Time‐dependent hartree–fock theory for atoms

The coupled and uncoupled versions of time‐dependent Hartree–Fock theory are presented. The theory provides a way of calculating the linear response of an atomic system to an external time‐dependent perturbation, and thence the Green's function. It is shown that the coupled version is equivalent to the Random Phase Approximation and that it contains correlation to at least first order, while the uncoupled version contains no correlation. The effect of the correlation included in the coupled version on the dipole spectrum of two electron systems is studied. This study is based on numerical solution of the equations for the dipole response of helium and lithium II. The coupled and uncoupled dipole spectra of helium and parts of these spectra of lithium II are given. Phase shifts for electron‐helium ion scattering are also given. Calculations for helium of long range forces, average excitation energies involved in the theory of range and straggling of fast charged particles and the Lamb shift, and the two photon decay spectrum and radiative lifetimes for the decay (1 s 2 s ) 1 S → (1 s 2 ) 1 S , are described. It is concluded that, for two electron systems, the correlation included in the coupled theory displaces rather too much dipole oscillator strength into the continuum (while maintaining the Thomas‐Kuhn sum rule) and overestimates exchange in the energy levels and low energy phase shifts, and that the coupled dipole spectrum is more accurate than the uncoupled one.