Residual Interaction Effect on Isoscalar Dipole Modes in Heavy Nuclei

Abstract

Isoscalar collective dipole excitations in heavy nuclei have been studied in the framework of the kinetic model for small vibrations in a finite Fermi system with a moving surface. An analytical expression for the second-order isoscalar response function of the dipole moment is obtained taking the residual interaction between nucleons into account in the separable approximation. It is shown that the inclusion of the residual interaction does not violate the translation invariance of the model. The strength function has a two-resonance structure, like in the zeroth-order approximation (i.e. neglecting the residual interaction). The account for the isoscalar dipole residual interaction decreases the compressibility of a system and shifts the resonances toward low frequencies, which improves the agreement with experimental data for both low-and highenergy isoscalar dipole modes in heavy nuclei.

Nature of Isoscalar Dipole Resonances in Heavy Nuclei

“…We consider the isoscalar dipole excitations of nuclei within a kinetic model, which is based on the Vlasov equation for finite Fermi systems with moving surface [14,[20][21]. In this model, a nucleus is treated as a gas of interacting fermions confined to a spherical cavity with moving surface.…”

“…where (3) ( ) = 3 is the second-order dipole moment, ( ) is the Dirac delta-function in time, and is a parameter that describes the external field strength. Our model is the translation-invariant [14,21] therefore the external field (1) does not excite the center of mass. We take into account the residual interaction between nucleons by using a separable effective interaction of the dipole-dipole type [21].…”

“…Our model is the translation-invariant [14,21] therefore the external field (1) does not excite the center of mass. We take into account the residual interaction between nucleons by using a separable effective interaction of the dipole-dipole type [21]. Within our kinetic model, we can find the explicit expression for the fluctuation of the phase-space distribution function related to the collective isoscalar dipole excitations.…”

“…Within our kinetic model, we can find the explicit expression for the fluctuation of the phase-space distribution function related to the collective isoscalar dipole excitations. By using this function, we can calculate the response function [21] as well as the local dynamical quantities, in particular, the velocity field. In our kinetic model, the time Fourier-transform of the velocity field in the linear approximation is determined as 0 1 ( , ) ( , , ) u r dp p n r p m…”

“…In Ref. [21], the isoscalar dipole response function was studied within the kinetic model [20], taking into account a residual interaction between nucleons. It was found that the response function has two-resonance structure and reproduces the experimental values for the centroid energies of the low-and high-energy isoscalar dipole resonances in heavy nuclei.…”