Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Statistical description of compound states of nuclei

G.G. Bunatyan

Published Nov 1, 1977• 2 citations
OpenAlex

Abstract

A systematic development of the theory of finite Fermi systems for non-zero temperatures (Tnot =0) is undertaken on the basis of the method of temperature Green's functions. The properties of compound nuclear states are considered. The variations of the density matrix deltarho, the self-energy part delta..sigma.., the mean square radius delta , the quadrupole moment delta, etc, are studied in a transition from the ground state (T=0) to an excited state with temperature T. The relationship connecting the excitation energy with temperature is obtained. Consistently taken into account is the strong interaction of the nucleons, in particular, the change in the one-particle nuclear potential as the temperature T is varied. Qualitative quasi-classical estimates are given for the effects considered, and the limits on the applicability of the statistical description of nuclei at large T are discussed.

Related papers

Green’s Functions

John W. Negele, Henri Orland

This chapter describes the salient properties of zero-temperature, real-time finite temperature, and thermal Green's functions in turn. It considers the effect of the energy and momentum dependence of the self-energy on quasiparticle propagation in an interacting Fermi system. The chapter illustrates the major points for the case of a nucleon in translationally invariant nuclear matter. Although Green's functions were introduced because of their physical connection to response functions, they contain sufficient information to evaluate all ground state observables or thermal averages. The real-time Green's function, which describes the physical response of a system, may thereby, be obtained from the thermal Green's function. The essential point in relating the optical potential to the self-energy is the observation that the wave function can be written in terms of the one-particle Green's function. A good approximation to the response may be obtained using the response function for a non-interacting Fermi gas corrected for the medium dependence of the nucleon self-energy.

CRC Press eBooks•Mar 5, 2018•0 citations

The self-consistent field model for Fermi systems with account of three-body interactions

Poluektov, A. A. Soroka, S.N. Shulga

On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained.It is shown that the delta-like three-body interaction gives no contribution into the selfconsistent field, and the description of three-body forces requires their nonlocality to be taken into account.The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces.The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature.Expansions of the effective mass and pressure in powers of density are obtained.It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass.The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction.The quasiparticle energy spectrum is calculated with account of three-body forces.

arXiv:1503.02428•Condensed Matter Physics•Dec 1, 2015•1 citation

Deuterization and Mott density in nuclear matter at finite temperatures

G. Roepke, M. Schlauges, D. Kremp +2 more

The theory of the thermodynamic properties of nuclear matter at finite temperatures is developed on the basis of thermodynamic Green functions for a system of interacting nucleons. The influence of the surrounding nuclear matter on the two-nucleon system leads to a weakening of the effective nucleon-nucleon interaction and at the Mott density, which depends on the temperature and total momentum of the two-nucleon system, the bound state disappears. The deuteron degree of association and the phase diagram of nuclear matter are discussed.

•Sep 1, 1982•0 citations

MEAN-FIELD THEORIES WITH MIXED STATES

João da Providência, Carlos Fiolhais

A variational derivation of the Liouville-von Neumann equation of quantum-statistical mechanics is presented, in order to formulate mean~field approximations appropriate to mixed states. The Hartree-Fock and the RPA at finite temperatures are particular cases of the general formalism. A thennal boson expansion is defined, which allows us to describe anhannonic motion around a thennal excited state. In a numerical application on the basis of the Lipkin model, temperature-dependent phase transitions are observed. I. Introduction Studies of the decay of the compound nuclei formed in heavy-ion reactions have added a new dimension to the field of nuclear structure. The temperature of the compound nucleus at a given excitation energy rises from zero at the yrast state to a few MeV at angular momentum zero. Recently the decay of high-excited states above the yrast line, like the giant dipole resonance, has been observed 1,2). These measurements were carried out making use of sum-spectrometer multiplicity techniques, thus allowing to determine the average angular momentum of the system and from this knowledge the temperature of the nucleus. One can then study experimentally the nuclear structure at finite values of both the angular momentum and temperature, and the corresponding theoretical analysis of giant resonances above thermal excited states is now the object of intensive research 3-7). On the other hand, the observation of deep-inelastic reactions has been an important sourCe of information on the behaviour of nuclei under strong external fields. In these reactions the two interacting ions emerge after the collision with approximatley the same charge and mass, but having lost a large fraction of the energy and angular momentum of relative motion they had in the entrance channel (cf. e.g. ref. 8) and references therein). Different mechanisms play a role in these reactions, like the transfer of particles and the excitation of giant resonances (cf. ref. 9) and references therein). Because these vibrations have a damping width the energy and angular momentum absorbed through them into the nuclei lead to a finite temperature and to rigid rotation. This

•Jan 1, 1985•0 citations

Statistical theory of finite Fermi systems with chaotic excited eigenstates

V. V. Flambaum, G. F. Gribakin

A theory of strongly interacting Fermi systems of a few particles is developed. At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual two-body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variables such as temperature in an isolated microscopic Fermi system of a few particles.

