state, and explicitly constructng the Coulomb-Volkov propagator (or Green's function). We employ them to derive the complete S-matrix series for the ionisation amplitude governed by the Coulomb-Volkov final state in all orders. The results are given in both "velocity" and "length" gauges. We also present a gauge independent version of the Coulomb-Volkov S-matrix series.