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

Abstract

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