Isoscalar Giant Dipole Resonance and Nuclear Matter Incompressibility Coefficient

Studies of compression modes of nuclei are of particular interest since their strength distributions, S(E), are sensitive to the value of the nuclear matter incompressibility coefficient, K [1]. At present, Hartree-Fock (HF) based random-phase-approximation(RPA) calculations for the isoscalar giant monopole resonance (ISGMR) reproduce the experimental data for effective interactions associated with incompressibility K = 210 ± 20 MeV. The study of the isoscalar giant dipole resonance (ISGDR) is very important since this compression mode provides an independent source of information on K. Early experimental attempts to identify the ISGDR in Pb resulted with a value of E1 ~ 21 MeV for the centroid energy. Very recent and more accurate data on the ISGDR obtained at our Cyclotron Institute for a wide range of nuclei seems to indicate that the experimental values for E1 are smaller than the corresponding HF-RPA results by 3–5 MeV. This discrepancy between theory and experiment raises doubts concerning the unambiguous extraction of K from energies of compression modes. In this work we address this discrepancy between theory and experiment by examining the relation between the strength function S(E) and the excitation cross section σ (E) of the ISGDR, obtained by ∀-scattering. We emphasize that it is quite common in theoretical work on giant resonance to calculate S(E) for a certain scattering operator F whereas in the analysis of experimental data of σ (E) one carries out distorted-wave-Born-approximation (DWBA) calculations with a certain transition potential. Here we present results of accurate microscopic calculations for S(E) and for ) (E σ with the folding model (FM) DWBA with transition densities ∆t(r) obtained from HF-RPA calculations and suggest a simple explanation for the discrepancy between theory and experiment concerning the ISGDR. In self-consistent HF-RPA calculation one starts by adopting specific effective nucleon-nucleon interaction, V12, carries out the HF calculation for the ground state of the nucleus and then solves the RPA equation using the particle-hole (p-h) interaction Vph which corresponds to V12. The RPA Green's function G is obtained from