The time-dependent Hartree-Fock method within a Gauss-lobe basis and application to proton-He collisions

For the description of ion-atom collisions in the semiclassical approximation, the time-dependent Hartree-Fock (TDHF) method is used. The TDHF equations are solved by expanding the electron wavefunctions within a basic set of Gauss-lobe functions. In this basis the matrix elements of the TDHF Hamiltonian can be obtained analytically, even if translational factors are included. As an application, the authors calculate the excitation cross sections of the (1s2s)1S and (1s2p) 1P states of He in proton-He collisions.