Systematics of characteristics of pygmy dipole resonances in medium-heavy and heavy atomic nuclei with neutron excess

The systematics of energies and the contribution of the pygmy dipole resonance (PDR) to the energy-weighted sum rule of dipole gamma transitions in medium-heavy and heavy nuclei with an excess of neutrons are considered. The modified macroscopic model of Isacker-Nagarajan-Warner was used for calculating PDR energies with the number of surface neutrons proportional to the thickness of the neutron skin according to the Pethick-Ravenhall expression (PR INW approach). Such modification of the macroscopic approach by Isacker-Nagarajan-Warner enables taking into account microscopic evidence of a direct relationship between skin thickness and low-energy dipole response. The results are compared with the microscopic calculations for the chains of Ni, Sn, and Pb isotopes. It was demonstrated that the dependence of the magnitudes of the energies within the PR INW approach on neutron excess is in rather good agreement with experimental data and microscopic calculations if the absolute value of the strength of the neutron-proton interaction is nearly three times as large as that obtained by Isacker-Nagarajan-Warner by the volume integral of the nucleon-nucleon interaction. While the macroscopic INW PR model can describe the main features of the PDR, the above-mentioned discrepancy of the strength values does not not provide reason enough for the conclusion that PDR is a pure collective state. The analytical expressions for the PDR fraction of the energy-weighted sum rule for electric dipole transitions (E1 EWSR) are used. They are based on the “molecular” energy-weighted E1 sum rule, considering the number of surface neutrons as a function of the neutron thickness (PR MSR approach). Systematics for the PDR fraction of E1 EWSR are proposed with parameters obtained by fitting the experimental data and microscopic calculations.