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

Abstract

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, n, is a relevant quantity that determines the probability to find the two nucleons with relative momentum k rel and center-of-mass (c.m.) momentum Kc.m.; at large values of the relative momentum and, at the same time, small values of the c.m. momentum, nprovides information on the short-range structure of nuclei.Purpose: calculation of the momentum distributions of proton-neutron and proton-proton pairs in 3 He, 4 He, 12 C, 16 O and 40 Ca, in correspondence of various values of k rel and Kc.m.. Methods: the momentum distributions for A > 4 nuclei are calculated as a function of the relative, k rel , and center of mass, Kc.m., momenta and relative angle Θ, 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 k rel > ∼ 1.5 ∼ 2f m −1 the momentum distributions exhibit the property of factorization, n I. AIM AND INTRODUCTIONThe investigation of short-range correlations (SRCs) in nuclei is ultimately aimed at unveiling the details of in-medium short-range nucleon-nucleon (NN) dynamics, a relevant physics issue that cannot be answered by scattering experiments of two free nucleons (see recent review papers on the subject [1-5]). A reliable way to gather information on SRCs would be to detect significant deviations of proper experimental data (e.g. electrodisintegration processes off nuclei) from theoretical predictions based upon ab initio solutions of the nuclear many-body problem, obtained from various NN interactions differing in the short-range part. In practice such an approach faces several problems because it implies the ex- *

Variational calculation of the ground state of closed-shell nuclei up to A=40

“…At higher momentum, the tail of n N (k) manifests the expected universal behavior determined by the short-range correlations, i.e., by the short-range structure of the employed Hamiltonian, as shown in Fig. 14 and discussed at length in a number of other works [24,53,59,62]. Such universality refers to the independence of the tail with respect to the specific nucleus.…”

“…With these definitions, ρ N (r) is normalized to the number of protons or neutrons, and ρ NN to the number of pp, np or nn pairs. Note that for some of the alternative expansion schemes normalization is ensured order-by-order by construction (either defining a "number conserving" expansion [24,[51][52][53], or requiring a normalization factor [54]). In our expansion scheme, the central oneand two-body densities are properly normalized orderby-order.…”

“…The cluster expansion drastically reduces the computational effort necessary for the study of an Abody system, and it enables the study of medium-mass nuclei. Another approach based on a cluster expansion of nuclear correlations has been recently used to study the high-momentum components of nuclear wave functions (see [24] and references therein). This work, not based on Monte Carlo techniques, has been carried out employing two-body nuclear interactions only and limiting the cluster expansion to the leading order.…”

The nuclear contacts and short range correlations in nuclei

“…These, and results of theoretical studies, indicate that the high-momentum (k > k F ) tail of the nuclear momentum distribution is dominated by SRC and described using a factorized wave function for the c.m. and relative momentum distributions of the pairs which results in similar two-body densities for different nuclei [22][23][24][25][49][50][51][52][53][54]. For recent reviews see [8,55].…”

Single- and two-nucleon momentum distributions for local chiral interactions

“…culations of single-and two-nucleon momentum distributions [9,12,14,15]. These currents provide a 30 − 40% constructive interference in the inclusive transverse quasielastic electron scattering [32] and in the axial response relevant to neutrino scattering [33].…”