Gaussian expansion methods under the absorbing boundary condition

Abstract

We have analyzed the applicability of the various Gaussian bases to the variational calculation under the absorbing boundary condition. Three kinds of Gaussian basis are investigated: shifted, tempered, and oscillating Gaussians. All the basis functions are successful in describing a resonance with a sharp width, but the features of the non-resonant continuum states are very different among the employed Gaussian bases. The energy eigenvalues calculated from the shifted Gaussian show the regular sequence in a complex energy plane, while the energy distribution obtained by the tempered and oscillating Gaussian deviates from the regular distribution. The wave functions in the non-resonant continuum are investigated for the individual Gaussian bases. The shifted Gaussian nicely describes the extensively oscillating feature over a wide spatial range, but the wave functions of the other two bases concentrate around the interaction area. The calculation of the shifted Gaussian and oscillating Gaussian largely reduces the errors contained in the resonance wave function. The trajectories of the resonance, obtained by a variation of the strength of the absorbing potential, are pursued in a complex energy plane. The resonance trajectories for the shifted and oscillating Gaussian bases become stationary around the optimal strength of the absorber, while such a stationary trajectory is not clearly observed in the calculation of the tempered Gaussian. An appropriate combination of the basis functions and the absorbing boundary condition is discussed. . . . . .