A modified Variable-Phase algorithm for multichannel scattering with long-range potentials

A new Variable-Phase (VP) algorithm for solving the close coupled equations of inelastic scattering in atom–molecule collisions driven by a strong long range potential is presented. The proposed method allows for a rigorous, gradual reduction of the number of closed channels during the outward propagation of the solution of the VP equations. In this way it allows a considerable saving of CPU time when dealing with strong, long-range potentials. A further saving of computational time is achieved by the use of a zero order effective potential in the reference problem which avoids the calculation of the computationally expensive Bessel functions. The K matrix version of the VP equations are solved with a standard Runge–Kutta integrator with adaptive step size. The low-energy, rotational excitation process in the LiH–H+ system is used to test the resulting algorithm and we show that the present method once applied to long-range interactions, can be orders of magnitude faster than the widely used, adaptive-step size LogDerivative/Airy propagator while keeping the same level of accuracy.