Philosophical Magazine B•Dec 1, 2000•13 citations

Statistical theory of finite Fermi systems with chaotic excited eigenstates

G. F. Gribakin V.V. Flambaum

A theory of strongly interacting Fermi systems of a few particles is developed.At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual twobody interaction.This regime can be described as many-body quantum chaos.Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy.Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g.rare earths) and multicharged ions, molecules, clusters and quantum dots in solids.The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis.A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix.We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variables such as temperature in an isolated microscopic Fermi system of a few particles.

Philosophical Magazine B•Dec 11, 2000•0 citations
A systematic development of the theory of finite Fermi systems for non-zero temperatures (Tnot =0) is undertaken on the basis of the method of temperature Green's functions. The properties of compound nuclear states are considered. The variations of the density matrix deltarho, the self-energy part delta..sigma.., the mean square radius delta , the quadrupole moment delta, etc, are studied in a transition from the ground state (T=0) to an excited state with temperature T. The relationship connecting the excitation energy with temperature is obtained. Consistently taken into account is the strong interaction of the nucleons, in particular, the change in the one-particle nuclear potential as the temperature T is varied. Qualitative quasi-classical estimates are given for the effects considered, and the limits on the applicability of the statistical description of nuclei at large T are discussed.
This chapter describes the salient properties of zero-temperature, real-time finite temperature, and thermal Green's functions in turn. It considers the effect of the energy and momentum dependence of the self-energy on quasiparticle propagation in an interacting Fermi system. The chapter illustrates the major points for the case of a nucleon in translationally invariant nuclear matter. Although Green's functions were introduced because of their physical connection to response functions, they contain sufficient information to evaluate all ground state observables or thermal averages. The real-time Green's function, which describes the physical response of a system, may thereby, be obtained from the thermal Green's function. The essential point in relating the optical potential to the self-energy is the observation that the wave function can be written in terms of the one-particle Green's function. A good approximation to the response may be obtained using the response function for a non-interacting Fermi gas corrected for the medium dependence of the nucleon self-energy.
On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained.It is shown that the delta-like three-body interaction gives no contribution into the selfconsistent field, and the description of three-body forces requires their nonlocality to be taken into account.The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces.The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature.Expansions of the effective mass and pressure in powers of density are obtained.It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass.The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction.The quasiparticle energy spectrum is calculated with account of three-body forces.
The theory of the thermodynamic properties of nuclear matter at finite temperatures is developed on the basis of thermodynamic Green functions for a system of interacting nucleons. The influence of the surrounding nuclear matter on the two-nucleon system leads to a weakening of the effective nucleon-nucleon interaction and at the Mott density, which depends on the temperature and total momentum of the two-nucleon system, the bound state disappears. The deuteron degree of association and the phase diagram of nuclear matter are discussed.
A variational derivation of the Liouville-von Neumann equation of quantum-statistical mechanics is presented, in order to formulate mean~field approximations appropriate to mixed states. The Hartree-Fock and the RPA at finite temperatures are particular cases of the general formalism. A thennal boson expansion is defined, which allows us to describe anhannonic motion around a thennal excited state. In a numerical application on the basis of the Lipkin model, temperature-dependent phase transitions are observed. I. Introduction Studies of the decay of the compound nuclei formed in heavy-ion reactions have added a new dimension to the field of nuclear structure. The temperature of the compound nucleus at a given excitation energy rises from zero at the yrast state to a few MeV at angular momentum zero. Recently the decay of high-excited states above the yrast line, like the giant dipole resonance, has been observed 1,2). These measurements were carried out making use of sum-spectrometer multiplicity techniques, thus allowing to determine the average angular momentum of the system and from this knowledge the temperature of the nucleus. One can then study experimentally the nuclear structure at finite values of both the angular momentum and temperature, and the corresponding theoretical analysis of giant resonances above thermal excited states is now the object of intensive research 3-7). On the other hand, the observation of deep-inelastic reactions has been an important sourCe of information on the behaviour of nuclei under strong external fields. In these reactions the two interacting ions emerge after the collision with approximatley the same charge and mass, but having lost a large fraction of the energy and angular momentum of relative motion they had in the entrance channel (cf. e.g. ref. 8) and references therein). Different mechanisms play a role in these reactions, like the transfer of particles and the excitation of giant resonances (cf. ref. 9) and references therein). Because these vibrations have a damping width the energy and angular momentum absorbed through them into the nuclei lead to a finite temperature and to rigid rotation. This
A theory of strongly interacting Fermi systems of a few particles is developed. At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual two-body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variables such as temperature in an isolated microscopic Fermi system of a few particles.
A theory of strongly interacting Fermi systems of a few particles is developed.At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual twobody interaction.This regime can be described as many-body quantum chaos.Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy.Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g.rare earths) and multicharged ions, molecules, clusters and quantum dots in solids.The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis.A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix.We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variables such as temperature in an isolated microscopic Fermi system of a few particles.