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

Dielectric Formulation of the Nuclear Many-Body Problem

O Mitran

Published Jun 1, 1971• 0 citations
Publisher

Abstract

It is known in the case of an electron gas that the Coulomb force between electrons is screened due to the density variation around the electrons. In a similar way the force acting between nucleons in nuclear matter may be appreciably different from the free nucleon-nucleon interactions. The main theme of this thesis is to examine the "Screening" effect of the nuclear force. To this end, first the dielectric formulation of the theory of an electron gas is reviewed. Relationship among the chain-diagram approximation, the random phase approximation and the dieledtric formulation is discussed in detail. These techniques are then applied to nuclear matter taking the one-pion exchange potential as an example. It is found that the screening effect on the nuclear force in nuclear matter is indeed quite appreciable. The validity of the approximations is discussed.

DOI
10.71548/9510

Related papers

Nuclear matter as a Fermi liquid

Helmut Hofmann

Abstract This chapter discusses the significance of two body interactions to many-body properties, beginning with a schematic model showing the relevance of short-range correlations beyond those of the Fermi gas. These correlations are studied within Brueckner theory and the help of the Bethe-Goldstone equation, mainly for nuclear matter proper but extensions to finite temperature are presented. Effective forces of Skyrme type are derived through an expansion of the G-matrix to small relative momenta. This scheme hinges essentially on the Brueckner-Hartree-Fock approximation, for which results for binding energy and equilibrium density are presented. An alternative variational method based on Jastrow functions is sketched, which demonstrates the necessity for considering effective three body forces. The concept of the nuclear equation of state is presented and parameterized by Skyrme forces with density dependent parameters. Finally, a semi-classical transport theory is presented which accounts for statistical collisions of the nucleons.

•Apr 17, 2008•0 citations

Self-Consistent Pair Interaction for Many-Fermion System

K. Sawada, Toshio Soda

The equations which determine the one-particle energy and effective two-body interaction in an interacting Fermi gas are constructed within the approximation which sums up all pair creation-annihilation processes. The equation corresponds to the familiar equation for the $K$ matrix which represents the interaction between particles (or holes) and sums up the particle-particle (or hole-hole) scattering processes. The method of the equation of motion is used in this paper. Our result for the one-particle energy is shown to lead to the result previously obtained by Quinn and Ferrell, and by Rockmore for the case of the electron gas with Coulomb interactions, when we replace screened potentials by bare potential in the self-consistent energy equation. For nuclear matter, it is shown that the presence of an attractive interaction in the equation of motion for number density causes an "enhancement" of exchange forces, whereas in the electron gas repulsive Coulomb interactions lead to "screening" of the exchange force. The strength of the isospin density interaction pseudopotential is enhanced by a factor of two when one solves the self-consistent equation; and a simple estimate shows that the Goldhaber-Teller mode lies about 15% higher than the value $\frac{{p}_{F}q}{m}$ previously estimated by Glassgold et al. ($q$: momentum of the oscillation, ${p}_{F}$: Fermi momentum).

Physical Review•Aug 15, 1961•1 citation

Retarded Interactions in Fermi Systems. II. Quasiparticle Lifetimes

C. B. Dover, Richard H. Lemmer

Properties of the inverse lifetime $\frac{1}{\ensuremath{\tau}}$ of quasiparticles in an infinite system of nucleons ("nuclear matter") interacting via the exchange of a neutral scalar boson are studied in the dielectric formulation of the many-body problem. It is shown that the polarization of the nuclear medium plays an essential role in determining $\frac{1}{\ensuremath{\tau}}$. The presence of the medium mediates the interaction between two nucleons in it through the introduction of an effective "dielectric constant" for nuclear matter. The interaction becomes "dressed" in a fashion analogous to, but different in its details from, the screening of the Coulomb interaction between electrons in metals. Calculations of $\frac{1}{\ensuremath{\tau}}$ are made for nuclear matter both in second-order perturbation theory, and using the fully dressed interaction calculated in the random-phase approximation (RPA). The RPA estimate is lower by about a factor of 3 over a wide range of momenta and is in good agreement with empirical optical-model estimates of $\frac{1}{\ensuremath{\tau}}$. The second-order perturbation estimate is by contrast entirely inadequate, emphasizing the importance of taking the polarization effects into account for scattering processes at actual nuclear densities. The use of a dielectric constant for the medium also introduces another feature into the properties of $\frac{1}{\ensuremath{\tau}}$. The behavior of $\frac{1}{\ensuremath{\tau}}$ near the Fermi surface now becomes sensitive to whether or not the interacting ground state is unstable with respect to a permanent density fluctuation. If it is, then $\frac{1}{\ensuremath{\tau}}$ behaves like ($p\ensuremath{-}{p}_{F}$) instead of ${(p\ensuremath{-}{p}_{F})}^{2}$ near the Fermi surface (${p}_{F}$ is the Fermi momentum). This is not a new physical result, but rather a reflection of the inadequacy of the RPA if the system becomes unstable. It is shown that as the momentum increases the effect of such an instability, if present, decreases, and becomes entirely negligible when $p\ensuremath{\gtrsim}\sqrt{2}{p}_{F}$.

