Inelastic scattering of electrons by metastable hydrogen atoms in a laser field

Gabriela Buica

Phys. Rev. A 92, 033421 – Published 24 September 2015

Abstract

The inelastic scattering of fast electrons by metastable hydrogen atoms in the presence of a linearly polarized laser field is theoretically studied in the domain of field intensities below $10^{10}$ W/ ${cm}^{2}$ . The interaction of the hydrogen atom with the laser field is described by first-order time-dependent perturbation theory, while the projectile electrons interacting with the laser field are described by the Gordon-Volkov wave functions. An analytic expression is obtained for the differential scattering cross section in the first-order Born approximation for laser-assisted inelastic $e^{-} − H (2 s)$ scattering for the $2 s \to n l$ excitation. Detailed analytical and numerical results are presented for inelastic scattering accompanied by one-photon absorption, and the angular dependence and resonance structure of the differential cross sections are discussed for the $2 s \to 4 l$ excitation of metastable hydrogen.

Received 15 June 2015

DOI:https://doi.org/10.1103/PhysRevA.92.033421

Authors & Affiliations

Gabriela Buica^*

Institute of Space Sciences, P.O. Box MG-23, Ro 77125, Bucharest-Măgurele, Romania

^*buica@spacescience.ro

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Issue

Vol. 92, Iss. 3 — September 2015

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Images

Figure 1
The specific scattering geometry G1 assumed for the numerical calculations of laser-assisted $e^{-} − H (2 s)$ scattering. $k_{i}$ and $k_{f}$ are the initial and final momentum vectors of the projectile electron, $θ$ is the angle between them, and $q$ is the momentum transfer vector. $ε$ represents the polarization vector of the linearly polarized laser field.
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Figure 2
Comparison of the DCSs for laser-assisted elastic scattering of electrons by $H (2 s)$ atoms, with $N = 1$ (one-photon absorption), for incident projectile electron energy $E_{k_{i}} = 100$ eV, at two photon energies, (a) 1.17 eV and (b) 2 eV, with the laser-atom interaction calculated within the first-order TDPT. Dashed lines represent the Bunkin-Fedorov approximation and dot-dashed lines represent the atomic contribution to DCSs. DCSs are normalized by the laser intensity $I$ and the polarization vector of the laser field $ε$ is parallel to the initial momentum vector of the projectile electron $k_{i}$ .
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Figure 3
The dynamic dipole polarizability of the $2 s$ state, $α_{2 s}$ , calculated from Eq. (42) as a function of the photon energy.
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Figure 4
Differential cross sections for the laser-assisted $e^{-} + H (2 s) \to e^{-} + H (4 l)$ inelastic scattering process for $N = 1$ as a function of the scattering angle $θ$ , at a projectile electron energy of $E_{k_{i}} = 500$ eV and photon energy of 1.17 eV with excitation of the (a) $4 s$ , (b) $4 p$ , (c) $4 d$ , and (d) $4 f$ subshells. Dashed lines represent DCSs given by Eq. (40), where the atomic dressing is neglected, and dot-dashed lines represent the atomic contribution to DCSs. The dot-dot-dashed line in (a) represents the total DCS for transition to any $n = 4$ subshell. DCSs are normalized by the laser intensity $I$ and the polarization vector of the laser field $ε$ is parallel to $k_{i}$ .
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Figure 5
Differential cross sections for the laser-assisted $e^{-} + H (2 s) \to e^{-} + H (4 l)$ inelastic scattering process for $N = 1$ with excitation of the $4 l$ subshells $(l = 0$ , 1, 2, and 3) as a function of the photon energy $ω$ , at a projectile electron energy of $E_{k_{i}} = 500$ eV and a scattering angle of $5^{\circ}$ , for the $2 s \to 4 s$ (short-dashed line), $2 s \to 4 p$ (dot-dashed line), $2 s \to 4 d$ (long-dashed line), and $2 s \to 4 f$ (solid line) excitations of hydrogen. The dot-dot-dashed line represents the total DCS for transition to any $n = 4$ subshell. DCSs are normalized by the laser intensity $I$ and the polarization vector of the laser field $ε$ is parallel to $k_{i}$ .
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Figure 6
Results similar to those in Fig. 5, but with a scattering angle of $30^{\circ}$ .
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