Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes ^{144,148,150,152,154}Sm

Abstract

A many body Hamiltonian consisting in a spherical shell model mean field term, a pairing interaction for alike nucleons and a dipole-dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, is studied within a quasiparticle random phase approximation (QRPA) and applied numerically to five even-even isotopes of Sm. The resulting wave functions are further used to calculate the B(E1) values which at their turn are employed to calculate the photo absorption cross section, the integrated moments of the cross section and the energy weighted sum rule (EWSR). The calculated cross section and its integrated moments are compared with the available data and a good agreement is pointed out. One distinguishes two regions
corresponding to the Pygmy Dipole Resonance (PDR), 1-10 MeV, and to the Giant Dipole Resonance (GDR), 10-20 MeV respectively, these being separately studied. The peaks belonging to each of the two ranges are in detail analyzed. The PDR states are located around the neutron separation energy and are mainly formed of collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutrons excess against the protons from the isospin saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8-2.7$\%$ of the total EWSR and 0.4-5.9$\%$ of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section split into two branches for deformed isotopes, is included. The r-cubic term and the nuclear deformation have opposite effect on the dipole strength. Also it diminishes the effect of the non-conservation of the center of mass momentum. The famous Thomas Reiche Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single particle basis used in our formalism allows for an unified description of the spherical transitional and deformed isotopes.