The nucleon properties and structure should be modified by short-range correlations (SRC) among nucleons. By analyzing SRC ratio data, we extract the mass of nucleon in the SRC pair and the expected number of pn-SRC pairs in deuterium, under the assumption that the SRC nucleon mass is universal in different nuclei. The nucleon mass of a two-nucleon SRC pair is $m_{\text{SRC}}=852\pm 18$ MeV, and the number of pn-SRC pairs in deuterium is $n^{\text{d}}_{\text{SRC}}=0.021\pm 0.005$. The mass deficit of the strongly overlapping nucleon can be explained by the trace anomaly contribution to the mass in QCD or alternatively by the vacuum energy in the MIT bag model.
In this paper, we examine the hypothesis that the nuclear EMC effect comes merely from the N-N SRC pairs inside the nucleus and that the properties of N-N SRC pair are universal among the various nuclei, using the conventional $x$-rescaling model for the EMC effect. With the previously determined effective mass of the short-range correlated nucleon and the number of N-N SRC pairs estimated, we calculate the EMC effect of various nuclei within the $x$-rescaling approach. From our calculations, the nuclear EMC effect due to the mass deficits of the SRC nucleons is not enough to reproduce the obs…
We investigate collective multipole excitations for closed shell nuclei from 16O to 208Pb using correlated realistic nucleon -nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations a re treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phase-shift equivalent correlated interaction V_UCOM adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using V_UCOM we sol…
A microscopic model for the $N\bar N\toππ$ process is presented in the meson exchange framework, which in the pseudophysical region agrees with available quasiempirical information. The scalar ($σ$) and vector ($ρ$) piece of correlated two--pion exchange in the pion--nucleon interaction is then derived via dispersion integrals over the unitarity cut. Inherent ambiguities in the method and implications for the description of pion--nucleon scattering data are discussed.
The influence of nucleon-nucleon short-ranged correlations (SRC) on nuclear super-allowed $β$ decay is examined. The need for this is driven by the observed depletion of spectroscopic strength obtained in studies of $(e,e')$ and $(d,^3{\rm He})$ reactions on a wide variety of nuclei. We show that the influence of SRC is model-dependent, but may be very substantial. The $^{46}$V nucleus is used as an example. The resulting impact on studies of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element is discussed.
Short-Range Correlated (SRC) nucleon pairs are a vital part of the nucleus, accounting for almost all nucleons with momentum greater than the Fermi momentum (kF). A fundamental characteristic of SRC pairs is having large relative momenta as compared to kF, and smaller center-of-mass (c.m.) which indicates a small separation distance between the nucleons in the pair. Determining the c.m. momentum distribution of SRC pairs is essential for understanding their formation process. We report here on the extraction of the c.m. motion of proton-proton (pp) SRC pairs in Carbon and, for the first time i…
This article reviews our current understanding of how the internal quark structure of a nucleon bound in nuclei differs from that of a free nucleon. We focus on the interpretation of measurements of the EMC effect for valence quarks, a reduction in the Deep Inelastic Scattering (DIS) cross-section ratios for nuclei relative to deuterium, and its possible connection to nucleon-nucleon Short-Range Correlations (SRC) in nuclei. Our review and new analysis (involving the amplitudes of non-nucleonic configurations in the nucleus) of the available experimental and theoretical evidence shows that the…
We present a novel scheme for nuclear structure calculations based on realistic nucleon-nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the Unitary Correlation Operator Method (UCOM). Short-range central and tensor correlations are imprinted into simple, uncorrelated many-body states through a state-independent unitary transformation. Applying the unitary transformation to the realistic Hamiltonian leads to a correlated, low-momentum interaction, well suited for all kinds of many-body models, e.g., Hartree-Fock…
We develop a new approach to production of the spectator nucleons in the heavy ion collisions. The energy transfer to the spectator system is calculated using the Monte Carlo based on the updated version of our generator of configurations in colliding nuclei which includes a realistic account of short-range correlations in nuclei. The transferred energy distributions are calculated within the framework of the Glauber multiple scattering theory, taking into account all the individual inelastic and elastic collisions using an independent realistic calculation of the potential energy contribution…
A linear correlation is found between the magnitude of nucleon-nucleon short-range correlations and the nuclear binding energy per nucleon with pairing energy removed. By using this relation, the strengths of nucleon-nucleon short-range correlations of some unmeasured nuclei are predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon short-range correlations are made. The found nuclear dependence of nucleon-nucleon short-range correlations may shed some lights on the short-range structure of nucleus.
The atomic nucleus is made of protons and neutrons (nucleons), that are themselves composed of quarks and gluons. Understanding how the quark-gluon structure of a nucleon bound in an atomic nucleus is modified by the surrounding nucleons is an outstanding challenge. Although evidence for such modification, known as the EMC effect, was first observed over 35 years ago, there is still no generally accepted explanation of its cause. Recent observations suggest that the EMC effect is related to close-proximity Short Range Correlated (SRC) nucleon pairs in nuclei. Here we report the first simultane…
Several recent studies have dealt with the effects of short range correlations on the momentum distribution of nucleons in nuclei. Here we investigate the correlation effects on the density and spectral distribution in coordinate space. A combination of experimental data and spectral functions calculated from realistic N-N interactions allows us to resolve a recently uncovered discrepancy with occupation of quasi-particle states derived from (e,e'p) data.
Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}\gtrsim 2\,\,fm^{-1}$ and small values of ${K}_{CM} \lesssim 1.0\,\,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short ra…
Different types of high-energy hadron-nucleus cross sections are discussed emphasizing the role played by Nucleon-Nucleon (NN) Short-Range Correlations (SRC) and Gribov Inelastic Shadowing (IS)
The target-mass number dependence of nucleon-nucleon pairs with short-range correlations is explored in a physically transparent geometrical model within a zero-range approximation. The observed $A$ dependence of 2-nucleon ejection cross sections in $(e,e')$ reactions is found to reflect the mass dependence of nuclear density distributions. A parametrization of this $A$ dependence is given. The $A$ dependence of proton-proton vs.\ proton-neutron pairs relative to $^{12}$C is also analyzed in this model. It can be understood using simple combinatorics without any additional isospin dependence.
We derive the cross-section for exclusive vector meson production in high energy deeply inelastic scattering off a deuteron target that disintegrates into a proton and a neutron carrying large relative momentum in the final state. This cross-section can be expressed in terms of a novel gluon Transition Generalized Parton Distribution (T-GPD); the hard scale in the final state makes the T-GPD sensitive to the short distance nucleon-nucleon interaction. We perform a toy model computation of this process in a perturbative framework and discuss the time scales that allow the separation of initial …
A finite temperature model of strongly correlated nucleons with underlying isospin symmetries is developed. The model can be used to study the role of bound states and Feshbach resonances on the thermal properties of a spin 1/2, isospin 1/2 system of protons and neutrons by varying the proton fraction. An analysis of features associated with a universal thermodynamic limit or unitary limit is given. In the limit of very large scattering length, the effective range to quantum thermal wavelength appears as a limiting scale in an interaction energy and equation of state.
Despite the progress made in understanding the NN interactions at long distances based on effective field theories, the understanding of the dynamics of short range NN interactions remains as elusive as ever. One of the most fascinating properties of short range interaction is its repulsive nature which is responsible for the stability of strongly interacting matter. The relevant distances, $\le 0.5$ fm, in this case are such that one expects the onset of quark-gluon degrees of freedom with interaction being dominated by QCD dynamics. We review the current status of the understanding of the QC…
Based on the Hugenholtz-Van Hove theorem, the symmetry energy $J$ and its density slope parameter $L$ are decomposed in terms of the nucleon self-energies within the covariant density functional (CDF) theory. It is found that two structural connections between the different ingredients of $J$ and $L$ construct the fundamental correlation between $L$ and $J$ in the relativistic covariant framework, while the additional contribution from the isovector scalar channel of nucleon-nucleon interaction and those from the second-order symmetry self-energies lead to a deviation, especially the latter li…
By analyzing recent microscopic many-body calculations of few-nucleon systems and complex nuclei performed by different groups in terms of realistic nucleon-nucleon (NN) interactions, it is shown that NN short-range correlations (SRCs) have a universal character, in that the correlation hole that they produce in nuclei appears to be almost A-independent and similar to the correlation hole in the deuteron. The correlation hole creates high-momentum components, missing in a mean-field (MF) description and exhibiting several scaling properties and a peculiar spin-isospin structure. In particular,…
We study the properties of hypernuclei containing one lambda hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of lambda hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the lambda particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani lambda-nucleon potential are adopted. The effect o…
We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.
