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

Physical Review C

Finite velocity meson exchange in nuclei

Michael A. Crecca, G. E. Walker

Published Apr 1, 1991• 2 citations
Publisher

Abstract

Many-body techniques are used to develop a practical formalism for including an energy-transfer dependence in the nucleon-nucleon interaction used in nuclear linear response models. An energy-transfer dependence is naturally expected from the exchange of finite mass, finite velocity mesons. The formalism is applied in a Tamm-Dancoff approximation model structure calculation for $^{16}\mathrm{O}$. The importance of meson retardation effects on the structure calculation is studied as a function of the magnitude of unperturbed particle-hole energies. The relative importance of ring and ladder contributions is also investigated. It is found that retardation effects can become qualitatively important when particle-hole energies are comparable to the mass of the exchanged meson as would be the case for ${\mathit{N}}^{\mathrm{*}}$ particle-nucleon hole configurations. While ladder kernels exhibit a significant energy-transfer dependence, the actual results obtained including retardation when solving for the ladder polarization propagator follow closely the results obtained using an instantaneous ladder kernel. This result suggests a simple procedure for including retardation effects.

DOI
10.1103/physrevc.43.1709

Related papers

Relativistic many-body theory of finite nuclei and the Schwinger-Dyson formalism

Masahiro Nakano, Akira Hasegawa

A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green's functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as c-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka et al.$---- The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states in a systematic way.

Physical Review C•Feb 1, 1991•6 citations

Linearized Many-Body Problem

Nobuyuki Fukuda, Fumiaki Iwamoto, K. Sawada

The theory of an electron gas at high density is generalized so as to include the exchange scattering of a particle and hole in the singlet as well as in the triplet spin state. This approximation is the maximum possible linearization of a quantum-mechanical many-body problem, and corresponds to the theory of small-amplitude oscillations of a classical many-body system. The linearized Hamiltonian is that of Wentzel's meson pair theory, in which now two kinds of mesons are involved, one with spin zero corresponding to the singlet state of a particle and hole and the other with spin one corresponding to the triplet state. The correlation energy is shown to be the sum of the change in zero-point energies of the two-meson fields with correction only in the second-order term. The theory is then formulated in terms of Green's function, and it is proved explicitly that the linearized theory (or the random-phase approximation with exchange effects taken into account) is equivalent to the "ladder approximation" for the particle-hole scattering. The particle-particle scattering by means of the screened interaction is also discussed. The case of the $\ensuremath{\delta}$-function potential is explicitly solved, and it is shown that the correlation energy becomes complex in the region where the instability of the paramagnetic state occurs.

Physical Review•Aug 17, 1964•75 citations

Toward an accurate strongly coupled many-body theory within the equation-of-motion framework

Елена Литвинова, Peter Schuck

Nonperturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with nonperturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons ($2\mathrm{q}\ensuremath{\bigotimes}2\mathrm{phonon}$), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of $^{42,48}\mathrm{Ca}$ and $^{68}\mathrm{Ni}$ nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.

arXiv:1908.05384•Physical Review C•Dec 24, 2019•45 citations

Stochastic solution of a model meson-nucleon field theory

Brian D. Serot, S. E. Koonin, John W. Negele

Ground-state properties in a model quantum field theory are calculated by stochastic evaluation of a path integral representation of the many-body propagator. The model consists of nonrelativistic nucleons coupled to vector and scalar mesons in one spatial dimension. Binding energies and density distributions are calculated for bound states of up to twenty nucleons. The binding energy as a function of density, the nucleon-nucleon correlation function, and the meson-meson correlation function are evaluated in nuclear matter. Exact ground-state solutions to the full field theory are shown to differ relatively little from those of the potential theory corresponding to the static limit. The exact solutions differ substantially from those of the mean-field (Hartree) approximation, but are quite similar to those obtained in the Hartree-Fock approximation.NUCLEAR STRUCTURE Meson-nucleon field theory. Monte Carlo solution. Nuclear matter.

