Many-Body Theory Calculations of Positron Scattering and Annihilation in ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{CH}}_{4}$

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Many-Body Theory Calculations of Positron Scattering and Annihilation in $H_{2}$ , $N_{2}$ , and ${CH}_{4}$

C. M. Rawlins, J. Hofierka, B. Cunningham, C. H. Patterson, and D. G. Green

Phys. Rev. Lett. 130, 263001 – Published 30 June 2023

Abstract

The recently developed ab initio many-body theory of positron molecule binding [J. Hofierka et al., Many-body theory of positron binding to polyatomic molecules, Nature (London) 606, 688 (2022)] is combined with the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Model-potential calculations of positron binding, scattering, and annihilation for atoms and small molecules using a Gaussian basis, Phys. Rev. A 101, 022702 (2020)] to calculate positron scattering and annihilation rates on small molecules, namely $H_{2}$ , $N_{2}$ , and ${CH}_{4}$ . The important effects of positron-molecule correlations are delineated. The method provides uniformly good results for annihilation rates on all the targets, from the simplest ( $H_{2}$ , for which only a sole previous calculation agrees with experiment), to larger targets, where high-quality calculations have not been available.

Received 3 March 2023
Accepted 22 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.263001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electron & positron scattering Electron correlation calculations for atoms & ions Scattering theory

Positrons

First-principles calculations Many-body techniques Quantum chemistry methods

Atomic, Molecular & Optical

Authors & Affiliations

C. M. Rawlins¹, J. Hofierka ¹, B. Cunningham ¹, C. H. Patterson², and D. G. Green ^1,*

¹Centre for Light-Matter Interactions, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom
²School of Physics, Trinity College Dublin, Dublin 2, Ireland

^*Corresponding author. d.green@qub.ac.uk

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Vol. 130, Iss. 26 — 30 June 2023

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Figure 1
The main contributions to the positron-molecule self-energy: (a) the $G W$ diagram; (b), (c) the infinite ladder series of electron-positron interactions (virtual-Ps formation “ $Γ$ block”) and positron-hole interactions (“ $Λ$ block”). Lines labeled $ν$ ( $μ$ ) [ $n$ ] are excited positron (electron) [hole] propagators; a single (double) wavy line denotes a bare (dressed) Coulomb interaction. See text and extended data, Fig. 1 of [24], for full details.
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Figure 2
The effects of positron-molecule many-body correlations shown via the calculated $s$ -wave scattering phase shift (left) and normalized annihilation rate $Z_{eff}$ (right) for $H_{2}$ (representative of the three molecules considered in this Letter) in different approximations to the positron-molecule self-energy (see Fig. 1): HF (black dotted), bare polarization $Σ^{(2)}$ (black dot-dashed), $G W$ (black dashed), $G W + Γ$ (black dot-dot-dashed), and $G W + Γ + Λ$ (solid line).
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Figure 3
MBT calculated scattering cross sections for $H_{2}$ , $N_{2}$ , and ${CH}_{4}$ : $s$ wave (thin dashed black line), $p$ wave (thin dash-dotted black line), and $s + p + d$ total (thick solid black line) for bond lengths of $R = 1.45$ , 2.014, and 2.06 a.u. for $H_{2}$ , $N_{2}$ , and the $C ─ H$ bond in ${CH}_{4}$ . Also shown are measurements by Zecca et al. [34, 86, 87] (green triangles) and Charlton et al. [88] (orange triangles), and recent model potential calculations of Swann and Gribakin [44] (blue solid line) for each molecule; and additionally for $H_{2}$ the measurements of Machacek et al. (purple triangles) [89], Schwinger multichannel [90] (orange line), Kohn variational [40] (blue diamonds), convergent close coupling [46] (red filled circles) calculations, and modified-effective-range-theory fit of measured cross sections [91] (red squares); for $N_{2}$ , the Schwinger multichannel [32] (orange line), local-complex-potential [92] (plus symbols), and correlation-polarization-model [93] (dashed red) calculations; and for ${CH}_{4}$ , correlation-polarization-model-potential calculations of Franz [94] (orange dashed line), Jain and Gianturco [95] (blue dashed line), and Dibyendu et al. [96] (magenta dashed line), Schwinger multichannel [34] (turquoise dashed), and measurements of Sueoka and Mori [97] (blue triangle) and Dababneh et al. [98] (red diamonds).
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Figure 4
MBT calculated annihilation rate $Z_{eff} (k)$ for $H_{2}$ , $N_{2}$ , and ${CH}_{4}$ : $s$ wave (thin dashed black line), $p$ wave (thin dashed-dotted), $d$ wave (dotted), and total $s + p + d$ (thick solid black line). Results are shown for bond lengths of $R = 1.4$ , 2.014, and 2.06 a.u. for $H_{2}$ , $N_{2}$ , and the C-H bond in ${CH}_{4}$ . Also shown are the room-temperature Maxwellian averaged ${\bar{Z}}_{eff}$ from our calculation (black open circle; for $H_{2}$ black triangle up is for $R = 1.45 a . u .$ for comparison) and experiment (red triangles) for $H_{2}$ [51, 52, 99], $N_{2}$ [53], and ${CH}_{4}$ [53], along with energy-resolved measurements for ${CH}_{4}$ [100] (red diamonds), the recent model potential calculations of [44] (solid blue line). Additionally for $H_{2}$ , the calculated room-temperature values from the Kohn variational method (blue diamonds) [41, 49, 101], molecular $R$ -matrix (magenta square) [27], and SVM at bond length of $R = 1.4 a . u .$ (green triangle down) and $R = 1.45 a . u .$ (green triangle up) [74], and the Schwinger multichannel method at $k = 0.05 a . u .$ (orange squares) [32, 50]. The latter is also shown for $N_{2}$ . For ${CH}_{4}$ we also show the individual $s$ -wave contributions from the $2 a_{1}$ and one of the triply degenerate $t_{2}$ highest occupied molecular orbitals (HOMOs).
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Physical Review Letters

Many-Body Theory Calculations of Positron Scattering and Annihilation in H2, N2, and CH4

C. M. Rawlins, J. Hofierka, B. Cunningham, C. H. Patterson, and D. G. Green

Phys. Rev. Lett. 130, 263001 – Published 30 June 2023

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Many-Body Theory Calculations of Positron Scattering and Annihilation in $H_{2}$ , $N_{2}$ , and ${CH}_{4}$