Physical Review•Jul 20, 1969•14 citations

Realistic and effective interactions in the study of nuclear matter

V. Somà

The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced

•Jan 1, 2006•0 citations

Many Body Problems and Quantum Field Theory: An Introduction

Michel Baranger

The book gives an introduction to the concepts and methods of many-body problems and quantum fields for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is put on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas in different domains of physics. The exposition is self-contained and displays in a coherent way all details of derivations starting from a basic knowledge of quantum mechanics and classical electromagnetism.

•Dec 6, 2001•30 citations

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
It is known in the case of an electron gas that the Coulomb force between electrons is screened due to the density variation around the electrons. In a similar way the force acting between nucleons in nuclear matter may be appreciably different from the free nucleon-nucleon interactions. The main theme of this thesis is to examine the "Screening" effect of the nuclear force. To this end, first the dielectric formulation of the theory of an electron gas is reviewed. Relationship among the chain-diagram approximation, the random phase approximation and the dieledtric formulation is discussed in detail. These techniques are then applied to nuclear matter taking the one-pion exchange potential as an example. It is found that the screening effect on the nuclear force in nuclear matter is indeed quite appreciable. The validity of the approximations is discussed.
Abstract This chapter discusses the significance of two body interactions to many-body properties, beginning with a schematic model showing the relevance of short-range correlations beyond those of the Fermi gas. These correlations are studied within Brueckner theory and the help of the Bethe-Goldstone equation, mainly for nuclear matter proper but extensions to finite temperature are presented. Effective forces of Skyrme type are derived through an expansion of the G-matrix to small relative momenta. This scheme hinges essentially on the Brueckner-Hartree-Fock approximation, for which results for binding energy and equilibrium density are presented. An alternative variational method based on Jastrow functions is sketched, which demonstrates the necessity for considering effective three body forces. The concept of the nuclear equation of state is presented and parameterized by Skyrme forces with density dependent parameters. Finally, a semi-classical transport theory is presented which accounts for statistical collisions of the nucleons.
The equations which determine the one-particle energy and effective two-body interaction in an interacting Fermi gas are constructed within the approximation which sums up all pair creation-annihilation processes. The equation corresponds to the familiar equation for the KKK matrix which represents the interaction between particles (or holes) and sums up the particle-particle (or hole-hole) scattering processes. The method of the equation of motion is used in this paper. Our result for the one-particle energy is shown to lead to the result previously obtained by Quinn and Ferrell, and by Rockmore for the case of the electron gas with Coulomb interactions, when we replace screened potentials by bare potential in the self-consistent energy equation. For nuclear matter, it is shown that the presence of an attractive interaction in the equation of motion for number density causes an "enhancement" of exchange forces, whereas in the electron gas repulsive Coulomb interactions lead to "screening" of the exchange force. The strength of the isospin density interaction pseudopotential is enhanced by a factor of two when one solves the self-consistent equation; and a simple estimate shows that the Goldhaber-Teller mode lies about 15% higher than the value pFqm\frac{{p}_{F}q}{m}mpF​q​ previously estimated by Glassgold et al. (qqq: momentum of the oscillation, pF{p}_{F}pF​: Fermi momentum).
Properties of the inverse lifetime $\frac{1}{\ensuremath{\tau}}$ of quasiparticles in an infinite system of nucleons ("nuclear matter") interacting via the exchange of a neutral scalar boson are studied in the dielectric formulation of the many-body problem. It is shown that the polarization of the nuclear medium plays an essential role in determining $\frac{1}{\ensuremath{\tau}}$. The presence of the medium mediates the interaction between two nucleons in it through the introduction of an effective "dielectric constant" for nuclear matter. The interaction becomes "dressed" in a fashion analogous to, but different in its details from, the screening of the Coulomb interaction between electrons in metals. Calculations of $\frac{1}{\ensuremath{\tau}}$ are made for nuclear matter both in second-order perturbation theory, and using the fully dressed interaction calculated in the random-phase approximation (RPA). The RPA estimate is lower by about a factor of 3 over a wide range of momenta and is in good agreement with empirical optical-model estimates of $\frac{1}{\ensuremath{\tau}}$. The second-order perturbation estimate is by contrast entirely inadequate, emphasizing the importance of taking the polarization effects into account for scattering processes at actual nuclear densities. The use of a dielectric constant for the medium also introduces another feature into the properties of $\frac{1}{\ensuremath{\tau}}$. The behavior of $\frac{1}{\ensuremath{\tau}}$ near the Fermi surface now becomes sensitive to whether or not the interacting ground state is unstable with respect to a permanent density fluctuation. If it is, then $\frac{1}{\ensuremath{\tau}}$ behaves like ($p\ensuremath{-}{p}_{F}$) instead of ${(p\ensuremath{-}{p}_{F})}^{2}$ near the Fermi surface (pF{p}_{F}pF​ is the Fermi momentum). This is not a new physical result, but rather a reflection of the inadequacy of the RPA if the system becomes unstable. It is shown that as the momentum increases the effect of such an instability, if present, decreases, and becomes entirely negligible when $p\ensuremath{\gtrsim}\sqrt{2}{p}_{F}$.
The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced
The book gives an introduction to the concepts and methods of many-body problems and quantum fields for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is put on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas in different domains of physics. The exposition is self-contained and displays in a coherent way all details of derivations starting from a basic knowledge of quantum mechanics and classical electromagnetism.
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.