Applicability of the Hartree-Fock (HF) based random phase approximation (RPA) with
several Skyrme effective interactions to the description of the isoscalar giant monopole
(ISGMR) and the isoscalar giant dipole resonance (ISGDR) in 90Zr, 116Sn, 144Sm and
208Pb nuclei has been investigated. The existing Skyrme interactions SL1, SkM*, SGII,
Sly4 and Sk255 were used. Hartree-Fock description of the ground state properties of all
nuclei of interest was obtained using these Skyrme interactions.
Transition strength distributions for the ISGMR and the ISGDR in nuclei of interest
were calculated using coordinate space representation for the RPA in the Green's
function formalism with discretized continuum. A method of projecting out the spurious
state contribution from the transition strength distribution and the transition density of
the ISGDR was employed to eliminate spurious state mixing, due to a not fully selfconsistent
description of the particle-hole interaction within the RPA.
Differential cross sections of 240 MeV alpha-particles inelastic scattering on all nuclei of
interest were calculated using the folding model within the distorted wave Born
approximation (DWBA). Optical potentials were obtained by folding HF ground state
densities with a alpha-nucleon density dependent Gaussian interaction. Parameters of the
interaction were obtained by fitting experimental angular distribution of alpha-nucleus
The inelastic differential cross sections were calculated using both collective and
microscopic transition densities. Possible underestimations of the energy weighted sum
rule for the case of the ISGDR are reported. An alternative description for the ISGDR in nuclei based on the Fermi liquid drop
model (FLDM) with the collisional Fermi surface distortion was investigated. The
FLDM dispersion relation was obtained from the linearized Landau-Vlasov equation.
Centroid energies, E0 and E1, and widths, gamma-0 and gamma-1, of the ISGMR and ISGDR,
respectively, were calculated as functions of the damping parameter using appropriate
boundary conditions. Comparison of the theoretical ratios of the ISGDR and ISGMR
centroid energies, E1/E0, to the experimental values resulted in a damping parameter
equal to 0.5, however, systematic overestimation of energy of the ISGMR and ISGDR
by 2.0-2.5 MeV was observed. The applicability of the HF-RPA to the description for
the ISGDR in nuclei is confirmed.
- Shlomo, Shalom Senior Scientist