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=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
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.
Many physical systems are not understood from first principles due to the presence of multi-body quantum correlations. The effort taken to simulate such systems on classical computers increases exponentially with increase in the system size. We study simple, yet non-trivial, three-body frustrated systems that can help in understanding the underlying quantum correlations. First we investigate the ground state of helium-like atoms using the variational method and physically meaningful ansatze, revealing how quantum entanglement arises due to frustration in the system. Next we consider another frustrated three-body system, the hydrogen molecular ion, and analytically demonstrate the nature of its wavefunction arising from the quantum tunneling phenomenon. Finally, we extend these results to model yet another physically important system, the hydrogen bond.