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Physical Review Research

Full-dimensional quantum mechanical study of He3+He3+X− → He3+He3X−(X=HorD)

Mingming Zhao, Binbin Wang, Yong‐Chang Han

Published Jan 13, 2022• 2 citations
Publisher

Abstract

The atom-atom-anion three-body recombination (TBR) of $^{3}\mathrm{He}+^{3}\mathrm{He}+{X}^{\ensuremath{-}}$($X=\mathrm{H}\phantom{\rule{4pt}{0ex}}\text{or}\phantom{\rule{4pt}{0ex}}\mathrm{D}$) systems at ultracold temperatures ($T=0.01\ensuremath{\sim}100$ mK) are studied by solving the Schr\"odinger equation in the adiabatic hyperspherical representation. It is found that for each system, $^{3}\mathrm{He}+^{3}\mathrm{He}+{\mathrm{H}}^{\ensuremath{-}}$ or $^{3}\mathrm{He}+^{3}\mathrm{He}+{\mathrm{D}}^{\ensuremath{-}}$, the ${J}^{\mathrm{\ensuremath{\Pi}}}={1}^{\ensuremath{-}}$ symmetry dominates the TBR process, and the rates of TBR into $l=1\phantom{\rule{4pt}{0ex}}^{3}\mathrm{He}{X}^{\ensuremath{-}}$ molecular anions are roughly three times as large as than that into $l=0\phantom{\rule{4pt}{0ex}}^{3}\mathrm{He}{X}^{\ensuremath{-}}$ molecular anions for $T\ensuremath{\in}[0.01,10]$ mK, where $l$ denotes the two-body rotational quantum number. In addition, for a given product state, the TBR rates of the $^{3}\mathrm{He}{+}^{3}\mathrm{He}+{\mathrm{H}}^{\ensuremath{-}}$ system are larger than that of the $^{3}\mathrm{He}+^{3}\mathrm{He}+{\mathrm{D}}^{\ensuremath{-}}$ system by roughly two orders of magnitude which could be ascribed to the major nonadiabatic couplings between the entrance and recombination channels.

DOI
10.1103/physrevresearch.4.013030

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The increase of the number of the two-body recombination channels strongly challenges the numerical calculation of the accurate rates for the three-body recombination (TBR) process and its reverse process, collision-induced dissociation (CID), at ultracold temperatures. By taking the 4He–4He–20Ne collision system as an example, we have obtained the rates for its TBR and CID processes involving all four recombination channels, including the two-body states 4He2 (l = 0) and 4He20Ne (l = 0, 1, 2) with l the rotational quantum number. By using the adiabatic hyperspherical method, we have considered not only total angular momentum J = 0 but also J > 0 in the ultracold collision energies (E = 0.01 − 100 mK × kB). It is found that 4He2 (l = 0) is the major product after the TBR process in the ultracold limit (E ≤ 0.1 mK × kB). The TBR rate into 4He2 (l = 0) is nearly one order of magnitude larger than the sum of the other three products, 4He20Ne (l = 0, 1, 2). Moreover, the CID rates for the three 4He20Ne (l = 0, 1, 2) + 4He initial states are close to each other and are smaller than that for the 4He2 (l = 0) + 20Ne initial state. Additionally, we have, for the first time, performed the channel-resolved scattering calculation that can explain the above-mentioned findings quantitatively.
The ultracold state-to-state chemistry for three-body recombination (TBR) in realistic systems has recently been experimentally investigated with full quantum state resolution. However, many detected phenomena remain challenging to be explored and explained from the theoretical viewpoints because this generally requires computational powers beyond state of the art. Here, the product-state distributions after TBR of 3He2–alkaline-earth-metal systems, i.e., after the processes of 3He + 3He + X → 3HeX + 3He with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, in the zero-collision-energy limit are theoretically studied. Two propensity rules for the distribution of the products found in current experiments have been checked, and the mechanism underlying these product-state distributions is explored. Particularly, two main intriguing transition pathways are identified, which may be responsible for the nonlinear distribution of the products vs their respective rotational quantum number. In addition, the TBR rates of these systems are also influenced by details of the interaction potential and relevant nonadiabatic couplings.
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Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length aaa of the He-He interaction and a three-body parameter a∗{a}_{*}a∗​ as input, where a∗{a}_{*}a∗​ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to 1/a∗1/{a}_{*}1/a∗​ versus 1/a1/a1/a should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational 1/a∗1/{a}_{*}1/a∗​ versus 1/a1/a1/a to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum J>0J>0J>0 are also discussed.