Effective operators within theab initiono-core shell model

We implement an effective operator formalism for general one- and two-body operators, obtaining results consistent with the no-core shell model (NCSM) wave functions. The Argonne V8’ nucleon-nucleon potential was used in order to obtain realistic wave functions for ${}^4\mathrm{He},{}^6\mathrm{Li}$, and ${}^{12}\mathrm{C}$. In the NCSM formalism, we compute electromagnetic properties using the two-body cluster approximation for the effective operators and obtain results which are sensitive to the range of the bare operator. To illuminate the dependence on the range, we employ a Gaussian two-body operator of variable range, finding weak renormalization of long range operators (e.g., quadrupole) in a fixed model space. This is understood in terms of the two-body cluster approximation which accounts mainly for short-range correlations. Consequently, short-range operators, such as the relative kinetic energy, will be well renormalized in the two-body cluster approximation.