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Physics of Particles and Nuclei

Pair correlations and the time-dependent Hartree-Fock-Bogoliubov method in the theory of nuclear structure

V. V. Voronov, R. V. Jolos, N. N. Arsenyev, A. P. Severyukhin

Published Nov 1, 2010• 0 citations
Publisher

Abstract

It is shown that an idea of the superfluidity of nuclear matter and the u -v transformation of Bogoliubov, time-dependent Hartree-Fock-Bogoliubov method have made a strong impact on the development of the modern nuclear theory. Some applications of the Bogoliubov methods to describe properties of the low-lying collective nuclear states and the giant resonances are demonstrated.

DOI
10.1134/s1063779610060109

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It is shown that an idea of the superfluidity of nuclear matter and the u -v transformation of Bogoliubov, time-dependent Hartree-Fock-Bogoliubov method have made a strong impact on the development of the modern nuclear theory. Some applications of the Bogoliubov methods to describe properties of the low-lying collective nuclear states and the giant resonances are demonstrated.
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To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.
We present simple equations for a canonical-basis (Cb) formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of E1E1E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.
Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form.