Shell model with realistic forces: spectra and the effects of correlations in A = 6 nuclei

Abstract

Correlated wave functions that describe the motion of two nucleons outside an inert core are found by solving the coupled integro-differential equations describing the shell-model problem. The eigenvalues that emerge from the solution of this problem give the two-particle interaction energies relative to the closed shell, and the eigenfunctions contain all possible two-particle correlations that arise from exciting valence nucleons to states outside the Fermi sea. The theory is applied to 6Li, and reasonable agreement with experiment is found when the Hamada-Johnston potential is used for the residual two-body force. The quantities compared with experiment are level scheme, E2 transition rates, M1 transition rates, and in 6Be, the Coulomb energy of the two valence nucleons. It is argued that better agreement with experiment would emerge if the tensor component of the Hamada-Johnston potential were weakened. The variation of the effective-interaction matrix elements with both the single-particle level scheme and the oscillator constant ħω is examined. This approach is shown to be equivalent to a reformulation of the Bloch-Horowitz theory in which not only the “model-space” states but also all other states allowed by the exclusion principle are treated on an equal footing.