Quantum Dynamics of Ultracold $\mathrm{N}\mathrm{a}+{\mathrm{N}\mathrm{a}}_2$ Collisions

Ultracold collisions between spin-polarized Na atoms and vibrationally excited ${\mathrm{N}\mathrm{a}}_2$ molecules are investigated theoretically, using a reactive scattering formalism (including atom exchange). Calculations are carried out on both pairwise additive and nonadditive potential energy surfaces for the quartet electronic state. The Wigner threshold laws are followed for energies below ${10}^{-5}\mathrm{K}$. Vibrational relaxation processes dominate elastic processes for temperatures below ${10}^{-3}–{10}^{-4}\mathrm{K}$. For temperatures below ${10}^{-5}\mathrm{K}$, the rate coefficients for vibrational relaxation ($v=1\to 0$) are $4.8\times {10}^{-11}$ and $5.2\times {10}^{-10}{\mathrm{c}\mathrm{m}}^3{\mathrm{s}}^{-1}$ for the additive and nonadditive potentials, respectively. The large difference emphasizes the importance of using accurate potential energy surfaces for such calculations.

Figure 1

Cross sections from quantum reactive scattering calculations for $\mathrm{N}\mathrm{a}+{\mathrm{N}\mathrm{a}}_2$ ($v=1,j=0$) ($s$-wave scattering). Elastic and quenching results are shown as solid and dotted lines. (a) Additive potential. (b) Nonadditive potential.

Figure 2

Normalized rotational distributions for ${\mathrm{N}\mathrm{a}}_2$ products in $v^{\prime }=0$ following the quenching reaction $\mathrm{N}\mathrm{a}+{\mathrm{N}\mathrm{a}}_2(v=1,j=0)\to \mathrm{N}\mathrm{a}+\mathrm{N}{\mathrm{a}}_{\mathrm{2}}(v^{\prime }=0,j^{\prime )}$ at a collision energy of ${10}^{-4}\mathrm{K}$. (a) Additive potential. (b) Nonadditive potential.