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

Abstract

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 ρ q constrained to given expectation values of nuclear Hamiltonian H, 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 ψ x , ψ *x , we construct the corresponding expressions for ρ q , P , and M, using a certain canonical transformation of ψ x , ψ *x , the equation of continuity and an assumption that the collective variables p n,t = tr (P n,t ρ q ) where P n,t are Heisenberg representations of P 1 = Q, P 2 = P , P 3 = M, change with time much slower than the number density and the momentum density, from which p n,t are built. The same assumption was used to get the closed-form solutions of the dynamic equations for p n,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.