M. Membrado

A description of semidegenerate self-gravitating spheres of fermions

The structure of a sphere of self-gravitating fermions, at low constant temperature, is analyzed, substituting the usual Fermi-Dirac distribution function by a trapezoidal approximation. This model coincides with the exact result up to the first correction in the low-temperature expansion while leading to finite equilibrium configurations; thus, it represents an alternative to the use of the habitual energy, or density, cutoffs. Analytical expressions (up to terms in T 2 ) are obtained for magnitudes such as total energy, radius of the sphere, and local value for the density and pressure

A mass formula for 4He clusters

An analytic expression for the total energy of 4He clusters composed of N atoms is obtained by means of a variational solution of the energy density functional. The energy is calculated as an expansion in decreasing powers of the cluster radius, R∝N1/3. Contributions of volume (R3), surface (R2), curvature (R), constant (R0), (1/R), and (1/R2) are clearly separated in the formula. Chemical potentials, fusion and fission potentials, surface thickness, and unit radii are also obtained.

Implication of Yukawa-like effects in a white dwarf structure

This paper analyzes the perturbation induced in a white dwarf when a Yukawa force impurity is added to the Newtonian gravitational field. A semiclassical statistical method a la Thomas-Fermi is developed for that purpose. It is shown that this effect depends on only one parameter. 19 references.

Short-range effects in large white dwarfs

Recent work of Membrado and Pacheco (1988) on the implication of Yukawa-like effects in small white dwarfs is extended to analyze the very massive case. Although the role of these impurities grows substantially as the radius of the star decreases, when reasonable supergravity parameters are used the predicted change in the white dwarf mass-radius relation is unobservably small. 8 references.

Hartree solution for the “bosonic atom”

Abstract A gedanken bosonic atom whose electrons are assumed to obey Bose-Einstein statistics is presented, and the Hartree solution for its ground state obtained. This solution, which is universal, exactly fulfills the virial theorem. Unlike real, fermionic, atoms, the radius and total energy of this system are proportional to Z -1 and Z 3 respectively.

Free atoms at finite temperature: coherent and incoherent scattering functions

We calculate the coherent and incoherent scattering functions for free atoms at finite temperature. This is performed within a finite-temperature Thomas-Fermi method recently proposed by us, which avoids — artificial — confining cells of the Wigner-Seitz type.

Lower bounds for the ground-state energy of4He clusters

SummaryLower bounds for the ground-state energy of droplets formed by4He atoms, interacting through the Azizet al. potential, are computed. For large systems, the saturation limit induced by this force is rigorously proved.

On the validity of the jellium model for describing small metal clusters

Using the Density-Functional formulation for the free electrons of a metal cluster, we define a simple criterion for the correct applicability of the jellium model to describe the ion background. In general, a hollow uniform-density sphere is proposed as a more correct model.

Semiclassical variational study of size effects in neutral and charged jellium droplets

An analytic expression for the total energy of metallic clusters composed ofN identical atoms of valencev and with net chargeQ is obtained by means of a variational solution of the Thomas-Fermi-Weizsäcker energy density functional within the spherical jellium model. The minimum energy is given as an expansion in decreasing powers of the cluster radiusR=rsZ1/3, withZ=vN andrs the radius per electron of the bulk metal. The coefficients are obtained as functions ofrs. Terms of volume (R3), surface (R2), curvature (R), constant (R0), (1/R) and (1/R2) are clearly separated in the formula, as well as the different contributions (kinetic, coulombic and exchange-correlation) to each of them. The asymptotic values (R→∞) for the work functions,W(rs), and surface energies σ(rs), are compared to analogous semiclassical and Kohn-Sham calculations of jellium-like surfaces and to the experimental values. The size dependent behaviour of chemical potentials, μ(R), electron affinities,AF(R), and ionization potentials,IP(R), are easily obtained for any kind of metallic clusters. In particular we discuss the Coulomb and quantum corrections to the coefficients β, δ in the asymptotic formulae:IP≃W+β/R andAF≃W+δ/R.

On galactic halos: Bosons and fermions

SummaryTwo self-gravitating collisionless quantum gases in their ground state, one formed by bosons and the other by fermions, are analysed and compared in order to explain the flatness of the rotation curves in galaxies. A realistic visible matter distribution has been taken into account in the calculations.