Nuclear shell model calculations of the effective interaction and other effective operators

Recent breakthroughs in effective interaction and effective operator techniques allow us to take a new look at this field that has seen limited progress in the past twenty years. A comparison of the old and new techniques will shed some new light on the use of effective interactions and effective operators in shell model calculations of light nuclei. Three different methods of calculating the effective interaction and effective operators are described and compared. A large model-space no-core shell-model calculation for ⁶Li is used as the basis for comparison. In the no-core calculation all nucleons are active in a model space involving all configurations with energies up to 8ħΩ. The second method is a perturbation expansion for the effective interaction and effective operators, using an inert ⁴He core and two valence particles. In particular, the electric quadrupole and magnetic dipole operators are studied to determine the effective charges to be used in connection with one-body operators in this shell-model space. The third method is a model-space truncation scheme, which maps operators in a large model space into operators in smaller, truncated model spaces. The effect of going to larger excitation spaces will be examined as well as the convergence trends regarding increases in the excitation space. The results from these three approaches are compared in order to gain new insight into the nature of effective interactions and operators in truncated model spaces. We find that by going to energies of 8ħΩ we can accurately reproduce the experimental values for the binding energy, excitation spectrum, electric quadrupole moment and magnetic dipole moment of ⁶Li and that there is a definite model-space dependence for these operators. To obtain results similar to the 8ħΩ ones in a truncated 2ħΩ model space we use effective operators and effective charges. Effective charges of approximately 1.1e for the effective proton charge and 0.3e for the effective neutron charge are obtained in the perturbation-expansion technique, while the model-space truncation calculations yield effective charges of 1.5e for the proton and.36e for the neutron. These values can be compared with empirically obtained values of eᵖ(eff) ≈ 1.5e and eⁿ(eff) ≈ 0.5e