Universality of nucleon-nucleon short-range correlations: The factorization property of the nuclear wave function, the relative and center-of-mass momentum distributions, and the nuclear contacts

Background: The two-nucleon momentum distributions of nucleons N1 and N2 in a nucleus A, nN1N2A(krel,Kc.m.), is a relevant quantity that determines the probability of finding two nucleons with relative momentum krel and center-of-mass (c.m.) momentum Kc.m.; at high values of the relative momentum and, at the same time, low values of the c.m. momentum, nN1N2A(krel,Kc.m.) provides information on the short-range structure of nuclei. Purpose: Our purpose is to calculate the momentum distributions of proton-neutron and proton-proton pairs in He3, He4, C12, O16, and Ca40, in correspondence to various values of krel and Kc.m.. Methods: The momentum distributions for A>4 nuclei are calculated as a function of the relative, krel, and center-of-mass, Kc.m., momenta and relative angle ?, within a linked cluster many-body expansion approach, based upon realistic local two-nucleon interaction of the Argonne family and variational wave functions featuring central, tensor, and spin-isospin correlations. Results: Independently of the mass number A, at values of the relative momentum krel?1.5-2 fm-1 the momentum distributions exhibit the property of factorization, nN1N2A(krel,Kc.m.)?nN1N2rel(krel)nN1N2c.m.(Kc.m.); in particular, for pn back-to-back pairs one has npnA(krel,Kc.m.=0)?CpnAnD(krel)npnc.m.(Kc.m.=0), where nD is the deuteron momentum distribution, npnc.m.(Kc.m.=0) the c.m. motion momentum distribution of the pair, and CpnA the pn nuclear contact measuring the number of back-to-back pn pairs with deuteron-like momenta (kp?-kn,Kc.m.=0). Conclusions: The values of the pn nuclear contact are extracted from the general properties of the two-nucleon momentum distributions corresponding to Kc.m.=0. The Kc.m.-integrated pn momentum distributions exhibit the property npnA(krel)?CpnAnD(krel) but only at very high values of krel, ?3.5-4 fm-1. The theoretical ratio of the pp/pn momentum distributions of He4 and C12 and the calculated c.m. motion momentum distributions are in agreement with recent experimental data.