Quantifying short-range correlations in nuclei

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 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 beyond-mean-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 H-2 and He-3 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

Stylized features of single-nucleon momentum distributions

Nuclear short-range correlations (SRC) typically manifest themselves in the tail parts of the single-nucleon momentum distributions. We propose an approximate practical method for computing those SRC contributions to the high-momentum parts. The framework adopted in this work is applicable throughout the nuclear mass table and corrects mean-field models for central, spin-isospin and tensor correlations by shifting the complexity induced by the SRC from the wave functions to the operators. It is argued that the expansion of these modified operators can be truncated to a low order. The proposed model can generate the SRC-related high-momentum tail of the single-nucleon momentum distribution. These are dominated by correlation operators acting on mean-field pairs with vanishing relative radial and angular-momentum quantum numbers. The proposed method explains the dominant role of proton-neutron pairs in generating the SRC and accounts for the magnitude and mass dependence of SRC as probed in inclusive electron scattering. It also provides predictions for the ratio of the amount of correlated proton-proton to proton-neutron pairs which are in line with the observations. In asymmetric nuclei, the correlations make the average kinetic energy for the minority nucleons larger than for the majority nucleons.Comment: 19 pages, 8 figure

Mass dependence of short-range correlations in nuclei and the EMC effect

An approximate method to quantify the mass dependence of the number of two-nucleon (2N) short-range correlations (SRC) in nuclei is suggested. The proposed method relies on the concept of the "local nuclear character" of the SRC. We quantify the SRC and its mass dependence by computing the number of independent-particle model (IPM) nucleon pairs in a zero relative orbital momentum state. We find that the relative probability per nucleon for 2N SRC follows a power law as a function of the mass number $A$. The predictions are connected to measurements which provide access to the mass dependence of SRC. First, the ratio of the inclusive inelastic electron scattering cross sections of nuclei to $^{2}$H at large values of the Bjorken variable. Second, the EMC effect, for which we find a linear relationship between its magnitude and the predicted number of SRC-prone pairs.Comment: 12 pages, 4 figures, preprint proceeding Thirty First International Workshop on Nuclear Theory (IWNT31-2012), organized by the Nuclear Theory Laboratory of the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Science

Mass dependence of nuclear short- range correlations and the EMC effect

We sketch an approximate method to quantify the number of correlated pairs in any nucleus $A$. It is based on counting independent-particle model (IPM) nucleon-nucleon pairs in a relative $S$-state with no radial excitation. We show that IPM pairs with those quantum numbers are most prone to short-range correlations and are at the origin of the high-momentum tail of the nuclear momentum distributions. Our method allows to compute the $a_2$ ratios extracted from inclusive electron scattering. Furthermore, our results reproduce the observed linear correlation between the number of correlated pairs and the magnitude of the EMC effect. We show that the width of the pair center-of-mass distribution in exclusive two-nucleon knockout yields information on the quantum numbers of the pairs.Comment: 4 pages, 2 figures, 1 table. Based on a talk given at INPC 2013 (Firenze, June 2-7 2013). Minor changes in the text. Accepted for publication in EPJ Web of conference

Counting the number of correlated pairs in a nucleus

We suggest that the number of correlated nucleon pairs in an arbitrary nucleus can be estimated by counting the number of proton-neutron, proton-proton, and neutron-neutron pairs residing in a relative $S$ state. We present numerical calculations of those amounts for the nuclei $^{4}$He, $^{9}$Be, $^{12}$C, $^{27}$Al, $^{40}$Ca, $^{48}$Ca, $^{56}$Fe, $^{63}$Cu, $^{108}$Ag, and $^{197}$Au. The results are used to predict the values of the ratios of the per-nucleon electron-nucleus inelastic scattering cross section to the deuteron in the kinematic regime where correlations dominate.Comment: 11 pages, 3 figure

Factorization of exclusive electroinduced two-nucleon knockout

We investigate the factorization properties of the exclusive electroinduced two-nucleon knockout reaction $A(e,e'pN)$. A factorized expression for the cross section is derived and the conditions for factorization are studied. The $A(e,e'pN)$ cross section is shown to be proportional to the conditional center-of-mass (c.m.) momentum distribution for close-proximity pairs in a state with zero relative orbital momentum and zero radial quantum number. The width of this conditional c.m. momentum distribution is larger than the one corresponding with the full c.m. momentum distribution. It is shown that the final-state interactions (FSIs) only moderately affect the shape of the factorization function for the $A(e,e'pN)$ cross sections. Another prediction of the proposed factorization is that the mass dependence of the $A(e,e'pp)$ $[A(e,e'pn)]$ cross sections is much softer than $\frac{Z(Z-1)}{2}$ $[NZ]$.Comment: 12 pages, 11 figures, 2 tables. Accepted for publication in PRC. Small differences in discussion throughout article ("scaling" replaced by "factorization"

What densities can be effectively probed in quasifree single-nucleon knockout reactions?

We address the issue whether quasifree single-nucleon knockout measurements carry sufficient information about the nuclear interior. To this end, we present comparisons of the reaction probability densities for $A(e,e'p)$ and $A(p,2p)$ in quasifree kinematics for the target nuclei $^{4}$He, $^{12}$C, $^{56}$Fe, and $^{208}$Pb. We adopt a comprehensive framework based on the impulse approximation and on a relativized extension of Glauber multiple-scattering reaction theory in which the medium effects related to short-range correlations (SRC) are implemented. It is demonstrated that SRC weaken the effect of attenuation. For light target nuclei, both the quasifree $(p,2p)$ and $(e,e'p)$ can probe average densities of the same order as nuclear saturation density $\rho_{0}$. For heavy nuclei like $^{208}$Pb, the probed average densities are smaller than $0.1\rho_{0}$ and the $(e,e'p)$ reaction is far more efficient in probing the bulk regions than $(p,2p)$.Comment: 11 pages, 12 figure

Does General Parenting Context Modify Adolescents' Appraisals and Coping with a Situation of Parental Regulation? The Case of Autonomy-Supportive Parenting

Theory and research suggest that adolescents differ in their appraisals and coping reactions in response to parental regulation. Less is known, however, about factors that determine these differences in adolescents’ responses. In this study, we examined whether adolescents' appraisals and coping reactions depend upon parents’ situation-specific autonomy-supportive or controlling communication style (i.e., the situation) in interaction with adolescents’ past experiences with general autonomy-supportive parenting (i.e., the parenting context). Whereas in Study 1 (N = 176) adolescents’ perceived general autonomy-supportive parenting context was assessed at one point in time, in Study 2 (N = 126) it was assessed multiple times across a 6-year period, allowing for an estimation of trajectories of perceived autonomy-supportive parenting context. In each study, adolescents read a vignette-based scenario depicting a situation of maternal regulation (i.e., a request to study more), which was communicated in either an autonomy-supportive or a controlling way. Following this scenario, they reported upon their appraisals and their anticipated coping reactions. Results of each study indicated that both the autonomy-supportive (relative to the controlling) situation and the perceived autonomy-supportive parenting context generally related to more positive appraisals (i.e., more autonomy need satisfaction, less autonomy need frustration), as well as to more constructive coping responses (i.e., less oppositional defiance and submission, more negotiation and accommodation). In addition, situation × context interactions were found, whereby adolescents growing up in a more autonomy-supportive context seemed to derive greater benefits from the exposure to an autonomy-supportive situation and reacted more constructively to a controlling situation