Exploring Correlations in Exotic Nuclei

Abstract

The difference in neutron total cross section between 40 Ca and 48 Ca is sensitive to the n/p asymmetry dependence of the surface imaginary potential in a dispersive optical model analysis, from which spectroscopic information can be extracted. The measured cross sections imply that the strength of neutron correlations changes little as neutron number increases in neutron-rich isotopes. In contrast, for the light-nucleus-induced knockout of the valence neutron in 36 Ca, the small experimental knockout cross section (as compared to an eikonal reaction theory) implies a very small spectroscopic factor (and a strong trend in correlations with asymmetry). If this type of knockout analysis is correct, it implies that standard shellmodel calculations miss spectroscopic strength as the Fermi energy nears the continuum. If this is not the case, it may be that there is a problem with the application of the eikonal theory to very deeply bound nucleons at these intermediate energies. The term correlations refers to interactions between nucleons that go beyond the mean field considered in an independent-particle-model (IPM) approach. The effect of these correlations is that in real nuclei, the spectroscopic strength of a singleparticle orbital is fragmented over energy. The spectroscopic factor (SF) quantifies the strength found at a discrete energy, and the sum of spectroscopic strength over all energies below the Fermi energy EF gives the occupation of the orbital. Correlations reduce the occupation of a single-particle state relative to its IPM value, since some of the fragmented spectroscopic strength is shifted above EF . The nuclear shell model (SM) can account for some of these correlations by including mixing between single-particle states (within a finite basis set). But due to the finite model space, the presence of the hard-core of the N-N interaction, and the tensor interaction (which further reduce the occupancies by shifting strength to high-momentum states), standard SM calculations still overestimate the occupancies of bound states. The reduction in occupancy due to correlations is not a direct experimental observable, but it will affect particle removal cross sections. By comparing experimental cross sections to calculated single-particle cross sections, one can learn about the strength of correlations. Electron-induced proton knockout (e,e’p) experiments have indicated a roughly constant 30% reduction in spectroscopic strength for valence protons in beta-stable nuclei. For unstable nuclei, light-nucleus-induced knockout experiments in inverse kinematics suggest that the affect of correlations is weaker for weakly-bound nucleons and much stronger for very deeply-bound nucleons (e.g.