Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density-matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density-matrix and the pairing-tensor. The variation of this projected-energy is shown to result in HFB equations with modified express...

Using the Kadanoff-Baym non-equilibrium Green’s function formalism, we derive the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic equations and the associated equation of motion for the condensate wavefunction for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and Kadanoff (KK) for a uniform Bose gas. We include the off-diagonal (anomalous) pair corr...

We discuss two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear matter calculations, whereas in the second approach the local-density approximation is used to account for the effects of correlations. The results obtained by the two ...

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We present a 2-dimensional Hartree-Fock-Roothaan code to calculate wave functions and energies of light to heavy atoms in strong external magnetic fields, as they occur in the vicinity of neutron stars. The code enhances the previously presented HFFER II method, resulting in a very high precision for the energies with typical deviations less than 1% compared to the extremely precise fixed-phase...

A. Singular integration algorithm A convenient method for numerical evaluation of singular integrals is to introduce an auxiliary function in order to transform the argument of the numerical integral into a nonsingular argument. The complete result involves also evaluating the singular integral of the auxiliary function, which can be accomplished by using analytic or efficient numerical methods...