Extensions of the Thomas-Fermi approximation for finite nuclei

Il Nuovo Cimento A

The role played by the isotropic harmonic oscillator in the shell model is extensively investigated. A Bohr-like model of the shell model is outlined with the purpose of providing a logical justification of the concept of harmonic-oscillator potential <(equivalent)) to the true shell model one as far as the calculation of nuclear energy levels is concerned. The potential (~ equivalence ~, defined according to different criteria, is used throughout. The consistency of the numerical results turns out to be excellent. Their criticM analysis has suggested a cMculational method of nucleon energy levels in finite nuclei which will be discussed in a forthcoming paper.

Nuclear Physics A

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.

We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we consider the simplest such modification by adding a linear gradient term to the Euler equation. For atoms, the coefficient of the gradient term can be chosen so that the correct exponential decay constant far from the nucleus is obtained. This model then gives a much improved description of the electron density at smaller distances, yielding in particular a finite density at the nucleus that is in good qualitative agreement with exact results. The cusp condition differs from the exact value by a factor of 2. Values for the total energy of atomic systems, obtained by coupling parameter integration of the densities given by the Euler equation, are about as accurate as those given by the very best Thomas-Fermi-Weizsäcker models, and the density is much more accurate. Possible connections to orbital-free methods for the kinetic-energy functional in density functional theory are discussed.

Nuclear Physics A, 1987

We present semi-classical calculations of hot nuclei performed within the framework of the procedure recently introduced by Bonche, Levit and Vautherin in Hartree-Fock calculations, in order to take consistently into account the effects of continuum states. We use zero and second order Thomas-Fermi approximations for describing the kinetic and spin-orbit energies. After having introduced the ingredients of the formalism and given the main features of our resolution scheme of the Thomas-Fermi equations, we perform a detailed comparison of our calculations with Hartree-Fock results in order to test the accuracy of our model. We discuss the zero-temperature limit case where TZ developments can be worked out. We show that, at low temperatures ( TS 2 MeV) the subtraction procedure is not indispensable, as expected from Hartree-Fock calculations. We also recall recent results obtained by using our formalism in estimating the temperature dependence of the level density parameter. As in Hartree-Fock calculations we find the existence of a limiting temperature TIi, beyond which the nucleus is unstable because of the Coulomb interaction. By comparing our theoretical values of TIi, with recent experimental data, we show that, in spite of the approximation's in our model, this limiting temperature could be related to the actual disappearance of fusion-like processes in medium energy heavy-ion collisions.

Il Nuovo Cimento B, 1994

The charge-density distribution of Fermi type is used to calculate the binding energies of some spherical, medium and heavy nuclei. The analysis is based on the energy-density formalism with a Yukawa shape potential. The obtained values of the binding energies are in good agreement with the corresponding experimental values.

Nuclear Physics A, 1969

A slightly modified deformed nuclear single-particle potential is investigated in detail in the rare earth and actinide regions. Its parameters are determined so as to reproduce optimally the observed single-particle level order in deformed nuclei. The most important single-particle matrix elements connected with decoupling factors and magnetic moments are calculated, and in these cases, a Y~ term in the potential is included. Some collective properties such as quadrupole moments are calculated. * A more extensive discussion is given in ref. ). *t As only the first part of the potential is later subject to the condition of volume conservation it is natural to apply a corresponding correction to the 12 term. ((1" s)sheu = 0.

Physical Review A, 1990

Atoms at finite temperature and with a nucleus of finite extension are analyzed by a modification of the Thomas-Fermi model for TWO. Applications to strange-matter atoms are included.

The momentum and density dependence of mean fields in symmetric and asymmetric nuclear matter are analysed using the simple density dependent finite range effective interaction containing a single Gaussian term alongwith the zero-range terms. Within the formalism developed, it is possible to reproduce the various diverging predictions on the momentum and density dependence of isovector part of the mean field in asymmetric matter. The finite nucleus calculation is formulated for the simple Gaussian interaction in the framework of quasilocal density functional theory. The prediction of energies and charge radii of the interaction for the spherical nuclei compares well with the results of other effective theories.

Physical Review C, 2016

The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.

Journal of Physics: Conference Series, 2015

A procedure for calculating microscopically the input for standard shell-model calculations, i.e., the core and single-particle energies plus the two-body effective model-space interactions, is presented and applied to nuclei at the start of the sd-shell. Calculations with the JISP16 and Idaho χEFT N 3 LO nucleon-nucleon interactions are performed and yield consistent results, which also are similar to phenomenological results in the sd-shell as well as with other theoretical calculations, utilizing other techniques. All results show only a weak A-dependence.