Comparison of techniques for computing shell-model effective operators

Different techniques for calculating effective operators within the framework of the shell model using the same effective interaction and the same excitation spaces are presented. Starting with the large-basis no-core approach, we compare the time-honored perturbation-expansion approach and a model-space truncation approach. Results for the electric quadrupole and magnetic dipole operators are presented for ${}^6\mathrm{Li}$. The convergence trends and dependence of the effective operators on differing excitation spaces and Pauli $Q$-operators are studied. In addition, the dependence of the electric-quadrupole effective charge on the harmonic-oscillator frequency and the mass number, for $A=5,6\mathrm{}$, is investigated in the model-space truncation approach.