The gap function [[DELTA].sub.p] can be different from zero in a neighbourhood of the surface of the Fermi sphere and satisfies
By means of a Bogoliubov transformation acting on the creation and annihilation operators of the electron fluctuations around the Fermi sphere, the full expression of [OMEGA](T, V, [mu]) satisfying the Maxwell relations is obtained.
The operators [d.sup.[??].sub.ps] and [d.sub.ps] should describe the one-particle fluctuations with respect to the configuration of the Fermi sphere. Then [d.sup.[??].sub.ps] and [d.sub.ps] are chosen in such a way that their vacuum state coincides with the free electrons ground state corresponding to the Fermi sphere.
The creation operator [d.sup.[??].sub.ps] of a quasi-particle corresponds to the creation of a one-electron hole in the Fermi sphere if [absolute value of p] < [p.sub.0] and the creation of a one-electron occupied state if [absolute value of p] > [p.sub.0].
The operator number of quasi-particles [[??].sub.qp] is given by [mathematical expression not reproducible] counts the number of holes inside the Fermi sphere plus the number of occupied states outside the Fermi sphere.
where [[summation].sub.p] denotes the integral in the neighbourhood of the surface of the Fermi sphere which is specified by the condition [mathematical expression not reproducible].
Accordingly, in the computations of [F.sub.q] and of [E.sub.0] the integral in momentum space is effectively dominated by the integration in a neighbourhood of the surface of the Fermi sphere and it can be written as
Consider the number of particles that can be excited by the energy [k.sub.B]T [much less than] [E.sub.F] from the d-dimensional Fermi sphere
. This number is approximately given by N[k.sub.B]T/[E.sub.F] while the number of available states above the Fermi energy can be approximated by g([E.sub.F])[k.sub.B]T.
As noted, this quantity measures deviation from a single Fermi sphere and hence represents local equilibrium.
In present case each local volume element of nuclear matter in coordinate space and time has some temperature defined by the diffused edge of the deformed Fermi distribution consisting of two colliding Fermi spheres, which is typical for a nonequilibrium momentum distribution in heavy-ion collisions.