Symmetry-Projected Hartree-Fock-Bogoliubov Equations

Garching; Germany); Javid A. Sheikh; Peter Ring (Physik-Department; Technische Universitat Munchen

Symmetry-Projected Hartree-Fock-Bogoliubov Equations

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arxiv nucl-th/9907065 v1 pith:GYYM4WZ7 submitted 1999-07-16 nucl-th

Symmetry-Projected Hartree-Fock-Bogoliubov Equations

Javid A. Sheikh , Peter Ring (Physik-Department , Technische Universitat Munchen , Garching , Germany) This is my paper

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keywords equationsdensity-matrixderivedexpressionshartree-fock-bogoliubovprojected-energysymmetry-projectedansatz

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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 expressions for the pairing-potential and the Hartree-Fock field. The expressions for these quantities are explicitly derived for the case of particle number-projection. The numerical applicability of this projection method is studied in an exactly soluble model of a deformed single-j shell.

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