Regular and singular integrals for relativistic and QED matrixelements of the Coulomb three-body problem, for an exponential basis set

Abstract

A general scheme is given for evaluating various matrix elementsrelated to relativistic and QED corrections for theSchrödinger Hamiltonian within a variational approach. Thenonrelativistic wavefunction is expanded using an exponentialbasis set of the Slater type for states of arbitrary angularmomentum, where the rotational symmetry is expanded in terms ofbipolar harmonics. Special emphasis is placed on numericalimplementation of the algorithms described.