Fourier transform method of calculating total cross sections using the time-dependent close-coupling theory

The calculation of total integral cross sections for electron-impact ionization of atoms and atomic ions has, in the last 8 years, greatly benefited from the development of several nonperturbative methods, which generally show very good agreement with each other and with experiment. For the electron-impact ionization of hydrogen, the convergent close-coupling @1#, the hyperspherical close-coupling @2#, the R-matrix with pseudostates @3#, the time-dependent closecoupling @4#, and the exterior complex scaling @5# methods yield results over a wide range of incident energies that are all within the error bars of the total cross section measurements of Shah et al. @6#. The convergent close-coupling, the R matrix with pseudostates, and the time-dependent closecoupling methods have been successfully used to calculate electron-impact direct ionization cross sections for many other atoms and their ions. The R-matrix with pseudostates method uses analytic functions and/or pseudo-orbitals obtained through diagonalization of the target Hamiltonian to represent the bound orbitals. The (N11)-electron Hamiltonian is then diagonalized and a total ionization cross section can be extracted via a simple analytic function involving the K matrix and the surface amplitudes. It is this diagonalization that forms the main computational aspect of this calculation. The resulting total ionization cross section contains unphysical pseudoresonances that oscillate about the true direct total cross section. This is due to the finite nature of the pseudostate expansion. Of course, since we know that the direct cross section must be smooth ~since it generally does not contain any resonance structure!, this oscillating function can be easily averaged to give the correct answer, which, in practice, works extremely well. The time-dependent close-coupling method usually only calculates the total cross section, at three or four points, since each energy point must be calculated separately. Again, this is satisfactory since, as the total cross section is a smooth function, one can easily draw a line through these points to obtain the cross section as a function of energy. The main requirement is to map out the peak of the cross section which then falls off asymptotically with incident electron energy. In this paper we describe a method that allows us to use the time-dependent close-coupling formalism to calculate total