A comparison of three time-dependent wave packet methods for calculating electron–atom elastic scattering cross sections

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Abstract
We compare three time‐dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials. The three methods are the time‐dependent amplitude density method (TDADM), what we term a Cayley‐transform method (CTM), and the Chebyshev propagation method of Tal‐Ezer and Kosloff. Both the TDADM and the CTM are based on a time‐dependent integral equation for the wave function. In the first, we propagate the time‐dependent amplitude density, ‖ζ(t)〉=U‖ψ(t)〉, where U is the interaction potential and ‖ψ(t)〉 is the usual time‐dependent wave function. In the other two, the wave function is propagated. As a numerical example, we calculate phase shifts and cross sections using a screened Coulomb, Yukawa type potential over the range 200–1000 eV. One of the major advantages of time‐dependent methods such as these is that we get scattering information over this entire range of energies from one propagation. We find that in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l=0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy.