Microscopic description of the pygmy and giant dipole resonances in even–even nuclei. Application to the isotopes 150,152,154,156,158,160Gd

This paper deals with a microscopic approach for the description of the pygmy dipole resonance (PDR) as well as of the giant dipole resonance (GDR). The formalism is based on a Hamiltonian which is summing a mean field term, the pairing for alike nucleons and the dipole–dipole interaction. Two features are specific for our description: (a) The use of a projected spherical single particle basis and (b) the involved dipole operator is a Schif-like operator including a corrective term which is cubic in the radial coordinate. The dipole strength distribution with energy is plotted for the PDR region, i.e., [0,10] MeV. The dominant transitions have an isovector character for three isotopes and isoscalar for another three. The PDR states carry only 0.4–1.8[Formula: see text] of the total EWSR. The dependence of the dipole strength on nuclear deformation is evidenced. For the whole interval of [0,20] MeV the dipole strength was first folded by Lorentzian of 1[Formula: see text]MeV width and then plotted as function of the QRPA energies. The peaks belonging to each of the two ranges are analyzed in detail and their nature, isovector/isoscalar, was pointed out. The r-cubic term and the nuclear deformation have opposite effects on the dipole strength. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new EWSR is very well satisfied. The photoabsorbtion cross-section is calculated and compared with experimental data in a figure showing its dependence on energy. The total cross-section, [Formula: see text], the moments of the integrated cross-sections, [Formula: see text], [Formula: see text], the dipole polarizability and the thickness of the neutron crust are also calculated. The main features of PDR and GDR are realistically described.