A self-confined Fermi-gas model for nuclear collective motion

The well-known phenomenological dynamic equation for the nuclear shape parameter was derived from first principles with the aim of obtaining the microscopic or many-body expressions for inertia B, deformation force f , and friction coefficient γ of collective motion in hot nuclei. Nuclear evolution, viewed as a sequence of quasiequilibrium stages, is described with the aid of the density matrix ρq constrained to given expectation values of nuclear HamiltonianH, number operator N , and operators Q, P , and M of coordinate, momentum, and inertia of collective motion. Having chosen an explicit expression for Q in terms of the nucleon field operators ψx, ψ x, we construct the corresponding expressions for ρq, P , and M, using a certain canonical transformation of ψx, ψ ∗ x, the equation of continuity and an assumption that the collective variables pn,t = tr (Pn,tρq) where Pn,t are Heisenberg representations of P1 = Q, P2 = P , P3 = M, change with time much slower than the number density and the momentum density, from which pn,t are built. The same assumption was used to get the closed-form solutions of the dynamic equations for pn,t, from which we extract the desired many-body expressions for B, f , and γ. After adaptation of those general expressions to a self-confined Fermi gas with the phenomenological effective force, they are used for critical analysis of the previous microscopic models of those quantities and for elucidating the distinctive features of dissipative collective motion in atomic nuclei. PACS numbers: 25.70.Lm, 24.10.Cn, 25.70.Jj