A general ab initio and nonperturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or quasi-two-electron targets, is described. The field-free Hamiltonian and the dipole matrices are generated using a flexible $B$-spline $R$-matrix method. This numerical implementation enables us to construct term-dependent, nonorthogonal sets of one-electron orbitals for the bound and continuum electrons. The solution of the TDSE is propagated in time using the Arnoldi-Lanczos method, which does not require the diagonalization of any large matrices. The method is illustrated by an application to the multiphoton excitation and ionization of Ne atoms. Good agreement with $R$-matrix Floquet calculations for the generalized cross sections for two-photon ionization is achieved.

• Received 24 April 2007

DOI:https://doi.org/10.1103/PhysRevA.76.053411