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A. A. Buchachenko

Numerical method for quantum capture probabilities with applications to ultracold molecular collisions


The simple numerical method proposed by Truhlar and Kuppermann [J. Am. Chem. Soc. 1971. 93, P. 1840] for tunneling problem is adapted for quantum capture probability calculations in the barrierless molecular processes by imposing absorbing boundary conditions in the short-range region. It is found that phase uncertainty inherent to the singular potential problem arising from the continuation of the long-range potentials to short distances manifests itself in the oscillatory dependence of the transmission coefficient on the distance where the boundary condition is applied. Such a behavior permits one the simple stabilization of the results by taking the mean transmission coefficient. The method is tested for KRb + KRb reactions and K2 + K vibrational relaxation at ultralow temperatures using the model dispersion and ab initio-based adiabatic channel potentials. Good agreement is found with the analytical models developed for solving the singular problem close to the Bethe-Wigner threshold and, within the accuracy of capture approximation, with the rigorous quantum scattering calculations.
Key words: Barrierless reactions, capture approximation, statistical adiabatic channel model, ultracold chemistry
Moscow University Chemistry Bulletin.
2012, Vol. 53, No. 4, P. 219

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