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Physical Review C

Free surface response in a finite Fermi system

Valery I. Abrosimov, O. I. Davidovskaya, V. M. Kolomietz, Shalom Shlomo

Published May 1, 1998• 7 citations
Publisher

Abstract

Collective vibrations in a finite Fermi system are studied within a phase space approach which is based on the Landau-Vlasov kinetic equation. The linear response theory is used and the semiclassical internal and collective response functions are evaluated with a continuous single-particle angular momentum $l.$ We focus on the strength function and fragmentation width of the vibrations. We determine the contributions to the collective strength function which are associated with different values of relevant single-particle angular momentum. Applications to the nuclear isoscalar vibrations with multipolarities $L=0,$ 2, and 3 are presented.

DOI
10.1103/physrevc.57.2342

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Collective vibrations in a finite Fermi system are studied within a phase space approach which is based on the Landau-Vlasov kinetic equation. The linear response theory is used and the semiclassical internal and collective response functions are evaluated with a continuous single-particle angular momentum l.l.l. We focus on the strength function and fragmentation width of the vibrations. We determine the contributions to the collective strength function which are associated with different values of relevant single-particle angular momentum. Applications to the nuclear isoscalar vibrations with multipolarities L=0,L=0,L=0, 2, and 3 are presented.
Using a quantum Boltzmann equation framework, we analyze the nature of generic low-energy deformations of a critical surface, which exists at the non-Fermi liquid fixed point of a system consisting of fermions interacting with massless bosons. The non-Fermi liquid behaviour arises due to the itinerant quasiparticles of the Fermi surface interacting strongly with the massless bosons, which on the other hand undergo Landau damping as result of the mutual interactions. Focussing on the collisionless regime, where we neglect the collision integral, we chalk out the possible excitations spanning the entire spectrum of angular momentum (`) channels (i.e., including both small and large values of `). The excitations are of two types: particle-hole like localized excitations forming an energy band (or continuum) and delocalized collective modes with discrete energies. Although we find a collective mode analogous to the zero sound of a Fermi liquid, its dispersion shows a crossover from a Ω ∼ |q|6 / 5 behaviour to the usual Ω ∼ |q| dependence, where Ω and q represent the frequency and momentum, respectively. We estimate the frequency scale at which this crossover takes place. We also determine the boundary for the particle-hole continuum in the Ω–q plane, and observe a crossover from Ω ∼ |q|3 / 2 to Ω ∼ |q| behaviour, determined by another crossover frequency scale.
The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in 40Ca{}^{40}\mathrm{Ca}40Ca are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent two-particle--two-hole states is small at low temperatures but increases rapidly at higher temperatures.
The collective excitation of the nuclear matter is analyzed in a bosonizated formula of Landau Fermi liquid theory. When the nonlinear self-interacting terms of the scalar meson are taken into account in the Walecka model, the collective excitation energies of the nuclear matter can be obtained self-consistently. It shows that the calculation results are consistent with the corresponding experimental data of the nucleus 208Pb{}^{208}Pb208Pb when the quantum number of the orientation of the orbital angular momentum mmm is zero. Moreover, the cases with the nonzero mmm values are also studied, it manifests that the collective excitation energy with the fixed nonzero mmm value are almost invariant when the quantum number of the orbital angular momentum lll changes. However, the collective excitation energy of the nuclear matter decreases with the absolute value of mmm increasing. The direct interaction between two nucleons near the Fermi surface only changes the Fermi velocity, while the exchange interaction causes the collective excitation of the nuclear matter. At this point, it is different from the traditional views in nuclear physics, which announce that the random phase approximation is essential to generate the nuclear collective excitation states.