Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermion ground state are further developed through a medium-dependent potential in terms of the Bethe-Peierls contact interaction model. The methods are exact in the unitary limit regime and they lead to self-consistent equations analogous to the Hartree ones. The single particle energy spectrum rearrangement effects on the thermodynamics due to the Hugenholtz-van Hove theorem constraint are addressed. These effects lead to an additional instantaneous correlation potential contribution to the system physical chemical potential and pressure, i.e., equation of state, in order to enforce the classical thermodynamic consistency. The Dyson-Schwinger equations represent implicitly the various Bethe-Goldstone expansion ones. In a thermodynamically selfconsistent way, the universal dimensionless factor is analytically calculated to be = 4 9 , which defines the ratio of the unitary fermions energy density to that of the ideal noninteracting ones at T =0.
An algebraic Hamiltonian for the two coupled nonlinear vibrations of highly excited nonrigid molecule HCP was presented. The Hamiltonian reduces to the conventional one in a limit which was expressed in terms of harmonic oscillator operators. It showed that the algebraic model can better reproduce the data than the conventional model by fitting the observed data of HCP.
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