Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

Figure 1

Illustrative drawing of the configuration space for ultracold $\mathrm{F}+{\mathrm{H}}_2\to \mathrm{HF}+\mathrm{H}$ reaction. The roman numeral I denotes the interaction region with the $\mathrm{F}–{\mathrm{H}}_2$ distance $R<R_2$, II denotes the asymptotic region with fewer open channels, and III labels the long-range region, where the wave packets are restricted to contain only one molecular state. The shaded regions show the absorption zones. The reactive flux is evaluated at the surface defined by $r=r_s$.

Figure 2

Probability of the chemical reaction $\mathrm{F}+{\mathrm{H}}_2(v=0,j=0)\to \mathrm{F}+\mathrm{HF}$ summed over all final states of the reaction products: full line, time-independent close coupling calculations; symbols, time-dependent wave packet calculations. The lower inset shows the low-energy reaction probabilities divided by the square root of the collision energy, illustrating the threshold behavior and the agreement of the two calculations in this limit. The upper inset shows the probability distribution of the reaction products versus $j^{\prime }$ for $v^{\prime }=2$ at collision energy $8\times {10}^{-3}{\mathrm{cm}}^{-1}$: TDWP, open bars; CC, full bars. The state-resolved probabilities are normalized by the total reaction probability.

Figure 3

Probability of the chemical reaction $\mathrm{F}+{\mathrm{H}}_2(v=0,j=1)\to \mathrm{F}+\mathrm{HF}$ summed over all final states of the reaction products: full line, time-independent close coupling calculations; symbols, time-dependent wave packet calculations. The inset shows an enhanced view of the low-energy part of the reaction probability.

Figure 4

Probability of the chemical reaction $\mathrm{F}+{\mathrm{H}}_2(v=1,j=2)\to \mathrm{F}+\mathrm{HF}$ summed over all final states of the reaction products: full line, time-independent close coupling calculations; symbols, time-dependent wave packet calculations. The calculations are for $J=0$, so the reaction probabilities shown are determined by $d$-wave scattering in the limit of ultralow collision energy.