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arXiv:1407.8030 · Physical Review A

Quantum-defect model of a reactive collision at finite temperature

Krzysztof Jachymski, Michał Krych, Paul S. Julienne, Zbigniew Idziaszek

Published Oct 10, 2014• 25 citations
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Abstract

We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum-defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary collision energy, and use it to analyze the elastic and reactive collision rates. Our theory is applicable for both universal and nonuniversal collisions. The former corresponds to the unit reaction probability at short range, while in the latter case the reaction probability is smaller than one. In the high-energy limit we present a method that allows us to incorporate quantum corrections to the classical reaction rate due to the shape resonances and the quantum tunneling.

DOI
10.1103/physreva.90.042705

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While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. Using multichannel quantum-defect theory, we derive a multichannel expression for the Smith lifetime QQQ matrix that is valid far away from scattering resonances. For collisions mediated by short-range interaction potentials of the form $\ensuremath{-}{C}_{6}/{R}^{6}$, we obtain the average time delay in the incident sss-wave collision channel in the limit of zero collision energy EEE as Q11=A/E+B{Q}_{11}=A/\sqrt{E}+BQ11​=A/E​+B, where AAA and BBB are constants. We show that the time delay is dominated by elastic scattering and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the SSS matrix and shortens with increasing the short-range loss parameter yyy.
We investigate collisions of polar molecules in quasi-2D traps in the presence of an external electric field perpendicular to the collision plane. We use the quantum-defect model characterized by two dimensionless parameters: yyy and sss. The first of them is related to the probability of the reaction at short distances, whereas the latter one defines the wave function phase at short distances. For yyy close to unity we obtain universal collision rates determined by the quantum reflection process from the long-range part of the interaction potential that depends only on the van der Waals coefficient, dipole-dipole interaction and the trap frequency. For small short-range reaction probabilities collision rates are highly nonuniversal and trap induced shape resonances are visible. For high dipole moments we observe the damping of reactive collisions, which can stabilize the ultracold gas of polar molecules. The calculations were performed with help of multichannel wave funcion propagation by imposing short-range boundary condition derived from the quantum-defect model.
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