Yukawa Potential

It appears that for the hard-core potential with Yukawa tail, thermodynamic properties calculated through the variational theory are obtainable in almost fully analytic form with the use of hard-core fluid as the reference system. For one negative Yukawa tail minimization of the right-hand side of the variational inequality for the Helm­holtz free energy gives diameters of hard-cores of both systems equal, independently of the temperature and the density. Therefore, the whole scheme of calculations is equivalent to adopting the first order Zwanzig 1/T expansion. Comparison with recent calculations of properties of Yukawa system with z = 1.8 presented by Henderson et al. (Mo/. Phys. 35, 241,1978) shows that our results-for free energy are very good, mainly due to the smallness of the A2 term for this system. The promising features of the variational method for other Yukawa type potentials are outlined.

Thermodynamic properties of simple fluids are calculated using variational theory for a system of h:1rd-cmc potential with a two-Yukawa tail. Like one Yukawa-tail case (C. Jedrzejek, G. A. Mansoori, Acta Phys. Pol. A56, 583, 1979) the working formulas are analytic. Five parameters of the two Yukawa system are chosen so as to get the best fit to a real argon potential or an "argon-like" Lennard-Jones potential. The results are fairly good in light of the extreme simplicity of the method. The discrepancies result from using the variational method and a different shape or Yukawa type potential in comparison to the real argon and L-J potentials.

A new and analytical thermodynamic model for simple fluids with an intermolecular pair potential consisting of a hard-sphere core and an attractive Yukawa tail is presented. The model yields simple analytic expressions for all thermodynamic properties of the fluid system. The self-consistent numerical results of the present model for the compressibility factor, internal energy, and Helmholtz free energy are in excellent agreement with the Monte Carlo "experiments" for the whole range of temperatures and densities in which experimental data are available.

I examine two fundamental forces via the math of line integrals using my candidate proportionality ratio (α) which: • Restates electrostatic force based upon Planck (ħc) and that ratio of field strength at the square root of particle radius distance (re) versus the Bohr radius (a0) equilibrium distance, root(a0/re), the fine structure constant (α), as a line integral relative to that field, not as a point force or quantum e f potential. So, electrostatic has a line integral format more useful for examining certain subatomic events. • Generates a revised equation for strong nuclear force via elimination of and integral and e f part as now =1 by that proportionality. That causes strong with my root(a0/re) change versus electrostatic which is the 1/r of Bohr's angular momentum properly scaled. • Generates force vector equations of 1/distance-squared restated electrostatic force vector versus redefined strong now as direct, isotropic 1/distance-cubed force. Electrostatic primary outside Bohr, strong as primary inside Bohr, and both in conflict and in equilibrium near Bohr, meaning that strong nuclear force keeps electrons in fields, not angular momentum. • Has both static equations constants with physical meaning as reduced Planck basic unit of energy, radiating via a line integral over the equilibrium, at the speed of light, the field propagation rate in time, via proportionality with the Bohr radius, a distance. No movement is necessary. • Also implies that the strong nuclear force should use mass units, rather than charge units. • Implies that 'charge' and 'mass' get determined by those line integrals for future papers.

It is proposed that in a core-collapse supernova, as a result of rotation of the progenitor and a departure from spherical symmetry, some of metals from the region intermediate between the outer layers of the progenitor which will be expelled in the explosion and the inner part which will collapse to form the neutron star will go into an eccentric orbit.  The metallic material will quickly form grains with an orbital period of the order of a few hours.  Within 100 to 1000 orbital periods the grains will rapidly coalesce to form one or more metallic planets orbiting the pulsar.