A general approach to few-cycle laser interactions with complex atoms

We are developing a general method to solve the time-dependent Schr\"odinger equation for the interaction of a strong laser pulse with a general atom, i.e., beyond the models of quasi-one or quasi-two-electron targets. The field-free hamiltonian matrices are generated in a $B$-spline $R$-matrix method~[1], and the laser field is coupled in through dipole matrices generated with the same program. The major advantages of our approach are i)~its generality and ii)~the possibility of generating highly accurate target descriptions with small configuration interaction expansions. We propagate the solution of the TDSE by the Arnoldi method~[2]. The generalized eigenvalue problem is transformed by diagonalizing the overlap matrix~$S$ of the non-orthogonal basis functions and generating new field-free hamiltonian and dipole matrix blocks through $ H' = S^{-1/2} H S^{-1/2}$ and $D' = S^{-1/2} DS^{-1/2}.$ Details of various numerical implementations will be discussed. \par\vspace{0.1truecm}\noindent [1] O.~Zatsarinny, Comp. Phys. Commun. {\bf 174}, 273 (2006). \par\noindent [2] T.J.~Park and J.C.~Light, J. Chem. Phys. {\bf 85}, 5870 (1986).