Exact solution of the nuclear pairing problem

Volya, Alexander; Brown, B. A.; Zelevinsky, Vladimir

doi:10.1016/s0370-2693(01)00431-2

Cited by 115 publications

(160 citation statements)

References 34 publications

(35 reference statements)

Supporting

Mentioning

157

Contrasting

Order By: Relevance

“…For instance, the multi-level pairing model with equally-spaced levels is of special interest for application to the spectra of superconducting grains [61]. Multi-level pairing models can also provide a foundation for realistic calculations with the nuclear shell model [62]. The models considered in the present work may be constructed as the "infinitelycoordinated" limit [49] of the Ising-type spin-lattice models, i.e., the limit in which all sites interact equally with all others by a long-range interaction.…”

Section: Discussionmentioning

confidence: 99%

Excited state quantum phase transitions in many-body systems

2008

View full text Add to dashboard Cite

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.

show abstract

Section: Discussionmentioning

confidence: 99%

Excited state quantum phase transitions in many-body systems

2008

View full text Add to dashboard Cite

show abstract

“…In the present paper we propose, for the very first time, a theoretical approach, which takes into account both the effects of exact thermal pairing and temperature-dependent resonance width. Within our approach, thermal pairing is treated based on the eigenvalues E S , obtained by diagonalizing the pairing Hamiltonian [21] …”

mentioning

confidence: 99%

Simultaneous Microscopic Description of Nuclear Level Density and Radiative Strength Function

2017

View full text Add to dashboard Cite

Nuclear level density (NLD) and radiative strength function (RSF) are described simultaneously within a microscopic approach, which takes into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for 170,171,172 Yb isotopes shows the importance of exact thermal pairing in the description of NLD at low and intermediate excitation energies and invalidates the assumption based on the Brink-Axel hypothesis in the description of the RSF. The rapid decrease in level spacing between the excited states as the excitation energy increases to several MeV leads to an exponential increase in the level densities and transition probabilities between the excited levels in the medium and heavy nuclei. In this condition it is impractical to deal with an individual state. Instead, it is meaningful and convenient to consider the average properties of nuclear excitations. Two main quantities, which are often employed to describe these properties, are the nuclear level density (NLD) and radiative γ-ray strength function (RSF). The NLD is defined as the number of excited levels per unit of excitation energy E * , whereas the RSF is the average transition probability per γ-ray energy E γ . The NLD provides the information on several properties of an atomic nucleus, namely the pairing correlations and nuclear thermodynamic properties such as temperature, entropy, heat capacity, etc. [1]. The RSF reveals the characteristics of average nuclear electromagnetic properties [2]. These two quantities have important contributions in the study of low-energy nuclear reactions and nuclear astrophysics such as the calculation of the stellar reaction rates and the description of nucleosynthesis in stars [3,4]. The study of NLD and RSF has therefore been one of the most important topics in nuclear structure physics. It became particularly attractive after the recent developments of the experimental technique proposed by Oslo's group (the Oslo method), which is able to extract simultaneously both NLD and RSF from the primary γ-decay spectrum of the residual compound nucleus created in the transfer and/or inelastic scattering reactions [5][6][7]. These experimental data also serve as a good testing ground for all the present theoretical approaches to NLD and RSF.Although the concepts of NLD and RSF are rather old [2,8], a unified theory, which can describe simultaneously and microscopically both the NLD and RSF is still absent so far. The NLD can be described quite well within the finite-temperature shell model quantum Monte-Carlo method [9], but this method is time consuming when it is applied to heavy nuclei. Regarding the γ-strength functions, which involve giant resonances and the related RSF, they are beyond the scope of this method. The Hartree-Fock BCS [10] and Hartree-FockBogolyubov plus combinatorial method (HFBC) [11] have provided a global description of NLD and might be consid...

show abstract

“…As a result, unphysical features are introduced into dynamics, the superfluid phase transition appears too sharp, and the correlational energy produced by pairing might be severely underestimated. As was shown earlier [4,5], the pairing part of the problem can be solved numerically quite easily with the help of the seniority representation in a spherical basis, and its exact solution significantly improves the results.…”

Section: Introductionmentioning

confidence: 70%

“…It was also sketched in [4] how other parts of the interaction can be incorporated into the exact pairing method in the approximate way that reminds the HF approach. This can be done in an iterative fashion: the exact pairing solution using the starting single-particle basis determines the actual occupation numbers; these (in general, fractional) occupancies self-consistently determine, in the HF spirit, an improved single-particle basis where we again solve the pairing problem etc.…”

Section: Introductionmentioning

confidence: 99%