On Some Properties of Nucleon in Nuclear Matter (original) (raw)
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Physical Review, 1958
The properties of nuclear matter have been determined by the solution of the nuclear many-body problem, using the reaction matrix theory of Brueckner. The nonlinear integral equations characteristic of the theory have been solved with the aid of the fast electronic computer IBM 704. The two-body interaction assumed is the phenomenological potential of Gammel, Christian, and Thaler. It is found that the binding energy of nuclear matter, neglecting Coulomb forces, is 14.6 Mev per particle at a density corresponding to a radius parameter ro-1. 00&(10 " cm. The Coulomb repulsion in a heavy nucleus is shown to drop the density by approximately 15%. The tensor force is shown to give approximately 6-Mev binding energy. The results are found to be very sensitive to the self-consistency requirements of the theory, the binding energy shifting from 14.6 Mev to 34.4 Mev if the velocity dependence of the single-particle potential is neglected. The actual solutions were made self-consistent by an iteration procedure which converged in five or six iterations, the final results being self-consistent to one part in 10' or 10'. The effective mass for nucleon motion in the Fermi sea is found to vary from 0.56M for slow particles to 0.66M for particles near the Fermi surface. This velocity dependence of the potential is closely related to the symmetry energy which also depends, however, on the shifting in the spin populations as the neutronproton ratio is changed from unity. The symmetry energy computed is 10 to 15/z larger than that deduced from experiment. I. INTRODUCTION ' 'N previous papers, ' ' one of us (K. A. B.) and others~h ave developed a method for determining the properties of extended nuclear matter. This theory was first used to make an approximate study of the equilibrium density and binding energy of nuclear matter' ' and to develop a theory of high-energy nuclear reactions,ẽ nergy-level fine structure, and conlguration mixing, ' and neutron reactions with nuclei at low energy. " Later studies, " " particularly that by Bethe, ' have made further analyses of the theoretical foundation of the method and also examined the problems which arise in applying the method to finite systems. Thus in this paper, it is not necessary to review the'foundations of the method. The purpose of this paper is to give the details" of *Work performed under the auspices of the U. S. Atomic Energy Commission.
Nuclear densities and the statistics of nucleonic constituents
Physical Review C, 1994
In the quark model of the nucleon, the Fermi statistics of the elementary constituents can in6uence significantly the properties of multinucleon bound systems. In the Skyrme model, on the other hand, the basic quanta are bosons, so that qualitatively different statistics effects can be expected a priori. In order to illustrate this point, we construct schematic one-dimensional quark and soliton models which yield fermionic nucleons with identical baryon densities. We then compare the baryon densities of a two-nucleon bound state in both models. Whereas in the quark model the Pauli principle for quarks leads to a depletion of the density in the central region of the nucleus, the soliton model predicts a slight increase of the density in that region, due to the bosonic statistics of the meson-field quanta.
On a four-nucleon model of nuclear matter
Nuclear Physics A, 2003
The nuclear matter saturation mechanism based on a four-nucleon interaction is proposed. The model describes rather well nuclear matter properties in the Hartree-Fock (HF) approximation. 0375-9474/03/$ -see front matter 0
The role of the distribution of nucleons in finite nuclei
Czechoslovak Journal of Physics, 1992
The total energy of many-nucleon system is expressed as a functional E[pp(r), pn(r)] of the proton and neutron densities pp(r) and pn(r), respectively. The distribution p(r) of nucleons in the nucleus, which is essential to determine the energy functional, is chosen. The energy density formalism is applied to finite nuclei, and then the binding energies per nucleon together with the mean square radii, for some medium and heavy nuclei, are obtained. Finally the achieved results are compared with the corresponding experimental values.
The Properties of Nuclear Matter at Zero and Finite Temperatures
Ядерная физика, 2014
The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T 2 -approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.
NUCLEAR MATTER EQUATION OF STATE, INCOMPRESSIBILITY
2009
A mean field calculation is carried out to obtain the equation of state (EoS) of nuclear matter from a density dependent M3Y interaction (DDM3Y). The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of the symmetric nuclear matter (SNM). In this work, the energy variation of the exchange potential is treated properly in the negative energy domain of nuclear matter in contrast to an earlier work where it was assumed to vary negligibly inside nuclear fluid. The EoS of SNM, thus obtained, is not only free from the superluminosity problem but also provides good estimate of nuclear incompressibility. The DDM3Y, whose density dependence is determined from nuclear matter calculation, provides excellent description for proton radioactivity.
