Pairing vibrational and isospin rotational states in a particle number and isospin projected generator coordinate method

Abstract

Pairing vibrational and isospin rotational states are described in different approximations based on particle number and isospin projected, proton-proton, neutron-neutron and proton-neutron pairing wave functions and on the generator coordinate method (GCM). The investigations are performed in models for which an exact group theoretical solution exists. It turns out that a particle number and isospin projection is essential to yield a good approximation to the ground state or isospin yrast state energies. For strong pairing correlations (pairing force constant equal to the single-particle level distance) isospin cranking (- ωT x ) yields with particle number projected pairing wave function also good agreement with the exact energies. GCM wave functions generated by particle number and isospin projected BCS functions with different amounts of pairing correlations yield for the lowest T = 0 and T = 2 states energies which are practically indistinguishable from the exact solutions. But even the second and third lowest energies of charge-symmetric states are still very reliable. Thus we conclude that also in realistic cases isospin rotational and pairing vibrational states may be described in the framework of the GCM method with isospin and particle number projected generating wave functions.