Abstract
We consider low energy threshold reactive collisions of particles interacting via a van der Waals potential at long range in the presence of external confinement and give analytic formulas for the confinement modified scattering in such circumstances. The reaction process is described in terms of the short range reaction probability. Quantum defect theory is used to express elastic and inelastic or reaction collision rates analytically in terms of two dimensionless parameters representing phase and reactivity. We discuss the modifications to Wigner threshold laws for quasi-one-dimensional and quasi-two-dimensional geometries. Confinement-induced resonances are suppressed due to reactions and are completely absent in the universal limit where the short-range loss probability approaches unity.
Highlights
Cold and ultracold molecular collisions are an important research topic for a number of reasons, as reviewed by [1, 2]
We present an analytic treatment of ultracold reactive collisions between particles interacting with an isotropic potential, such as S-state atoms or rotationless polar molecules in the absence of an external electric field, confined in a trap that effectively reduces the dimensionality of the system
We have given the analytical formulas in the near-threshold limit for the scattering lengths (Eqs. (24)(25) nad (41)-(42)) as well as elastic and reactive rate constants (Eqs. (30)-(33) nad (53)-(56)) for atomic or molecular species interacting by a long range van der Waals potential and undergoing inelastic loss or chemical reactions in the presence of strong confinement of the initial reactant species
Summary
Cold and ultracold molecular collisions are an important research topic for a number of reasons, as reviewed by [1, 2]. Such trapping potentials can result in confinement-induced resonances (CIR) [27, 28], which have been studied theoretically [29,30,31,32,33,34,35] and observed experimentally [36,37,38] Our theory extends these conventional treatments to give the proper energy-dependent complex scattering length that is needed to calculate such resonances accurately [23], including the effect of loss channels due to chemical reactions or inelastic collisions, if they be present.
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