Three-body recombination in cold helium–helium–alkali-metal-atom collisions

Three-body recombination in helium-helium–alkali-metal collisions at cold temperatures is studied using the adiabatic hyperspherical representation. The rates for the three-body recombination processes ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+X\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}X$ and ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+X\to {{}^4\text{H}\text{e}}_2+X$, with $X={}^7\text{L}\text{i}$, ${}^{23}\text{N}\text{a}$, ${}^{39}\text{K}$, ${}^{85}\text{R}\text{b}$, and ${}^{133}\text{C}\text{s}$, are calculated at nonzero collision energies by including not only zero total angular momentum, $J=0$, states but also $J>0$ states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the ${}^4\text{H}\text{e-}{}^4\text{H}\text{e-}{}^{23}\text{N}\text{a}$ system.

Figure 1

(Color online) Helium dimer potential curve $v_{\text{HeHe}}\left(r\right)$ taken from Ref. [21]. and helium–alkali-metal $v_{\text{He}X}\left(r\right)$ potential curves from Ref. [26].

Figure 2

(Color online) Adiabatic hyperspherical potential curves $U_{\nu }\left(R\right)$ for the ${}^4\text{H}\text{e-}{}^4\text{H}\text{e-}{}^7\text{L}\text{i}$ system with $J^{\Pi }=0^{+}$. The first and second lowest potential curves are the atom-molecule channels, and correspond asymptotically to ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^7\text{L}\text{i}$ and ${{}^4\text{H}\text{e}}_2+{}^7\text{L}\text{i}$, respectively. The higher channels represent the three-body continuum channels, and the values of $\lambda$ indicate the asymptotic behavior of the potential curves, as given in Eq. (16). The inset shows the threshold region at large hyper-radii.

Figure 3

(Color online) Partial rates $K_3^{J\Pi }$ and their total $K_3$ for the $J^{\Pi }=0^{+}$, $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $5^{-}$ symmetries as functions of the collision energy $E$ for the three-body recombination processes (a) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^7\text{L}\text{i}\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^7\text{L}\text{i}$ and (b) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^7\text{L}\text{i}\to {{}^4\text{H}\text{e}}_2+{}^7\text{L}\text{i}$.

Figure 4

(Color online) Partial rates $K_3^{J\Pi }$ and their total $K_3$ for the $J^{\Pi }=0^{+}$, $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $5^{-}$ symmetries as functions of the collision energy $E$ for the three-body recombination processes (a) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{23}\text{N}\text{a}\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^{23}\text{N}\text{a}$ and (b) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{23}\text{N}\text{a}\to {{}^4\text{H}\text{e}}_2+{}^{23}\text{N}\text{a}$.

Figure 5

(Color online) Partial rates $K_3^{J\Pi }$ and their total $K_3$ for the $J^{\Pi }=0^{+}$, $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $5^{-}$ symmetries as functions of the collision energy $E$ for the three-body recombination processes (a) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{39}\text{K}\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^{39}\text{K}$ and (b) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{39}\text{K}\to {{}^4\text{H}\text{e}}_2+{}^{39}\text{K}$.

Figure 6

(Color online) Partial rates $K_3^{J\Pi }$ and their total $K_3$ for the $J^{\Pi }=0^{+}$, $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $5^{-}$ symmetries as functions of the collision energy $E$ for the three-body recombination processes (a) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{85}\text{R}\text{b}\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^{85}\text{R}\text{b}$ and (b) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{85}\text{R}\text{b}\to {{}^4\text{H}\text{e}}_2+{}^{85}\text{R}\text{b}$.

Figure 7

(Color online) Partial rates $K_3^{J\Pi }$ and their total $K_3$ for the $J^{\Pi }=0^{+}$, $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $5^{-}$ symmetries as functions of the collision energy $E$ for the three-body recombination processes (a) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{133}\text{C}\text{s}\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}{}^{133}\text{C}\text{s}$ and (b) ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+{}^{133}\text{C}\text{s}\to {{}^4\text{H}\text{e}}_2+{}^{133}\text{C}\text{s}$.

Figure 8

(Color online) The filled circles show the mass-scaled recombination rates $\mu K_3$ for the processes ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+X\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}X$ plotted against the ${}^4\text{H}\text{e-}X$ scattering length $a_{\text{He}X}/r_0$ ($X={}^7\text{L}\text{i}$, ${}^{23}\text{N}\text{a}$, ${}^{39}\text{K}$, ${}^{85}\text{R}\text{b}$, and ${}^{133}\text{C}\text{s}$). The filled triangles correspond to recombination to the ${}^4\text{H}\text{e}$ dimer. The dashed line indicates the ${\left(a_{\text{He}X}/r_0\right)}^4$ dependency of the mass-scaled rate.