Comparison of quantum mechanical and semi-classical scattering amplitudes for the calculation of elastic collision kernels with Lennard-Jones intermolecular potentials

It is first shown that, for a non-degenerate two-level system, collision kernels Wαα'(v' → v) can be written, if v' ≠ v, as the integral of a simple function expressed in terms of the scattering amplitudes fα and fα', and containing no Dirac distribution. It is then recalled that the familiar expression of semi-classical small angle scattering amplitude for Van der Waals potentials can be expressed in terms of convenient dimensionless parameters and this function is numerically evaluated The quantum mechanical elastic scattering amplitudes are also calculated in the case of several Lennard-Jones systems and semi-classical and quantum results are compared. The validity of semi-classical scattering amplitudes in the calculation of collision kernels for Lennard-Jones potentials is discussed. A comparison between elastic collision kernels for diagonal and off-diagonal density matrix elements is finally given.