The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross-sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross-sections are significantly suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross-sections for some ultracold collision processes will be much less sensitive to details of the potential than has been expected.
Collisions at ultracold temperatures between ${}^{1}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$-state diatomic polar molecules in a circularly polarized microwave field are theoretically analyzed. We demonstrate that elastic and inelastic collisions of polar molecules at ultracold temperatures are affected by an external microwave field and that they are enhanced at resonance frequencies. We show that the collision dynamics of polar molecules in a microwave field is largely determined by the long-range dipole-dipole interaction. Through this interaction, two polar molecules can resonantly exchange internal energy by undergoing a transition between neighboring rotational levels. This process may stabilize the system and enable the successive evaporative cooling of molecules. This paper discusses fermionic polar molecules at ultralow temperatures (1 $\ensuremath{\mu}$K).
Collisions of cold and ultracold BH in the ν = 0 level with the He atom are investigated using the quantum mechanical scattering formulation. The elastic and the inelastic cross sections are calculated using the two-dimensional ab initio potential energy surface. It is shown that the elastic cross section is larger than the inelastic one. When the collision energy is very low, the elastic cross section follows the Wigner threshold law and is one order of magnitude larger than that of He-O 2 , while it is much smaller than that of He-H 2 . The efficiency of the rotationally quenching state is given. The Δ j = −1 transition is most efficient. The resonances are also found to occur at about the same translational energy (0.1–1 cm −1 ), which gives rise to steps in the rate coefficient at temperatures around 0.1–1 K.
A theoretical study of the low-energy scattering properties of two aligned identical bosonic and fermionic dipoles in the presence of isotropic spin-orbit coupling is presented. A general treatment of particles with arbitrary (pseudo)spin is given in the framework of multichannel scattering. At ultracold temperatures and away from shape resonances or closed-channel dominated resonances, the cross section can be well described within the Born approximation to within corrections due to the
s-wave scattering. We compare our findings with numerical calculations and find excellent agreement.
We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, F\"orster resonance, or angular momentum exchange) exhibit a near-threshold scaling ${E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}}$, where
E is the collision energy, $\mathrm{\ensuremath{\Delta}}{m}_{12}={m}_{1}^{\ensuremath{'}}+{m}_{2}^{\ensuremath{'}}\ensuremath{-}{m}_{1}\ensuremath{-}{m}_{2}$, and
mi and ${m}_{i}^{\ensuremath{'}}$ are the initial and final angular momentum projections of the colliding species (
i=1,2). In particular, the inelastic cross sections for $\mathrm{\ensuremath{\Delta}}{m}_{12}=0$ transitions display an unconventional
E0 scaling similar to that of elastic cross sections, and their rates vanish as ${T}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\ensuremath{\sigma}}_{\text{inel}}\ensuremath{\propto}{E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1}$ if $\mathrm{\ensuremath{\Delta}}{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold
Rb+Rb and
O2+O2 collisions. Our results illustrate that the well-known ${k}^{\ensuremath{-}1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.