Time dependent integral equation approaches to quantum scattering: Comparative application to atom–rigid rotor multichannel scattering

In this paper we generalize earlier work on potential scattering to atom–rigid rotor scattering. We compare six approaches including the interaction picture, modified Cayley, amplitude density, and symmetric split operator methods. All methods derive from the integral equation form of the time-dependent Schrödinger equation. The methods were tested using the standard Lester–Bernstein model potential. All methods were found to perform well with the same parameters. Fast Fourier transforms were not used in these methods, and an average execution time for a 16 channel problem on CRAY YMP supercomputer was about 45 s. This single calculation yields results at any energy significantly contained in the initial packet. In the present study, the S matrix was computed at a total of 42 energies, but results could have been obtained at many more energies without a large increase in computing time. Timing results for one of the methods are reported for 25, 64, 144, and 256 coupled channels.