Momentum distributions in time-dependent density-functional theory: Product-phase approximation for nonsequential double ionization in strong laser fields

We investigate the possibility to deduce momentum space properties from time-dependent density functional calculations. Electron and ion momentum distributions after double ionization of a model helium atom in a strong few-cycle laser pulse are studied. We show that, in this case, the choice of suitable functionals for the observables is considerably more important than the choice of the correlation potential in the time-dependent Kohn-Sham equations. By comparison with the solution of the time-dependent Schrödinger equation, the insufficiency of functionals neglecting electron correlation is demonstrated. We construct a functional of the Kohn-Sham orbitals, which in principle yields the exact momentum distributions of the electrons and the ion. The product-phase approximation is introduced, which reduces the problem of approximating this functional significantly.