Apply the VDPC algorithm to the constraint Hatree–Fock theory: In the BCS case

Abstract

L. Y. Jia recently proposed an algorithm that applies the variational method directly to coherent-pair condensates (VDPC) [L. Jia, Phys. Rev. C (2019).] Now I’ll make changes to the VDPC algorithm that applies it to the Constraint Hatree–Fock theory. I derived expressions of the mean energy extremum with linear constraints and the analytic form of the Lagrangian multiplier. In addition, I acquire an angle through the inverse tangent of the energy minimum to the electric quadrupole moment in Fig. 3, which describes the unconstrained energy under an equivalent rotating system. I demonstrate the new algorithm in a semirealistic example using the realistic [Formula: see text] interaction in the large model spaces (up to 15 harmonic-oscillator major shells). In this work, I am interested in a wave function [Formula: see text], which minimizes the total energy under the constraint that has a fixed expectation [Formula: see text]. I graphed the results as just an energy extreme versus electric quadrupole moment graph. The result shows that Fig. 3 is similar to Fig. 7.2 in [P. Ring and P. Schuck, The Nuclear Many-body Problem (Springer Science & Business Media, 2004)].