Systematics of pygmy dipole resonance energies in medium and heavy atomic nuclei with neutron excess

Systematics of the energies of the pygmy dipole resonances (PDR) in medium and heavy nuclei with neutron excess is considered. The macroscopic Isacker - Nagarajan - Warner model, incorporating a relative shift between the proton core density and the surface neutron density, is used to describe the PDR energies. Modified expressions for calculating energy with the number of near-surface neutrons proportional to the neutron skin thickness according to the Pethick - Ravenhall approach are presented. The results are compared with microscopic calculations for Nickel, Tin, and Lead isotope chains. It is demonstrated that the calculated PDR energies, depending on the neutron excess, exhibit the same behavior as those calculated in microscopic approaches and experimental data. Simple expressions for the PDR energy as a function of the neutron skin thickness are proposed to describe the values of PDR energies calculated using microscopic models and can be considered as systematics of microscopic calculations of PDR energies in medium and heavy neutron-rich nuclei.