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The Journal of Chemical Physics

Full-dimensional quantum mechanical study of three-body recombination for cold 4He–4He–20Ne system

Mingming Zhao, Binbin Wang, Gao‐Ren Wang, Bina Fu, Maksim B. Shundalau, Yong‐Chang Han

Published Mar 13, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1063/5.0144619

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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 atom-atom-anion three-body recombination (TBR) and collision induced dissociation (CID) processes of the 3He–3He–T− system at ultracold temperatures are investigated by solving the Schrödinger equation in the adiabatic hyperspherical representation. The variations of the TBR and CID rates with the collision energies in the ultracold temperatures are obtained. It is found that the JΠ = 1− symmetry dominates the TBR and CID processes in most of the considered collision energy range. The rate of TBR (CID) into (from) the l = 1 anion is larger than those for the l = 0 and l = 2 anions, with the l representing the rotational quantum number of 3HeT−. This can be understood via the nonadiabatic couplings among the different channels.
Atom-atom-anion three-body recombination (TBR) in mixed 4He and xLi− (x = 6 or 7) is investigated in the adiabatic hyperspherical representation by quantum mechanically solving the Schrödinger equation. The distributions of product states following these TBR processes are found to be relatively different for the two systems when the collision energy is less than roughly 0.6 mK × kB or 0.3 mK × kB for 4He4He6Li− and 4He4He7Li− systems, respectively, with kB being the Boltzmann constant. For 4He4He6Li− systems, the rate of recombination into (v=0) l = 04He6Li− molecular anions is the largest with v and l denoting the rovibrational quantum numbers, while the TBR rate that leads to the formation of l = 14He6Li− molecular anions is a little smaller than that of neutral 4He2 molecules. For 4He4He7Li− systems, neutral 4He2 molecules tend to be the most products, following the yields of l = 0 and 1 4He7Li− molecular anions. However, in spite of these distinctly different distributions, the products of molecular anions, the sum of l = 0 and 1 4HexLi− products, are relatively larger than that of neutral 4He2 molecules for both the two systems.
The atom-atom-anion three-body recombination (TBR) of $^{3}\mathrm{He}+^{3}\mathrm{He}+{X}^{\ensuremath{-}}$(X=HorDX=\mathrm{H}\phantom{\rule{4pt}{0ex}}\text{or}\phantom{\rule{4pt}{0ex}}\mathrm{D}X=HorD) 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 lll 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.
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.
We have developed a method for calculating the rates for three-body recombination of cold atoms. This method allows us to treat not only zero total angular momentum, J=0,J=0,J=0, states but also J>0J>0J>0 states, so that recombinations at nonzero collision energies can be considered. Our method is applied to ground-state helium atoms 4He,{}^{4}\mathrm{He},4He, using a realistic interaction potential. In addition, we obtain the rates for collision induced dissociation.