Cold three-body recombination in helium-helium-silver-atom collisions using the hybrid slow-variable-discretization–adiabatic hyperspherical $R$-matrix approach

We study three-body recombination in the helium-helium-silver system at cold collision energies. The three-body Schrödinger 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 ${}^4\mathrm{He}+{}^4\mathrm{He} +$ Ag system. Recombination at collision energies less than 10 mK is found to take place dominantly to the product molecule ${}^4\mathrm{He}\mathrm{Ag}$ in its least bound state, while the three atoms recombine mainly to the ${}^4\mathrm{He}_2$ molecule in its ground state at higher collision energies.

Figure 1

(a) Helium dimer potential $v_{\mathrm{HeHe}}\left(r\right)$ and ${}^4\mathrm{He}_2(l=0)$ bound-state wave function. (b) Helium-silver potential $v_{\mathrm{HeAg}}\left(r\right)$ and ${}^4\mathrm{He}\mathrm{Ag}$ ($l=0,1,2,3$) bound-state wave functions.

Figure 2

The lowest adiabatic hyperspherical potential curves $U_{\nu }\left(R\right)$ ($\nu =1,2,...,12$) as functions of the hyperradius $R$ for ${}^4\mathrm{He}+{}^4\mathrm{He} +$ Ag in the $J^{\mathrm{\Pi }}=0^{+}$ symmetry. The dashed curves denote the recombination channels, and the solid curves the entrance channels.

Figure 3

The lowest adiabatic hyperspherical potential curves $U_{\nu }\left(R\right)$ ($\nu =1,2,...,18$) as functions of the hyperradius $R$ for ${}^4\mathrm{He}+{}^4\mathrm{He} +$ Ag in the $J^{\mathrm{\Pi }}=1^{-}$ symmetry.

Figure 4

Product-state-selective total and partial ${}^4\mathrm{He}+{}^4\mathrm{He} +$ Ag recombination rates, $K_3$ and $K_3^{J\mathrm{\Pi }}$, as functions of the collision energy $E$ to the final states (a) ${}^4\mathrm{He}\mathrm{Ag}(l=0)+{}^4\mathrm{He}$, (b) ${}^4\mathrm{He}\mathrm{Ag}(l=1)+{}^4\mathrm{He}$, (c) ${}^4\mathrm{He}\mathrm{Ag}(l=2)+{}^4\mathrm{He}$, (d) ${}^4\mathrm{He}\mathrm{Ag}(l=3)+{}^4\mathrm{He}$, and (e) ${}^4\mathrm{He}_2(l=0) +$ Ag. The solid curves denote the total rates, and the dashed curves the partial rates labeled $J^{\mathrm{\Pi }}$.

Figure 5

(a) Product-state-selective total three-body recombination rates $K_3$ as functions of the collision energy $E$ for the processes ${}^4\mathrm{He}+{}^4\mathrm{He}+\mathrm{Ag}\to {}^4\mathrm{HeAg}(l=0,1,2,3)+{}^4\mathrm{He}$ and ${}^4\mathrm{He}+{}^4\mathrm{He}+\mathrm{Ag}\to {}^4\mathrm{He}_2(l=0) +$ Ag. (b) Branching ratio of the three-body recombination rates in panel (a) as functions of the collision energy $E$.

Figure 6

Schematical three $J^{\mathrm{\Pi }}=0^{+}$ hyperspherical potential curves associated with the ${}^4\mathrm{He}\mathrm{Ag}(l=3)+{}^4\mathrm{He}, {}^4\mathrm{He}_2+\mathrm{Ag}$ recombination channels, and three-body ${}^4\mathrm{He}+{}^4\mathrm{He} +$ Ag entrance channel from bottom to top (solid blue, solid brown, and solid violet curves respectively). The gray box indicates the hyperradial nonadiabatic transition region. The blue dashed and brown dash-dotted lines denote respectively the recombination pathways dominant at lower collision energies and at higher collision energies, respectively.