Center-of-mass Momentum Dependence of Short-Range Correlations with the Coarse-Grained Granada Potential

The effect of the center-of-mass motion on the high-momentum distributions of correlated nucleon pairs is studied by solving the Bethe-Goldstone equation in nuclear matter with the Granada nucleon-nucleon potential. We show that this coarse-grained potential reduces the problem to an algebraic linear system of five (ten) equations for uncoupled (coupled) partial waves that can be easily solved. The corresponding relative wave functions of correlated $pn, pp$, and $nn$ pairs are computed for different values of their center-of-mass (CM) momentum. We find that the $pn$ pairs dominate the high-momentum tail of the relative momentum distribution, and that this only depends marginally on center-of-mass momentum. Our results provide further justification and agreement for the factorization approximation commonly used in the literature. This approximation assumes that the momentum distribution of nucleon pairs can be factorized as the product of the center-of-mass momentum distribution and the relative momentum distribution.