A manifestly gauge-invariant description of interaction of atomic systems with strong fields in the dipole approximation

TL;DR

This paper introduces a new gauge-invariant method for calculating atomic ionization probabilities in strong electromagnetic fields, which improves upon previous approaches by maintaining gauge invariance at each order of approximation.

Contribution

It presents a novel gauge-invariant expansion of ionization amplitudes that does not depend on gauge-specific Hamiltonian partitions, differing from traditional strong field approximation methods.

Findings

The method ensures gauge invariance order by order in the expansion.

Numerical examples demonstrate differences from standard SFA calculations.

The approach separates direct ionization and rescattering contributions distinctly.

Abstract

We propose a new type of gauge-invariant expansion of the ionization probability amplitudes of atoms by short pulses of electromagnetic radiation. Contrary to previous gauge-invariant approaches to this problem it does not require different partitions of the total Hamiltonian depending on the choice of gauge. In a natural way the atomic potential is treated as perturbation acting on an electron interacting with strong pulse. Whereas this is a standard assumption of strong field approximation (SFA), we show that grouping consequently together \textit{all} terms of the same order in the atomic potential results in the expansion of the amplitude which is gauge invariant \textit{order by order}, and not only in the limit of infinite series. In this approach, which is illustrated by numerical examples, the "direct ionization" and "rescattering" contributions are different from those commonly used in SFA - calculations.