Time-dependent lattice methods in both Cartesian and cylindrical coordinates are applied to calculate excitation cross sections for $p+\mathrm{H}$ collisions at $40\mathrm{keV}$ incident energy. The time-dependent Schrödinger equation is solved using a previously formulated Cartesian coordinate single-channel method on a full 3D lattice and a newly formulated cylindrical coordinate multichannel method on a set of coupled 2D lattices. Cartesian coordinate single-channel and cylindrical coordinate five-channel calculations are found to be in reasonable agreement for excitation cross sections from the $1s$ ground state to the $2s$, $2p$, $3s$, $3p$, and $3d$ excited states. For extension of the time-dependent lattice method to handle the two electron dynamics found in $p+\mathrm{He}$ collisions, the cylindrical coordinate multichannel method appears promising due to the reduced dimensionality of its lattice.

• Received 28 September 2007

DOI:https://doi.org/10.1103/PhysRevA.77.014701