Preliminary Study on Uncertainty of Central Force and Effect of Cross-Shell Excitation in Shell Model

The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.