Physical Review C•Oct 1, 1983•11 citations

Effective interactions and the nuclear shell-model

D. J. Dean, T. Engel, Morten Hjorth-Jensen +2 more

This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

•Jan 1, 2004•44 citations

SOME CONSEQUENCES OF DRESSING NUCLEONS

Chris Gearhart, Willem H Dickhoff, A. Polls +1 more

A representation of nucleon spectral functions in nuclear matter is developed. Various contributions are identified including a quasiparticle term, broad background contributions below and above the Fermi energy, and a high-energy tail which has no significant momentum dependence. A convenient analytical energy dependence supplemented by a numerical dependence on momentum allows computationally tractable studies of the consequences associated with the considerable dressing of the nucleons. Applications are presented for high-momentum components as a function of energy, density of states, dressed particle-hole response, and the dressed particle-particle/hole-hole propagator.

International Journal of Modern Physics E•Sep 1, 1996•6 citations
Many-body techniques are used to develop a practical formalism for including an energy-transfer dependence in the nucleon-nucleon interaction used in nuclear linear response models. An energy-transfer dependence is naturally expected from the exchange of finite mass, finite velocity mesons. The formalism is applied in a Tamm-Dancoff approximation model structure calculation for 16O^{16}\mathrm{O}16O. The importance of meson retardation effects on the structure calculation is studied as a function of the magnitude of unperturbed particle-hole energies. The relative importance of ring and ladder contributions is also investigated. It is found that retardation effects can become qualitatively important when particle-hole energies are comparable to the mass of the exchanged meson as would be the case for N∗{\mathit{N}}^{\mathrm{*}}N∗ particle-nucleon hole configurations. While ladder kernels exhibit a significant energy-transfer dependence, the actual results obtained including retardation when solving for the ladder polarization propagator follow closely the results obtained using an instantaneous ladder kernel. This result suggests a simple procedure for including retardation effects.
A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green's functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as c-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka et al.$---- The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states in a systematic way.
The theory of an electron gas at high density is generalized so as to include the exchange scattering of a particle and hole in the singlet as well as in the triplet spin state. This approximation is the maximum possible linearization of a quantum-mechanical many-body problem, and corresponds to the theory of small-amplitude oscillations of a classical many-body system. The linearized Hamiltonian is that of Wentzel's meson pair theory, in which now two kinds of mesons are involved, one with spin zero corresponding to the singlet state of a particle and hole and the other with spin one corresponding to the triplet state. The correlation energy is shown to be the sum of the change in zero-point energies of the two-meson fields with correction only in the second-order term. The theory is then formulated in terms of Green's function, and it is proved explicitly that the linearized theory (or the random-phase approximation with exchange effects taken into account) is equivalent to the "ladder approximation" for the particle-hole scattering. The particle-particle scattering by means of the screened interaction is also discussed. The case of the $\ensuremath{\delta}$-function potential is explicitly solved, and it is shown that the correlation energy becomes complex in the region where the instability of the paramagnetic state occurs.
Nonperturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with nonperturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons ($2\mathrm{q}\ensuremath{\bigotimes}2\mathrm{phonon}$), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of 42,48Ca^{42,48}\mathrm{Ca}42,48Ca and 68Ni^{68}\mathrm{Ni}68Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.
Ground-state properties in a model quantum field theory are calculated by stochastic evaluation of a path integral representation of the many-body propagator. The model consists of nonrelativistic nucleons coupled to vector and scalar mesons in one spatial dimension. Binding energies and density distributions are calculated for bound states of up to twenty nucleons. The binding energy as a function of density, the nucleon-nucleon correlation function, and the meson-meson correlation function are evaluated in nuclear matter. Exact ground-state solutions to the full field theory are shown to differ relatively little from those of the potential theory corresponding to the static limit. The exact solutions differ substantially from those of the mean-field (Hartree) approximation, but are quite similar to those obtained in the Hartree-Fock approximation.NUCLEAR STRUCTURE Meson-nucleon field theory. Monte Carlo solution. Nuclear matter.
This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.
A representation of nucleon spectral functions in nuclear matter is developed. Various contributions are identified including a quasiparticle term, broad background contributions below and above the Fermi energy, and a high-energy tail which has no significant momentum dependence. A convenient analytical energy dependence supplemented by a numerical dependence on momentum allows computationally tractable studies of the consequences associated with the considerable dressing of the nucleons. Applications are presented for high-momentum components as a function of energy, density of states, dressed particle-hole response, and the dressed particle-particle/hole-hole propagator.