Classical vacuum versus quantum vacuum

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].…”

“…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]. On the other hand, the scattering length (or amplitude) b may be obtained from concrete equations and can have a sign different than the Born length [21,[23][24][25][26][27][28] so that this difference is really very important to fix the sign of the optical potential [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).…”