A new approach to physics of nuclei
Physics of Atomic Nuclei, 2012
We employ the QCD sum rules method for description of nucleons in nuclear matter. We show that this approach provides a consistent formalism for solving various problems of nuclear physics. Such nucleon characteristics as the Dirac effective mass m * and the vector self-energy Σ V are expressed in terms of the in-medium values of QCD condensates. The values of these parameters at saturation density and the dependence on the baryon density and on the neutron-to-proton density ratio is in agreement with the results, obtained by conventional nuclear physics method. The contributions to m * and Σ V are related to observables and do not require phenomenological parameters. The scalar interaction is shown to be determined by the pion-nucleon σ-term. The nonlinear behavior of the scalar condensate may appear to provide a possible mechanism of the saturation. The approach provided reasonable results for renormalization of the axial coupling constant, for the contribution of the strong interactions to the neutron-proton mass difference and for the behavior of the structure functions of the in-medium nucleon. The approach enables to solve the problems which are difficult or unaccessible for conventional nuclear physics methods. The method provides guide-lines for building the nuclear forces. The threebody interactions emerge within the method in a natural way. There rigorous calculation will be possible in framework of self-consistent calculation in nuclear matter of the scalar condensate and of the nucleon effective mass m * .
The Hot and Cold Properties of Nuclear Matter
The properties of nuclear matter at zero and finite temperatures in the frame of the Brueckner theory realistic nucleon-nucleon potentials are studied. Comparison with other calculations is made. In addition we present results for the symmetry energy obtained with different potentials, which is of great importance in astrophysical calculat ion. Properties of asymmetric nuclear matter are derived fro m various many-body approaches. This includes phenomenological ones like the Skyrme Hartree-Fock and relat ivistic mean field approaches, which are adjusted to fit properties of nuclei, as well as mo re microscopic attempts like the BHF appro ximation, a Self-Consistent Greens Function (SCGF) method and the so-called V lowk approach, which are based on realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts. These microscopic approaches are supplemented by a density-dependent contact interaction to achieve the empirical saturation property of symmet ric nuclear matter. Special attention is paid to behavior o f the isovector and the isoscalar co mponent of the effective mass in neutron-rich matter. The nuclear sy mmetry potential at fixed nuclear density is also calculated and its value decreases with increasing the nucleon energy. In particu lar, the nuclear symmet ry potential at saturation density changes fro m positive to negative values at nucleon kinetic energy of about 200 MeV. The hot properties of nuclear matter are also calculated using T 2 -approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data especially at low densities.
Fundamentals of Nuclear Physics
2012
Use in any way except education purpose is prohibited. Every student may print out no more than one copy for personal use. 11. Nuclear physics 11.1. Internal structure of an atomic nucleus All nuclei (besides the ordinary hydrogen nucleus which is a single proton) are composed of two types of particles: protons and neutrons. Some of the properties of nuclei, such as their charge, structure and composition, radius and symbols are shown by the following scheme: Symbols of nucleus X : Nucleons proton 1p 1 number of protons Z Q=Z|e| neutron 0n 1 number of neutrons N (charge) ZX A radius 10-15 m A-atomic mass
Nuclear medium modification of the structure function
Nuclear Physics A, 2011
We study the nuclear effects in the electromagnetic structure function F 2 (x, Q 2) in the deep inelastic lepton nucleus scattering process by taking into account Fermi motion, binding, pion and rho meson cloud contributions. Calculations have been done in a local density approximation using relativistic nuclear spectral functions which include nucleon correlations. The ratios R A F 2 (x, Q 2) = 2F A 2 (x,Q 2) AF D 2 (x,Q 2) are obtained and compared with recent JLab results for light nuclei with special attention to the slope of the x distributions. This magnitude shows a non trivial A dependence and it is insensitive to possible normalization uncertainties. The results have also been compared with some of the older experiments using intermediate mass nuclei.