Research Article

Nondipole effects in helium ionization by intense soft x-ray laser pulses

¹ Centre des Lasers Intenses et Applications (CELIA, UMR5107 du CNRS-CEA-Université de Bordeaux), 351 Cours de la Libération, 33405, Talence Cedex, France
² Unité de Formation et de Recherche Sciences Appliquées et Technologies de l’Information et de la Communication (SATIC), Université Alioune DIOP de Bambey, B.P. 30, Bambey (Diourbel), Senegal

^a e-mail: henri.bachau@u-bordeaux.fr
^b e-mail: topdigne@yahoo.fr

Received: 1 February 2019
Received in final form: 13 March 2019
Published online: 18 June 2019

Abstract

We consider the helium atom exposed to laser pulses in soft-x regime at intensities of the order of 10¹⁷–10²⁰ W/cm². Two cases are investigated, first a pulse with a central frequency of 20 a.u. (~522.2eV) and a pulse with a central frequency of 50 a.u. (~1.36keV). We solve the time-dependent Schrödinger equation (TDSE), nondipole (retardation) effects are included up to O(1/c) (c being the velocity of light). We study the single photoionization of helium with a focus on nondipole effects. We calculate the total and partial photoelectron energy spectra, and the photoelectron angular distributions. The nondipole effects associated with the A·P and A² coupling terms in the Hamiltonian (A denoting the vector potential of the field and P the momentum operator) are thoroughly analyzed in the region of one-photon resonance. We show that the nondipole contribution associated with A·P varies linearly with the intensity I while a three-photon transition involving A² increases like I³, in agreement with lowest order perturbation theory (LOPT). At high intensities these contributions compete and the nondipole transition becomes nonlinear. The physical mechanisms associated with nondipole couplings are discussed, as well as their effects on photoelectron energy and angular distributions.