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Title: Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method

Abstract

Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. In this paper, we give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculating $V$-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H$$_2$$ and electron scattering from the vibrationally excited molecular hydrogen ion H$$_2^+$$ and its isotopologues (D$$_2^+$$, T$$_2^+$$, HD$^+$, HT$^+$ and TD$^+$). Finally, convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron- and positron-molecule scattering calculations is demonstrated over a broad energy-range and discussed in detail. In general the CCC results are in good agreement with experiments.

Authors:
; ; ;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR); Curtin Univ. (Australia)
OSTI Identifier:
1356147
Report Number(s):
LA-UR-17-20546
Journal ID: ISSN 0953-4075
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Physics. B, Atomic, Molecular and Optical Physics
Additional Journal Information:
Journal Volume: 50; Journal Issue: 12; Journal ID: ISSN 0953-4075
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Zammit, Mark C., Fursa, Dmitry V., Savage, Jeremy S., and Bray, Igor. Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method. United States: N. p., 2017. Web. doi:10.1088/1361-6455/aa6e74.
Zammit, Mark C., Fursa, Dmitry V., Savage, Jeremy S., & Bray, Igor. Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method. United States. doi:10.1088/1361-6455/aa6e74.
Zammit, Mark C., Fursa, Dmitry V., Savage, Jeremy S., and Bray, Igor. Mon . "Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method". United States. doi:10.1088/1361-6455/aa6e74. https://www.osti.gov/servlets/purl/1356147.
@article{osti_1356147,
title = {Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method},
author = {Zammit, Mark C. and Fursa, Dmitry V. and Savage, Jeremy S. and Bray, Igor},
abstractNote = {Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. In this paper, we give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculating $V$-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H$_2$ and electron scattering from the vibrationally excited molecular hydrogen ion H$_2^+$ and its isotopologues (D$_2^+$, T$_2^+$, HD$^+$, HT$^+$ and TD$^+$). Finally, convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron- and positron-molecule scattering calculations is demonstrated over a broad energy-range and discussed in detail. In general the CCC results are in good agreement with experiments.},
doi = {10.1088/1361-6455/aa6e74},
journal = {Journal of Physics. B, Atomic, Molecular and Optical Physics},
number = 12,
volume = 50,
place = {United States},
year = {Mon May 22 00:00:00 EDT 2017},
month = {Mon May 22 00:00:00 EDT 2017}
}

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Cited by: 7works
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  • We extend the convergent-close-coupling method for the calculation of electron-hydrogen scattering to hydrogenlike targets, atoms, or ions. These include H, Li, Na, and K, atoms, as well as the multitude of ions which have the same isoelectronic sequence as any of these atoms. The reliability of the method is independent of the projectile energy, and we demonstrate its applicability by achieving excellent agreement with a large set of measurements for electron scattering on sodium at projectile energies ranging from 1 to 54.4 eV. These measurements include spin asymmetries, singlet and triplet [ital L][sub [perpendicular]], reduced Stokes parameters, differential, integrated, andmore » total cross sections, as well as the total ionization spin asymmetry. The method is found to give better agreement with experiment than any other over this entire energy range.« less
  • We report on the extension of the recently formulated relativistic convergent close-coupling (RCCC) method to accommodate two-electron and quasi-two-electron targets. We apply the theory to electron scattering from mercury and obtain differential and integrated cross sections for elastic and inelastic scattering. We compared with previous nonrelativistic convergent close-coupling (CCC) calculations and for a number of transitions obtained significantly better agreement with the experiment. The RCCC method is able to resolve structure in the integrated cross sections for the energy regime in the vicinity of the excitation thresholds for the (6s6p) {sup 3}P{sub 0,1,2} states. These cross sections are associated withmore » the formation of negative ion (Hg{sup -}) resonances that could not be resolved with the nonrelativistic CCC method. The RCCC results are compared with the experiment and other relativistic theories.« less
  • The convergent close-coupling approach developed by the authors is applied to positron scattering from atomic hydrogen below the first excitation threshold. In this approach the multichannel-expansion one-electron states are obtained by diagonalizing the target Hamiltonian in a large Laguerre basis. It is demonstrated that this expansion of the scattering wave function is sufficient to reproduce the very accurate low-energy variational results, provided target states with [ital l][le]15 are included in the expansions.
  • The convergent close-coupling method has been applied to positron scattering on a helium atom in the 2 {sup 3}S metastable state. For this system the positronium (Ps) formation channel is open even at zero scattering energy making the inclusion of the Ps channels especially important. Spin algebra is presented for the general case of arbitrary spins. A proof is given of the often-used assumption about the relationship between the amplitudes for ortho-positronium and para-positronium formation. The cross sections for scattering from 2 {sup 3}S are shown to be significantly larger than those obtained for the ground state.
  • The single-center convergent close-coupling method has been applied to positron-magnesium scattering at incident energies from 0.01 to 100 eV. Cross sections are presented for elastic scattering and excitation of 3 {sup 1}P, as well as for the total ionization and total scattering processes. We also provide an estimate of the positronium formation cross section. The results agree very well with the measurements of the total cross section by Stein et al. [Nucl. Instrum. Methods Phys. Res. Sect. B 143, 68 (1998)], and consistent with the positronium formation measurements of Surdutovich et al. [Phys. Rev. A 68, 022709 (2003)] for positronmore » energies above the ionization threshold. For energies below the positronium formation threshold (0.8 eV) we find a large P-wave resonance at 0.17 eV. A similar resonance behavior was found by Mitroy and Bromley [Phys. Rev. Lett. 98, 173001 (2007)] at an energy of 0.1 eV.« less