Compton scattering of keV photons at helium atom near the He(1s) threshold for small momentum transfer

Henri Bachau; Matabara Dieng

doi:10.1140/epjd/s10053-021-00048-0

2024 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Eur. Phys. J. D (2021) 75: 34
https://doi.org/10.1140/epjd/s10053-021-00048-0

Regular Article - Atomic Physics

Compton scattering of keV photons at helium atom near the He $^{+}$ (1s) threshold for small momentum transfer

Henri Bachau¹^a and Matabara Dieng²

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 henri.bachau@u-bordeaux.fr

Received: 14 September 2020
Accepted: 8 January 2021
Published online: 25 January 2021

Abstract

We study Compton scattering at helium atom exposed to an electromagnetic field with a central frequency of 80 a.u. ( $\sim 2.18$ $\sim 2.18$ keV). We consider the situation where the incident light and scattered light are polarized along the same direction with small relative propagation angle $β$ $\beta$ . The energy of the emitted electron ranges from 0.2 to 2.1 a.u. ( $\sim 5.44$ $\sim 5.44$ –57.14 eV). The approach is based on previous works on stimulated Compton scattering (see Bachau et al. Phys Rev Lett 112:073001, 2014). We consider a field intensity of $3.51 \times 10^{16}$ $3.51\times 10^{16}$ W/cm $^{2}$ $$^2$$ , where stimulated Compton scattering can be treated in perturbative regime. In lowest order perturbation theory, the process results from the contribution of $A \cdot P$ $\mathbf{A\cdot \mathbf{P}}$ in second order and $A^{2}$ $\mathbf{A}^2$ in first order ( $P$ $\mathbf{P}$ is the electron momentum operator and $A$ $\mathbf{A}$ the vector potential of the field); both terms induce two-photon transitions. The Compton matrix element $| M_{fg} |^{2}$ $|{{\mathcal {M}}}_{fg}|^2$ is extracted numerically resolving the time-dependent Schrödinger equation, and in perturbation theory, emphasis is put on the calculation of the second-order amplitude associated with $A \cdot P$ $\mathbf{A\cdot \mathbf{P}}$ . We investigate the cases of relative propagation angle $β = 0$ $\beta =0$ and 10 degrees. The photoelectron energy distributions are dominated by the nondipole term $A^{2}$ $\mathbf{A}^2$ ; they increase by orders of magnitude when $β$ $\beta$ grows from 0 to 10 degrees. At $β = 0$ $\beta =0$ degree, both $A \cdot P$ $\mathbf{A\cdot \mathbf{P}}$ and $A^{2}$ $\mathbf{A}^2$ are at play and we show that the electrons are emitted in the (forward) direction of the momentum transfer $Q$ ${{\mathcal {Q}}}$ and to a lesser extent in the backward direction. When $β$ $\beta$ increases, the nondipole contribution $A^{2}$ $\mathbf{A}^2$ tends to dominate and the forward/backward asymmetry vanishes.