On the Optical Potential of an Attractive Nonrelativistic Degenerate Electron Gas Interacting With Nuclear Matter

Abstract

The optical potential of an attractive nonrelativistic electron gas interacting with nuclear matter is determined on the basis of the concept of degenerate Fermi gas. In fact, the involved electrons are treated as three-dimensional quantum harmonic oscillators confined at the surface of a spherical (approximately ideal) potential well. Within this picture, the Fermi velocity is calculated as well as the spatial electron density at the surface of the potential well and the attractive force between the electron gas and the nuclear matter. In addition, considerations related to the Lippmann–Schwinger model are made.

Lipmann-Schwinger Equations for a System of Multiband Energy-Eigenvalue Spectrum

“…[11,12]): Now we are interested in extrapolate formula (1) to a quantum system of multiband energyeigenvalue spectrum. In this case, the corresponding time-independent Schrödinger equations are:…”

“…Therefore, it is natural to think on generalizing for many bands so that elaborating analytical models to characterize multiband systems is desirable. On the other hand, the so-called Lippmann-Schwinger model is suitable to discuss relevant issues in Nuclear Physics as, for example, neutron-nucleus scattering [11] and in Solid State Physics as, for instance, problems related to optical potential [12]. It is well-known (see, for instance, ref.…”

The shift in the optical band-gap of cadmium oxide as chemical potential minus optical potential

“…[21,[25][26][27][28] other hand, it is well-known that the shift in the optical band-gap of cadmium oxide (which always is n-type) coincides with its Fermi energy so this shift, for low absolute temperature, reads within the quasi-free electron theory:…”

“…(2) arises from the original expression namely V = 2 2 bn/m where m stands for neutron rest-mass. This last expression corresponds, in reality, to a pseudo-potential energy relative to neutron-nucleus interaction [20][21][22][23][24][25][26][27][28][29], V and n being functions of spatial coordinates; generalizing, m is fermion rest-mass. Since b < 0, then V < 0; let us assume that the integral of V over its spatial domain is finite.…”

“…In this treatment, the concept of optical potential arises. This concept, coming from the many-body problem, is really very significant in several branches of Physics [20][21][22][23][24][25][26][27][28][29] as, for instance, nuclear astrophysics, Bose condensation, superfluidity, and superconductivity, but not much has been done upon it. In particular, the notion of optical potential is manifestly relevant in Condensed Matter Physics (consider, for example, superconductivity in solids).…”