We review topics of current interest in the physics of electronic, atomic and molecular scattering in the vicinity of thresholds. Starting from phase space arguments, we discuss the modifications of the Wigner law that are required to deal with scattering by Coulomb, dipolar and dispersion potentials, as well as aspects of threshold behaviour observed in ultracold atomic collisions. We employ the tools of quantum defect and semiclassical theories to bring out the rich variety of threshold behaviours. The discussion is then turned to recent progress in understanding threshold behaviour of many-body break-ups into both charged and neutral species, including both Wannier double ionization and three-body recombination in ultracold gases. We emphasize the dominant role that hyperspherical coordinate methods have played in understanding these problems. We assess the effects of external fields on scattering, and the corresponding modification of phase space that alters the Wigner law. Threshold laws in low dimensions and examples of their applications to specific collision processes are discussed.

We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from universality are expected to occur in the intermediate energy range.

No abstract

No abstract

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 dipoledipole 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 univeral characteristics are predicted. PACS numbers: 34.50. Cx, 31.15.ap, 34.20 One might naturally expect that as dilute polar gases are cooled toward the absolute zero of temperature, a regime should emerge in which only the longest ranged forces -dipole-dipole interactions -are relevant; in which case these different polar gases would share a universal equation of state. Myriad theoretical models of ultracold dipolar gases, most based on mean-field theory, assume purely dipolar interactions between molecules, modified only by a short-ranged species-dependent contact potential. [6]. However, recent detailed calculations of ultracold molecular collisions show strong speciessensitive resonant characteristics of elastic scattering cross sections, and display universality only in the hightemperature regime of semi-classical collision dynamics [7].One purpose of this Letter is to demonstrate several universal characteristics of dipole-dipole collisions that will emerge at the lowest temperatures where collective phenomena associated with quantum degeneracy are expected [8]. Among these universal properties are: 1) an absolute minimum elastic scattering cross-section for zero-energy collisions of all bosonic dipoles; 2) a strong correlation between threshold angular distributions and the magnitude of threshold elastic scattering cross sections; 3) several sequences of threshold resonant states that can be tuned with an applied electric field; and 4) a set of effective barrier heights which retard threshold scattering in all but one elastic channel. These features are independent of short-range interactions between the molecular collision partners.The near-threshold resonances mentioned above have appeared in earlier calculations of RbCs and SrO scattering [9,10], and have also recently appeared in calculations of two molecules in a trap [11]. A second purpose of this Letter is to provide a complete classification and interpretation of these resonances.Many molecules possess polar charge distributions in their lowest electronic energy states. However, in the absence of external fields, as a consequence of parity conservation, even strongly "polar" molecules have no net dipole moment. Strong anisotropic molecular interactions therefore require an external electric field, E, coupling opposite parity states, and producing a fiel...