Showing papers on "Thomas–Fermi model published in 1976"

A simple nuclear model

Abstract: A nuclear model is considered in which the nuclear forces are taken to be a Yukawa potential acting between nucleons, such as would be produced by a neutral scalar meson, and a repulsive core. The model is very similar to the Fermi-Thomas model of the atom. It is first worked out in the absence of the Coulomb interaction, and it is shown how the the binding energy, surface energy, and shape of the nuclear density at the surface of the nucleus are determined. The Coulomb interaction is then included and the model is worked out for a heavy nucleus, the parameters of the model being chosen to give the correct radius and binding energy. One predicts the right value of Z/A, and obtains a charge density distribution not too different from that deduced from electron scattering experiments. (AIP)

Quantum-statistical equation of state

Abstract: An atomic model is employed to deduce the equation of state of an equilibrium plasma over very wide density and temperature ranges.(AIP)

On alternative forms of the variational principle implying the generalized Thomas-Fermi theory

Abstract: A gas of fermions in a static potential is investigated within the framework of the March-Murray perturbation scheme equivalent to a generalization of the Thomas-Fermi theory. The corresponding variational principle, due to Stoddart and March, is complemented by an alternative form. In contrast with the Stoddart-March formulation whose nature is Hamiltonian and which requires variations of the particle density in the total energy functional, the author's formulation, found to be of Lagrangian nature, does variations with respect to the potential function. Both the (alternative) quantum variational (many-body) principles are formulated self-consistently, with due attention to the Poisson equation of electrodynamics. They are considered first for zero temperature and afterwards for arbitrary temperatures. The functional considerations involved in the present paper are related with thermodynamics of quantum microcontinuum. An Appendix is added, to clarify the functional concepts by demonstrating them on some simple analogy. Therefore, a variational calculation of the ground state energy of π− “mesoatoms” or “mesoions” is given. It leads mathematically to the well-known problem of calculating the ground 1 S (parastate) energy of two electrons in the helium atom.

Critique of the locally linearized approximation to the nuclear single particle density matrix

Abstract: Approximations to the density matrix of a Fermi gas in an external potential by Baltin and by Balazs and Zipfel are shown to be closely related. Predictions for the kinetic energy density using these approximations are compared to exact solutions for two harmonic oscillator problems and for Woods- Saxon wave functions in the lead nucleus. In all three cases, the approximations yield substantial systematic discrepancies, indicating that they are inadequate for quantitative description of the nuclear density matrix. (AIP)