J.M. Pearson

Nuclear mass formula with Bogolyubov-enhanced shell-quenching: application to r-process

The ETFSI mass table, which is based entirely on microscopic forces, has been modified to take account of the strong quenching of shell effects found in HFB calculations on highly neutron-rich nuclei. The general effect of this modification is to reduce nuclear deformations; we discuss the implications for the r-process nuclidic abundances, as calculated in the canonical model.

Static nuclear properties and the parametrisation of Skyrme forces

Abstract We present a systematic study of the dependence of static nuclear properties on the parameters of the effective interaction used in the Hartree-Fock (HF) and extended-Thomas-Fermi (ETF) models. For this purpose, a set of trial Skyrme forces, which are constrained by a fit to nuclear radii and binding energies, is developed. This leaves six free parameters: the spin-orbit strength, the nuclear-matter compression modulus, the isoscalar and isovector contributions to the effective masses, the value of the exchange parameter x3 (governing the surface-symmetry properties) and the coefficient of the “gradient-symmetry” term |▽ρn − ▽ρp|2 in the energy-density functional. The influence of these parameters on various properties is studied: droplet-model parameters, quality of the fit to experimental masses, extrapolation of masses, fit to charge radii, charge distributions and neutron-skin thicknesses, semiclassical fission barriers, and Landau parameters. Indications are given of the directions which could be followed in order to improve the fit to experimental data. Several correlations remaining in the results suggest that a larger number of degrees of freedom obtained by additional terms could be useful.

Thomas-Fermi approach to nuclear mass formula: (III). Force fitting and construction of mass table

Abstract The ETFSI method, developed in two earlier papers, is here used to construct a complete mass table. Since the method allows for interpolation both in the ( N , Z ) plane and with respect to deformations, without losing the characteristic shell-model fluctuations, it is some 2000 times faster than the HF-BCS method for a given force. The present table is calculated using a preliminary Skyrme-type force with δ-function pairing, fitted to a restricted data set of 491 spherical nuclei. The resulting rms error for all 1492 measured nuclei, spherical and deformed, with A ⩾ 36 is e rms = 0.868 MeV, achieved with just 9 parameters. The main experimental trends in ground-state deformations are well followed. The symmetry coefficient of nuclear matter corresponding to our force is 27.5 MeV. Ways of rapidly improving the fit are indicated.

The incompressibility of nuclear matter and the breathing mode

Abstract It is shown that a unique value of the nuclear-matter incompressibility K v cannot be extracted from the breathing-mode data. There is thus no basis for the often quoted figure of 300 MeV. However, the data establish a correlation between K v and the third-order derivative of the nuclear-matter saturation curve.

Thomas-fermi approach to nuclear mass formula

Abstract With a view to having a more secure basis for the nuclear mass formula than is provided by the drop(let) model, we make a preliminary study of the possibilities offered by the Skyrme-ETF method. Two ways of incorporating shell effects are considered: the “Strutinsky-integral” method of Chu et al., and the “expectation-value” method of Brack et al. Each of these methods is compared with the HF method in an attempt to see how reliably they extrapolate from the known region of the nuclear chart out to the neutron-drip line. The Strutinsky-integral method is shown to perform particularly well, and to offer a promising approach to a more reliable mass formula.

The anomalies of the droplet model

Abstract The droplet model predictions for nuclear density distributions are systematically compared with the results of a self-consistent model with Strutinsky smoothing. The discrepancies between the two predictions for stable nuclei are as large as the discrepancies between the old liquid drop model and the self-consistent one: although the droplet model reproduces quite well the trends of the variations of nuclear radii and neutron skins, it is not able to predict correctly their values. A preliminary discussion is given as to which hypothesis of the droplet model should be modified to generalise it, and two possible variants are suggested.

Hartree-Fock calculation of superheavy magic numbers

Abstract The Vautherin-Brink force is modified by making the two-body term much more realistic, while maintaining the fit to the known nuclei in Hartree-Fock calculations. Not only 342 228 114 but also 348 228 120 are found to be doubly-magic.

Skyrme Hartree–Fock method and the spin–orbit term of the relativistic mean field☆

Abstract It is shown that Hartree–Fock BCS calculations made with a conventional form of Skyrme force reproduce the isospin dependence of the spin–orbit field generated by relativistic mean-field calculations, provided the parameters of the respective theories have been well fitted to the mass data.

Determination of nuclear-matter density: Hartree-fock versus droplet model

Abstract The density of nuclear matter indicated by Hartree-Fock phenomenological interactions, combined with the measured incompressibility, is k F 0 = 1.35 fm −1 ( r 0 = 1.13 fm, while the droplet model leads to k F 0 = 1.30 fm −1 ( r 0 = 1.17 fm). A fundamental incompatibility between the two approaches is discussed.

Bubbles and the odd-state force

Abstract We show that the formation of bubbles in spherical Hartree-Fock calculations on 36 A depends sensitively on the odd-state effective interaction, being strongly favoured, like alpha clustering, when this is repulsive