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arXiv:nucl-th/0302010 · Annals of Physics

Pair fluctuations in ultra-small Fermi systems within self-consistent RPA at finite temperature

Aleksej Nikolaevich Storozhenko, Peter Schuck, J. Dukelsky, GERD RÖPKE, A.I. Vdovin

Published Jun 30, 2003• 21 citations
arXivHTMLPDF
DOI
10.1016/s0003-4916(03)00095-2

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Study of nuclear structure by using many-body theory

Nguyễn Quang Hưng

Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.

•Jan 1, 2011•0 citations
The self-consistent random-phase approximation (SCRPA) is extended to nonzero temperature. Within the SCRPA, the collective dynamics of nucleon pairs is built on the occupation numbers that deviate from the Fermi-Dirac distribution as a result of temperature-dependent correlations beyond the RPA. The equations for single-particle occupation numbers are derived using the method of the double-time Green's functions. The approach is applied to the Richardson model of pairing. The results of numerical calculations for energies of states and occupation numbers, as well as for the thermodynamic quantities such as the excitation energy and heat capacity of the system, are compared with those obtained within the conventional RPA and the perturbative thermal SCRPA and with the exact results. We find that, overall, the SCRPA offers a better agreement with the exact results.
A self-consistent version of the thermal random phase approximation (TSCRPA) is developed within the Matsubara Green’s function formalism. The TSCRPA is applied to the many-level pairing model, and the normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the grand canonical ensemble. Advantages of the TSCRPA over the thermal mean-field approximation and the standard thermal random phase approximation are demonstrated. Results for correlation functions, excitation energies, etc., as a function of temperature are presented.
Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.