Central nuclear interaction potentials

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

In a simplistic and conservative picture the core of a neutron star is modeled as a uniform fluid of neutron rich nuclear matter in equilibrium with respect to the weak interaction (/3-stable nuclear matter). However, due to the large value of the stellar central density and to the rapid increase of the nucleon chemical potentials with density, hyperons (A, E, E°, E+, E and E° particles) are expected to appear in the inner core of the star. Other exotic phases of hadronic matter such as a Bose-Einstein condensate of negative pion (7r ) or negative kaon (K ) could be present in the inner part of the star. 

The formulation of spatially separated a and 7r interactions between a pair of atoms is grossly misleading. Critical point compressibility studies show [71] that N2 has essentially the same spherical shape as Xe. A total wave-mechanical model of a diatomic molecule, in which both nuclei and electrons are treated non-classically, is thought to be consistent with this observation. Clamped-nucleus calculations, to derive interatomic distance, should therefore be interpreted as a one-dimensional section through a spherical whole. Like electrons, wave-mechanical nuclei are not point particles. A wave equation defines a diatomic molecule as a spherical distribution of nuclear and electronic density, with a common quantum potential, and pivoted on a central hub, which contains a pith of valence electrons. This valence density is limited simultaneously by the exclusion principle and the golden ratio. 

The potential F(l, 2) is the total interaction energy between the two atoms, and includes contributions from electron-nuclear attraction terms as well as from electron-electron repulsion effects. As a result Xfls, Is ) is negative, and is primarily responsible for the stability of the H-H bond. Central to this description is the fact that the wavefunctions of the participating atoms, and overlap. The magnitude of K ls , Is,), and consequently the strength of the covalent bond, is determined by the degree of non-orthogonality between the two orbitals. 

In the nuclear shell model, the mutual interaction between the nucleons adds up to a singleparticle average potential consisting of a (spherical) central potential and a spin-orbit interaction. The nucleons are assumed to move independently in this potential. The solutions of the Schrbdinger equation yield single-particle energy levels and wave functions for the individual nucleons (Haxel et al. 1949 Goeppert-Mayer 1949). 

Efforts to use relativistic dynamics to describe nuclear phenomena began in the 1950s with application to infinite nuclear matter. Johnson and Teller [Jo 55] developed a nonrelativistic field theory for interacting nucleons and neutral, scalar mesons which served as a catalyst for Duerr, who, in a landmark paper [Du 56], developed a relativistic invariant version of the Johnson and Teller model which included both scalar and vector meson fields. He showed that nuclear saturation and the strong spin-orbit potential of the shell model could be readily understood. He also predicted a single particle potential which qualitatively reproduced the real part of the central optical potential well depth and its energy dependence for incident kinetic energies up to 200 MeV. 

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