Supersymmetric phase-equivalent potentials for atoms in intense laser fields

Our work tests the basic assumption of the single-active-electron approximation: that any model which reproduces the bound spectrum --- and ideally also the scattering properties --- should provide a good approximation to the entire multi- electron system. In particular, we use two distinct methods that reproduce the energetic properties of the original effective one-electron potential and still exactly remove the Pauli excluded states. The first is a close- coupling approach, and the second is a grid method that utilizes principles of supersymmetric quantum mechanics~[1] to create a phase- equivalent potential that removes the unwanted states and exactly reproduces the scattering phase shifts at all energies~[2]. Despite retaining all of the properties of the original effective potential, we find quantitative differences in the physical observables given by the two methods and discuss their origin. [1] E.~Witten, Nuc. Phys. B {\bf 188}, 513 (1981). [2] D.~Baye, Journal of Physics A {\bf 20}, 5529 (1987); R.~D.~Amado, Phys.~Rev.~A {\bf 37}, 2277 (1988); D.~Baye and J.~M.~Sparenberg, Phys.~Rev.~Lett. {\bf 73}, 2789 (1994); E.~Garrido, D.~V.~Fedorov, and A.~S.~Jensen, Nuc. Phys. A {\bf 650}, 247 (1999).