Pairing correlations and simultaneous projection of particle number and angular momentum in light nuclei

Abstract

The Hartree-Bogolubov theory with simultaneous projection on sharp angular momentum quantum number and sharp particle number is presented as a description of the ground state rotational bands of doubly even nuclei. Calculations with effective G-matrix elements of the Hamada-Johnston potential and also of the Yale potential have been performed within this framework for the nuclei 20Ne, 22Ne, 24Ne, 24Mg, 26Mg, 28Si, 30Si, 32S and 34S. Rotational energies, moments of inertia, pairing correlations, quadrupole moments and B(E2) values are discussed and compared with available experimental data. The effect of particle number fluctuation on the ground state rotational spectrum and on the intrinsic wave function is investigated. The particle number projection turns out to be important for the description of the rotational levels, whereas it has only a negligible effect on the properties of the intrinsic wave function. Comparison with Hartree-Fock results and with experimental data shows that the inclusion of pairing correlations provides a significant improvement on the excitation energies, their relative ratios and the angular momentum dependence of the moments of inertia. All solutions show an antistretching effect in the quadrupole moments and especially in the B(E2) values. The rotational bands in 20Ne, 22Ne, 24Ne and 28Si turn out to be well described in the framework presented.