Average Nuclear Properties Research Articles

On the quantization of linear maps: A. Lakshminarayan and N. L. Balazs. Department of Physics, State University of New York Stony Brook, Stony Brook, New York 11794

The Thomas-Fermi model of average nuclear properties described in Part I (Myers and Swiatecki, Ann. Phys. (N.Y.)204, 1990, 401–431) is simplified further and then applied to the calculation of fission barriers and charge distributions. An extensive comparison with experimental data reveals a small but clear-cut barriers vs size discrepancy: if the radius constant r0 is chosen to be 1.13 fm so as to reproduce measured nuclear sizes, the calculated fission barriers are too high. The suggestion is made that an extension of the Thomas-Fermi method is called for in order to describe the presence in nuclei of the “quantal halo”, i.e., of the classically forbidden region around the nuclear surface where matter exists at negative kinetic energy.

Some average nuclear properties with an effective interaction

Nuclear matter properties — binding energy (BE), compressibility, single particle potential, re-arrangement energy and effective mass — have been studied in first order with a density dependent effective interaction. Second order contribution to BE, single particle potential, and effective mass have been estimated. Ground state energy of4He and8Be and their r.m.s. radii have also been studied.

Sensitivity studies of the neutron multiplicity spectrum in the spallation of Pb targets

The number of neutrons produced per incident proton in the spallation of Pb targets is of direct relevance to the design of accelerator breeders. The nuclear cascade initiated by high-energy protons in spallation targets is usually described by an intranuclear cascade evaporation (INCE) model. Even though this model describes various average nuclear properties of spallation targets fairly well, differential quantities such as energy spectra, angular spectra etc. are not reproduced within the limits of experimental uncertainty. One of the reasons for this is the uncertainty in the magnitude of the parameters involved in the model, notably the level density parameter B 0 whose magnitude is quoted by different workers to be in the range of 8–20 MeV. The accuracy of B 0 could be improved if we could experimentally determine a quantity which is much more sensitive to B 0 than the average neutron yield. In this paper we discuss one such quantity, namely the neutron multiplicity spectrum (MS). We compute the MS due to the spallation of Pb targets of different sizes at proton energies of 1.5, 1.0 and 0.59 GeV using the Monte Carlo code HETC. It is noticed that for the 1.5 GeV proton case the probability P( v) for leakage of v neutrons for v in the range of 60–65, changes by about 70% when B 0 is varied from 8 to 20 MeV. The corresponding change in the average neutron yield is <20%. It is therefore suggested that an accurate measurement of the MS can serve as a useful tool to narrow down the range of uncertainty in the B 0 parameter.

Thomas Fermi model of finite nuclei

A relativistic Thomas-Fermi model of finite nuclei is considered. The effective nuclear interaction is mediated by exchanges of isoscalar scalar and vector mesons. We include also a self-interaction of the scalar meson field and the Coulomb repulsion of the protons. The parameters of the model are constrained by the average nuclear properties. The Thomas-fermi equations are solved numerically for finite, stable nuclei. The particular case of 208 82Pb is considered in more detail.

Self-consistent calculations for highly excited compound nuclei

A method for self-consistently calculating average nuclear properties at high excitation energies is derived. Calculations using this formalism have been performed for a double-magic and a deformed nucleus employing the Skyrme force for the nucleon-nucleon interaction. The effects of excitation energy on the nuclear structure are discussed and a comparison of self-consistently calculated level densities with those obtained in the usual statistical method is made. The calculations for the deformed nucleus show the transition from the deformed to a spherical shape with increasing excitation.

Droplet model nuclear density distributions and single-particle potential wells

Abstract A description is given of the nuclear density distributions and single-particle potential wells that arise in the course of Thomas-Fermi calculations of average nuclear properties. Simple expressions are given for the calculation of the essential characteristics of these distributions, and it is shown how the results obtained here may be used to approximate the densities and potential wells in terms of Fermi functions.

Average nuclear properties

A generalized treatment of average nuclear properties is presented. The theory is developed on two levels: First a refinement of the Liquid Drop Model, called the Droplet Model, is described. The degrees of freedom in this model, in addition to the usual shape variables, are variables specifying deviations from uniformity of the neutron and proton densities. The form of the Hamiltonian defining the Droplet Model, of which only the potential energy part is considered in this paper, is derived by expanding the volume, surface, and Coulomb energies in Taylor series around the standard Liquid Drop Model values. Such an expansion, designed to retain all terms in the total energy up to order A 1 3 , I 2A 2 3 , and I 4 A, where I = (N − Z) A , turns out to contain eleven parameters, two of which may be eliminated. Four of the resulting nine parameters are the standard adjustable parameters of the Liquid Drop Model and five are new coefficients specifying various properties of nuclear systems. (Nuclear compressibility and the curvature correction to the surface tension are two examples.) Minimizing the Droplet Model potential energy with respect to density variations leads to equations, in closed form, specifying the separate neutron and proton radii and the density nonuniformities. The minimized energy expression leads to a refined Droplet Model Mass Formula with nine parameters. The second level at which average nuclear properties are treated is based on assuming a concrete model of a two-component saturating system, consisting of neutrons and protons interacting by velocity-dependent Yukawa forces (and Coulomb forces). When this model is treated in the Thomas-Fermi approximation a pair of coupled integral equations results, which can be used as the basis of a self-contained model of all average static nuclear properties. The solutions of these equations are discussed in the idealized situations of nuclear matter and semi-infinite nuclear matter, and for finite nuclei both with and without Coulomb energy. One result of these studies is the determination of the values of the five new Droplet Model parameters. Other results have to do with the nuclear density distributions, and the binding energies. The applications of the Droplet Model and Thomas-Fermi Model discussed in this paper include predictions concerning neutron and proton radii (in particular the presence of a neutron skin), the isotope effect in proton radii, the compression of the nucleus by the surface tension and the dilatation by the Coulomb energy, and the central depression in the densities caused by the Coulomb repulsion. Calculations are made for the surface curvature correction, for the surface symmetry energy, and for a modification to the volume symmetry energy at a large neutron excess. A revised estimate is made for the value of the symmetry energy of nuclear matter. Also treated is the question of whether or not neutron matter is bound, and some discussion is given of the spatial distribution, the energy dependence, and the composition dependence to be expected for nuclear optical model potentials on the basis of the statistical methods used in this paper.

Average nuclear properties: William Don Myers. Lawrence Radiation Laboratory, University of California, Berkeley, California

Average nuclear properties: William Don Myers. Lawrence Radiation Laboratory, University of California, Berkeley, California