Quantifying short-range correlations in nuclei

Abstract

Background Short-range correlations (SRC) are an important ingredient of the dynamics of nuclei.Purpose An approximate method to quantify the magnitude of the two-nucleon (2N) and three-nucleon (3N) short-range correlations (SRC) and their mass dependence is proposed.Method The proposed method relies on the concept of the "universality" or "local nuclear character" of the SRC. We quantify the SRC by computing the number of independent-particle model (IPM) nucleon pairs and triples which reveal beyondmean-field behavior. It is argued that those can be identified by counting the number of nucleon pairs and triples in a zero relative orbital momentum state. A method to determine the quantum numbers of pairs and triples in an arbitrary mean-field basis is outlined.Results The mass dependence of the 2N and 3N SRC is studied. The predictions are compared to measurements. This includes the ratio of the inclusive inelastic electron scattering cross sections of nuclei to 2 H and 3 He at large values of the Bjorken variable. Corrections stemming from the center-of-mass motion of the pairs are estimated.Conclusions We find that the relative probability per nucleon for 2N and 3N SRC has a soft dependence with mass number A and that the proton-neutron 2N SRC outnumber the proton-proton (neutron-neutron) 2N SRC. A linear relationship between the magnitude of the EMC effect and the predicted number of proton-neutron SRC pairs is observed. This provides support for the role of local nuclear dynamics on the EMC effect.

Quasifree (p,2p) and (p,pn)

“…On the other hand, momentum distributions should depend on the angular momentum of the single-particle state probed in the reaction, according to Eqs. (29), (31), and (33). Unless stated otherwise, we use spectroscopic factors equal to the unity for the sake of concentrating on the dependence on other physical inputs in the calculations.…”

“…But it is still useful for physical understanding of most results. Although (p,2p) reactions have been carried out with high-energy protons, only rather recently, eikonal waves, and the Glauber treatment of multiple scattering have been used to account for distortions and absorption [25][26][27][28][29]. One probable reason is that measurements have been carried out for large angle scattering and sometimes large energy transfer, conditions that invalidate the use of the eikonal approximation, although attempts along these lines have been tried already at very early studies of (p,2p) reactions [57,58].…”

“…Due to the nuclear spin-orbit coupling and absorption of the projectile and secondary protons in the nuclear matter the proton knocked out from a particular nuclear shell with orbital moment l = 0 can be polarized [1,2,[26][27][28][29].…”

High-momentum tails from low-momentum effective theories

“…In the standard interpretation, the idea of factorization between long-and short-distance physics follows from the presence of shortrange correlations between nucleon pairs, and has been applied to describe high-momentum tails of nuclear momentum distributions and spectral functions [11][12][13][14][15][16]. It will be interesting to connect the approach of the present work, in which factorization is ascribed to the RG decoupling of high-and low-momentum degrees of freedom and A-dependent scale factors are given by the low-momentum matrix element of a zero-range contact operator, to conventional approaches where factorization follows from short-range correlations and A-dependence is tied to the center-of-mass motion of the correlated pairs [11,13,14].…”

“…A prototypical example is the (e, e ′ p) process at large momentum transfers, where theoretical analyses relate such experiments to nuclear momentum distributions if the impulse approximation is assumed valid for a high-cutoff interaction [10]. Calculations find nearly universal scaling of the high-momentum tails of one-and two-body momentum distributions [11][12][13][14][15][16], which is interpreted in terms of short-range correlations in the nuclear wave functions [13][14][15][16][17][18]. Naively it might be thought that this physics is beyond the reach of low-momentum approaches, for which wave functions have drastically reduced short-range correlations.…”