Nuclear matter

About: Nuclear matter is a research topic. Over the lifetime, 10180 publications have been published within this topic receiving 248261 citations.

Elements of the brueckner--goldstone theory of nuclear matter.

Abstract: The basic ideas of the Brueckner-Goldstone theory of nuclear matter are presented in a simple way. The treatment is aimed at beginners and nonspecialists. It is supposed to provide the necessary background for the review article by Bethe and Rajaraman which follows this paper. Therefore, the discussion is limited to a few important topics, and these are considered in some detail.The Goldstone expansion is presented (but not derived) and the construction and evaluation of the Goldstone diagrams are explained. The reaction matrix and the correlated two-body wave function are defined, and their properties are discussed. The reference-spectrum method for calculating the reaction matrix is derived, and its use is illustrated. Finally, the related topics of convergence and the definition of single-particle energies are considered. The choice of the single-particle potential energy for occupied states is treated in detail. (Intermediate-state energies will be discussed by Bethe and Rajaraman.) The reason for the divergence of the perturbation series for the binding energy is exhibited; and this series is rearranged into a convergent expansion, for which the density plays the role of small parameter.

Chiral Symmetry and the Bag Model: A New Starting Point for Nuclear Physics

Abstract: Classical nuclear theory deals with a many-body system of neutrons and protons interacting nonrelativistically through two-body potentials. It has, of course, long been realized that there must be corrections to this simple picture—for example, the meson exchange effects which preclude a simple interpretation of the magnetic moment of the deuteron in terms of d-state probability. Nevertheless, the availability of beams of pions, and the consequent ability to study the excitation of real isobars in nuclei, has been critical in the realization that for many problems one must develop a theoretical model which explicitly includes pion and isobar degrees of freedom (see, for example, the proceedings of recent topical conferences Cat+ 82, MT 80).

Microscopic mass formulas

Abstract: By assuming the existence of a pseudopotential smooth enough to do Hartree-Fock variations and good enough to describe nuclear structure, we construct mass formulas that rely on general scaling arguments and on a schematic reading of shell model calculations. Fits to 1751 known binding energies for N,Z\ensuremath{\ge}8 lead to rms errors of 375 keV with 28 parameters. Tests of the extrapolation properties are passed successfully. The Bethe-Weizs\"acker formula is shown to be the asymptotic limit of the present one(s). The surface energy of nuclear matter turns out to be probably smaller than currently accepted.

Optical-model potential in finite nuclei from Reid's hard core interaction

Abstract: Starting from the Brueckner-Hartree-Fock approximation and Reid's hard core nucleon-nucleon interaction, we calculate and parametrize the energy---and the density---dependence of the isoscalar, isovector, and Coulomb components of the complex optical-model potential in infinite nuclear matter, for energies up to 160 MeV. We then construct the optical-model potential in a finite nucleus. In a first step, we adopt a local density approximation which implies that the value of the complex potential at each point of the nucleus is the same as in a uniform medium with the local density. We compute the corresponding volume integrals per nucleon and mean square radii of the real and of the imaginary parts of the optical-model potential, in particular for protons scattered by $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. We compare these results with a compilation of empirical values and find that the calculated and experimental volume integrals are in good agreement but that the theoretical mean square radii are too small. We ascribe this discrepancy to the fact that our local density approximation does not include accurately the effect in a nonuniform medium of the range of the effective interaction. We include this range in a semiphenomenological way suggested by the Hartree approximation. With a reasonable value for this range parameter, which is the only one occurring in our work, good agreement is obtained between the theoretical and the empirical values of the volume integrals and mean square radii of the real and, to a lesser extent, of the imaginary parts of the optical-model potential, for mass numbers $12\ensuremath{\le}A\ensuremath{\le}208$ and for energies $E$ up to 160 MeV. Our results are given in analytic form and can thus be used in analyses of experimental data. We also discuss the difference between the optical-model potentials for protons and for neutrons.[NUCLEAR REACTIONS Calculation of the complex optical-model potential for finite nuclei from Reid's hard core interaction; comparison with a compilation of empirical potentials.]