Nuclear rho transparencies in a relativistic Glauber model

[Background] The recent Jefferson Lab data for the nuclear transparency in $\rho^ {0}$ electroproduction have the potential to settle the scale for the onset of color transparency (CT) in vector meson production. [Purpose] To compare the data to calculations in a relativistic and quantum-mechanical Glauber model and to investigate whether they are in accordance with results including color transparency given that the computation of $\rho$-nucleus attenuations is subject to some uncertainties. [Method] We compute the nuclear transparencies in a multiple-scattering Glauber model and account for effects stemming from color transparency, from $\rho$-meson decay, and from short-range correlations (SRC) in the final-state interactions (FSI). [Results] The robustness of the model is tested by comparing the mass dependence and the hard-scale dependence of the $A(e,e'p)$ nuclear transparencies with the data. The hard-scale dependence of the $(e,e' \rho ^ {0})$ nuclear transparencies for $^ {12}$C and $^ {56}$Fe are only moderately affected by SRC and by $\rho^ {0}$-decay. [Conclusions] The RMSGA calculations confirm the onset of CT at four-momentum transfers of a few (GeV/c)$^2$ in $\rho$ meson electroproduction data. A more precise determination of the scale for the onset of CT is hampered by the lack of precise input in the FSI and $\rho$-meson decay calculations.Comment: 18 pages, 5 figures. Revised version to appear in PRC. Minor corrections, added discussion and figure about CT parameters dependence. Results and conclusions remain the sam

Modeling final-state interactions with a relativistic multiple-scattering approximation

We address the issue of nuclear attenuation in nucleon and pion knockout reactions. A selection of results from a model based on a relativistic multiple-scattering approximation is presented. We show transparency calculations for pion electroproduction on several nuclei, where data are in very good agreement with calculations including color transparency. Secondly, we discuss the density dependence of reactions involving one or double proton knockout. The latter reaction succeeds in probing the high density regions in the deep interior of the nucleus.Comment: 6 pages, 4 figures, "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT$^*$, October 19-13 200

On the density dependence of single-proton and two-proton knockout reactions under quasifree conditions

We consider high-energy quasifree single- and two-proton knockout reactions induced by electrons and protons and address the question what target-nucleus densities can be effectively probed after correcting for nuclear attenuation (initial- and final-state interactions). Our calculations refer to ejected proton kinetic energies of 1.5 GeV, the reactions (e,e'p), (\gamma,pp) and (p,2p) and a carbon target. It is shown that each of the three reactions is characterized by a distinctive sensitivity to the density of the target nucleus. The bulk of the (\gamma,pp) strength stems from the high-density regions in the deep nuclear interior. Despite the strong attenuation, sizable densities can be probed by (p,2p) provided that the energy resolution allows one to pick nucleons from s orbits. The effective mean densities that can be probed in high-energy (e,e'p) are of the order of 30-50% of the nuclear saturation density.Comment: 10 pages, 2 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

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

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

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

Final-state interactions in two-nucleon knockout reactions

Background: Exclusive two-nucleon knockout after electroexcitation of nuclei ($A(e,e'NN)$ in brief) is considered to be a primary source of information about short-range correlations (SRC) in nuclei. For a proper interpretation of the data, final-state interactions (FSI) need to be theoretically controlled. Purpose: Our goal is to quantify the role of FSI effects in exclusive $A(e,e'pN)$ reactions for four target nuclei representative for the whole mass region. Our focus is on processes that are SRC driven. We investigate the role of FSI for two characteristic detector setups corresponding with a "small" and "large" coverage of the available phase space. Results: The transparency $T^{pN}_{A}$, defined as the ratio of exclusive $(e,e'pN)$ cross sections on nuclei to those on "free" nucleon pairs, drops from $0.2-0.3$ for $^{12}$C to $0.04-0.07$ for $^{208}$Pb. For all considered kinematics, the mass dependence of the $T^{pN}_{A}$ can be captured by the power law $T^{pN}_{A} \propto A^{- \lambda}$ with $0.4 \lesssim \lambda \lesssim 0.5$. Apart from an overall reduction factor, we find that FSI only modestly affects the distinct features of SRC-driven $A(e,e'pN)$ which are dictated by the c.m. distribution of close-proximity pairs. Conclusion: The SCX mechanisms represent a relatively small (order of a few percent) contribution of SRC-driven $A(e,e'pN)$ processes. The mass dependence of FSI effects in exclusive $A(e,e'pN)$ can be captured in a robust power law and is in agreement with the predictions obtained in a toy model

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"