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Nuclear Physics and Atomic Energy

Dipole excitations in an asymmetric nuclear Fermi-gas

Valery I. Abrosimov, O. I. Davidovskaya

Published Jun 30, 2000• 0 citations
Publisher

Abstract

Dipole excitations of a neutron-proton finite Fermi gas are considered within a semiclassical approach based on the kinetic equation. The independent-particle dipole strength functions connected with the external fields, which are exploited in quantum random phase approximation approaches for studying the isoscalar and isovector resonances in nuclei, are found.

DOI
10.15407/jnpae2000.01.025

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Dipole excitations of a neutron-proton finite Fermi gas are considered within a semiclassical approach based on the kinetic equation. The independent-particle dipole strength functions connected with the external fields, which are exploited in quantum random phase approximation approaches for studying the isoscalar and isovector resonances in nuclei, are found.
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.
We investigate the properties of a degenerate dilute gas of neutral fermionic particles in a harmonic trap that interact via dipole-dipole forces. We employ the semiclassical Thomas-Fermi method and discuss the Dirac correction to the interaction energy. A nearly analytic as well as an exact numerical minimization of the Thomas-Fermi-Dirac energy functional are performed in order to obtain the density distribution. We determine the stability of the system as a function of the interaction strength, the particle number, and the trap geometry. We find that there are interaction strengths and particle numbers for which the gas cannot be trapped stably in a spherically symmetric trap, but both prolate and oblate traps will work successfully.
The role of Pauli potentials in the semiclassical simulation of Fermi gases at low temperatures is investigated. An alternative Pauli potential to the usual bivariate Gaussian form by Dorso et al. is proposed. This new Pauli potential allows for a simultaneous good reproduction of not only the kinetic energy per particle but also the momentum distribution and the two-body correlation function. The reproduction of the binding energies in finite nuclei in the low and medium mass range is also analyzed. What is found is that given a reasonable short-range atractive nuclear interaction one can include correlation effects in a suitable chosen density dependent Pauli potential.
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.
We perform a random-phase approximation study of collective excitations in a Bose-Fermi mixed degenerate gas of alkali-metal atoms at T=0.T=0.T=0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of Bose and Fermi multipole (L) operators with L=0,1,2,3.L=0,1,2,3.L=0,1,2,3. Transition densities and dynamical structure factors are calculated for collective excitations. A comparison with the sum rule prediction for the collective frequency is given. The time dependent behavior of the system after an external impulse is studied.