Bulletin of the Russian Academy of Sciences Physics

Spatial dependence of pair correlations (Nuclear scissors)

E. B. Balbutsev, L.A. Malov

Published Jun 1, 2010• 0 citations

Abstract

The solution of time dependent Hartree-Fock-Bogoliubov equations by the Wigner function moments method leads to the appearance of low lying modes whose description requires the accurate knowledge of the anomalous density matrix. It is shown, that calculations with the Woods Saxon potential satisfy to this requirement.

DOI: 10.3103/s1062873810060262

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Bulletin of the Russian Academy of Sciences Physics

Spatial dependence of pair correlations (Nuclear scissors)

E. B. Balbutsev, L.A. Malov

Published Jun 1, 2010• 0 citations

Publisher

Abstract

DOI: 10.3103/s1062873810060262

Related papers

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 +1 more

Physics of Particles and NucleiNov 1, 20100 citations

An a priori Quantized Time-Dependent Hartree-Bogoliubov Theory: A Generalization of the Schwinger Representation of Quasi-Spin to the Fermion-Pair Algebra

Masao Yamamura, Seiya Nishiyama

Progress of Theoretical PhysicsJul 1, 197622 citations

Extension of time-dependent Hartree-Fock-Bogoliubov equations

M. Tohyama, Peter Schuck

An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a pairing model and a fermion system trapped in a harmonic potential to test its feasibility by comparison with exact solutions. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a pairing model and a fermion system trapped in a harmonic potential to test its feasibility by comparison with exact solutions. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.

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A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian $H{\^{}}_{\mathrm{pair}}={\ensuremath{\sum}}_{\ensuremath{\alpha}\ensuremath{\beta}}{G}_{\ensuremath{\alpha}\ensuremath{\beta}}{c}_{\ensuremath{\alpha}}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}\ifmmode\bar\else\textasciimacron\fi{}}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}\ifmmode\bar\else\textasciimacron\fi{}}{c}_{\ensuremath{\beta}}$ with an arbitrary set of matrix elements ${G}_{\ensuremath{\alpha}\ensuremath{\beta}}.$ Symmetries of the Hamiltonians on the many-body level are discussed using the language of $\mathcal{P}$ symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of $\mathcal{P}$ symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to $p\ensuremath{\sim}40$ particles on $n\ensuremath{\sim}80$ levels and for several dozens of lowest lying states with precision $\ensuremath{\sim}$(1--2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority $s=0$ solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei.A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian $H{\^{}}_{\mathrm{pair}}={\ensuremath{\sum}}_{\ensuremath{\alpha}\ensuremath{\beta}}{G}_{\ensuremath{\alpha}\ensuremath{\beta}}{c}_{\ensuremath{\alpha}}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}\ifmmode\bar\else\textasciimacron\fi{}}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}\ifmmode\bar\else\textasciimacron\fi{}}{c}_{\ensuremath{\beta}}$ with an arbitrary set of matrix elements ${G}_{\ensuremath{\alpha}\ensuremath{\beta}}.$ Symmetries of the Hamiltonians on the many-body level are discussed using the language of $\mathcal{P}$ symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of $\mathcal{P}$ symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to $p\ensuremath{\sim}40$ particles on $n\ensuremath{\sim}80$ levels and for several dozens of lowest lying states with precision $\ensuremath{\sim}$(1--2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority $s=0$ solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei.

Physical Review COct 1, 199795 citations

\mathcal{P}

symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of

\mathcal{P}

symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to $p\ensuremath{\sim}40$ particles on $n\ensuremath{\sim}80$ levels and for several dozens of lowest lying states with precision $\ensuremath{\sim}$(1--2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority

s=0

solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei.