Semi-empirical description of low energy nuclear collective states

Abstract

The low-lying collective quadrupole and octupole states in spherical nuclei are described as superpositions of quasi-particle excitations coupled to the isoscalar L = 2 or L = 3 giant resonance states, identified as the coherent states of the nucleus with angular momenta L = 2 and 3, respectively. The scheme can also be interpreted as an economical way of performing RPA calculations. The energy density method provides all the necessary ingredients so that the model is in principle free of adjustable parameters. The double counting problem is handled by requiring the energy weighted sum rule to be fullfilled “after diagonalization.” The calculations have been made for closed shell nuclei, as well as for the Samarium-isotopes. The bulk properties of low-lying levels are reproduced. The model predicts interesting features for the proton and neutron transition densities.