Ba, are investigated in the hyperspherical representation by quantum mechanically solving the Schrödinger equation. It is found that the weakly bound (dimer) product states are preferentially populated for all of these cases, which could be understood from the joint effects of the lowest incident channel and the relatively long-range behavior of the corresponding nonadiabatic couplings among these lowest incident and shallow recombination channels. For the strongly bound products, since the flow is accessible in the small hyperradial region, their distributions are closely related to the behavior of the nonadiabatic couplings among the corresponding deep recombination channels. Particularly, our results indicate that the products are not always formed exclusively in the most weakly bound state when the scattering lengths among the reactants are relatively large and that there may exist a large fluctuation of the strongly bound products versus their binding energies in the universal region. In addition, the total TBR rates of these nonuniversal systems are also accounted for by the joint effects of the main adiabatic potentials and nonadiabatic couplings.
Ba, are investigated in the hyperspherical representation by quantum mechanically solving the Schrödinger equation. It is found that the weakly bound (dimer) product states are preferentially populated for all of these cases, which could be understood from the joint effects of the lowest incident channel and the relatively long-range behavior of the corresponding nonadiabatic couplings among these lowest incident and shallow recombination channels. For the strongly bound products, since the flow is accessible in the small hyperradial region, their distributions are closely related to the behavior of the nonadiabatic couplings among the corresponding deep recombination channels. Particularly, our results indicate that the products are not always formed exclusively in the most weakly bound state when the scattering lengths among the reactants are relatively large and that there may exist a large fluctuation of the strongly bound products versus their binding energies in the universal region. In addition, the total TBR rates of these nonuniversal systems are also accounted for by the joint effects of the main adiabatic potentials and nonadiabatic couplings.
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.
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 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 scattering length scaling rules for three-body recombination (TBR) of the 4He4He6Li- system in the zero-energy limit (E → 0) are investigated by considering various post-Born-Oppenheimer (post-BO) contributions to the standard BO potential of He-He interaction. It is found that these post-BO effects on the TBR rates that lead to different dimer products could be well fitted by the scattering length scalings Cab with a being the scattering length of the He-He interaction, and b and C the constants. It is interesting to find that the powers b about both the weakly and deeply bound dimer products are quite different from the well-known powers given by the scattering length scaling laws in the fields of ultracold neutral atomic gases. Such difference and the distinct powers associated with various dimer products are qualitatively accounted for by the properties of the major effective potentials and relatively long-range nonadiabatic couplings. Particularly, from these properties, the scaling powers are expected to be dependent on systems, but the power scattering length scaling behaviors to be universal, which has also been checked to apply to a wide range of a by tuning the He-He interaction.
We investigate the low-energy collision properties of the 4He-4He-X (X = 40K, 85Rb, 133Cs) systems using the R-matrix propagation method within the hyperspherical coordinate framework. The atom-dimer scattering length and atom-molecule collisional exchange rates are derived by solving the three-body Schrödinger equation using a potential energy surface obtained by summing three realistic pairwise potentials. Our results show that the atom-molecule collision exchange rates in the 4He2 + X → 4HeX + 4He process are primarily governed by the 4HeX two-body scattering lengths. Furthermore, when scaled by this parameter, the inelastic cross sections for all three systems collapse onto a single curve, demonstrating universal behavior. These findings provide new insights into the fundamental properties of weakly bound helium-helium-alkali-metal systems and their role in low-energy three-body collisions.
We study three-body recombination in the helium-helium-silver system at cold collision energies. The three-body Schr\"odinger equation is solved combining the slow variable discretization and adiabatic approaches with the R-matrix propagation method, in order to calculate the product-state-selective total and partial recombination rates in the 4He+4He+ Ag system. Recombination at collision energies less than 10 mK is found to take place dominantly to the product molecule 4HeAg in its least bound state, while the three atoms recombine mainly to the 4He2 molecule in its ground state at higher collision energies.