Long- and short-range correlations in the ab-initio no-core shell model

In the framework of the ab-initio no-core shell model (NCSM), we describe the longitudinal-longitudinal distribution function, part of the inclusive (e,e') longitudinal response. In the two-body cluster approximation, we compute the effective operators consistent with the unitary transformation used to obtain the effective Hamiltonian. When short-range correlations are probed, the results display independence from the model space size and length scale. Long-range correlations are more difficult to model in the NCSM and they can be des-cribed only by increasing the model space or increasing the cluster size. In order to illustrate the model space independence for short-range observables, we present results for a large set of model spaces for 4He, and in 0-4(ℎ/2π)Ω model spaces for 12C