The optical potential for photons interacting with matter

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.…”

“…On the other hand, the expression namely V = 2 2 bn/m becomes formula (2) through a transformation of spatial-coordinate space into P-space. Formula (2) is applicable to non-relativistic (attractive or repulsive) neutron-neutron scattering [21,[25][26][27][28] as well as electron-nuclei scattering. In the context of neutron-neutron scattering, optical potential and refractive index may be derived from the so-called Born forward scattering amplitude [21,[23][24][25][26][27][28].…”

“…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).…”

A Rigorous Approach for Calculating the Chemical Potential of an Ultrarelativistic Spherical Degenerate Fermi Gas Interacting with Nuclear Matter

“…The second factor (which, as one sees, is the sum of three terms) on the right-hand side of (1) holds in the relativistic case [2,4,7], so it is clear that the chemical-potential energy at zero absolute temperature is obtained by multiplying the right-hand side of (4) by the aforementioned sum of three terms on the right-hand side of (1). The scattering amplitude depends now on energy (Fermi energy) so, looking at the right-hand side of (4), one concludes that the above amplitude depends upon distance; then we consider the function b(r).…”