Gamow-Hartree-Fock-Bogoliubov method: Representation of quasiparticles with Berggren sets of wave functions

Single-particle resonant states, also called Gamow states, as well as bound and scattering states of complex energy form a complete set, the Berggren completeness relation. It is the building block of the recently introduced Gamow shell model, where weakly bound and resonant nuclear wave functions are expanded with a many-body basis of Slater determinants generated by this set of single-particle states. However, Gamow states have never been studied in the context of Hartree-Fock-Bogoliubov theory, except in the Bardeen-Cooper-Schriefer (BCS) approximation, where both the upper and lower components of a quasiparticle wave function are assumed to possess the same radial dependence with that of a Gamow state associated with the Hartree-Fock potential. Hence, an extension of the notion of Gamow state has to be effected in the domain of quasiparticles. It is shown theoretically and numerically that bound, resonant and scattering quasiparticles are well defined and form a complete set, by which bound Hartree-Fock-Bogoliubov ground states can be constructed. It is also shown that the Gamow-Hartree-Fock single-particle basis can be used to solve the Gamow-Hartree-Fock-Bogoliubov problem. As an illustration, the proposed method is applied to neutron-rich nickel isotopes close to the neutron drip-line.

Figure 1

Location of quasiparticle S-matrix poles and deformed complex contour $L^{+}$ of scattering quasiparticle states used in the Berggren completeness relation. Here, $\alpha =\sqrt{2m}/\hslash$.

Figure 2

Neutron densities ${\rho }_n$ both in normal (left-hand side) and logarithmic (right-hand side) scales. Results of the HFB/Box, GHFB/Coord., and GHFB/Config. calculations are displayed by solid, dashed, and dotted lines, respectively.

Figure 3

Same as Fig. 2 but for neutron pairing densities.