A theory of short-range correlations in two-nucleon removal due to elastic breakup (diffraction dissociation) on a light target is developed. Fingerprints of these correlations will appear in momentum distributions of back-to-back emission of the nucleon pair. Expressions for the momentum distributions are derived and calculations for reactions involving stable and unstable nuclear species are performed. The signature of short-range correlations in other reaction processes is also studied.
The deep inelastic scattering cross section for scattering from bound nucleons differs from that of free nucleons.This phenomena, first discovered 30 years ago, is known as the EMC effect and is still not fully understood. Recent analysis of world data showed that the strength of the EMC effect is linearly correlated with the relative amount of Two-Nucleon Short Range Correlated pairs (2N-SRC) in nuclei. The latter are pairs of nucleons whose wave functions overlap, giving them large relative momentum and low center of mass momentum, where high and low is relative to the Fermi momentum of the …
One of the primary goals of nuclear physics is providing a complete description of the structure of atomic nuclei. While mean-field calculations provide detailed information on the nuclear shell structure for a wide range of nuclei, they do not capture the complete structure of nuclei, in particular the impact of small, dense structures in nuclei. The strong, short-range component of the nucleon-nucleon potential yields hard interactions between nucleons which are close together, generating a high-momentum tail to the nucleon momentum distribution, with momenta well in excess of the Fermi mome…
Three nucleon short range correlations~(SRCs) are one of the most elusive structures in nuclei. Their observation and the subsequent study of their internal makeup will have a significant impact on our understanding of the dynamics of super-dense nuclear matter which exists at the cores of neutron stars. We discuss the kinematic conditions and observables that are most favorable for probing 3N-SRCs in inclusive electro-nuclear processes and make a prediction for a quadratic dependence of the probabilities of finding a nucleon in 2N- and 3N- SRCs. We demonstrate that this prediction is consiste…
Quantitative information on the tensor force induced isospin-dependence of short-range nucleon-nucleon correlation (SRC) extracted from recent J-Lab experiments was used in constraining the high-momentum tails of single nucleon momentum distributions in both symmetric nuclear matter (SNM) and pure neutron matter (PNM). Its effects on the Equations of State of SNM and PNM as well as the nuclear symmetry energy are investigated. It is found that the tensor force induced isospin-dependence of SRC softens significantly the nuclear symmetry energy especially at supra-saturation densities.
Recent developments in understanding the influence of the nucleus on deep-inelastic structure functions, the EMC effect, are reviewed. A new data base which expresses ratios of structure functions in terms of the Bjorken variable $x_A=AQ^2/(2M_A q_0)$ is presented. Information about two-nucleon short-range correlations from experiments is also discussed and the remarkable linear relation between short-range correlations and teh EMC effect is reviewed. A convolution model that relates the underlying source of the EMC effect to modification of either the mean-field nucleons or the short-range co…
Realistic nucleon-nucleon interaction induce correlations to the nuclear many-body system which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function which can be evaluated in terms of the self-energy obtained in the Self-Consistent Green's Function approach. Results for the density and temperature dependences of the entropy per particle for symmetric …
Recent experimental data on inclusive and exclusive lepton and hadron scattering off nuclei have renewed the interest in theoretical and experimental studies of Short Range Correlations (SRC), due to the relevant impact they may have not only on the structure of ordinary nuclei but on the structure of hadronic matter at high densities as well. One of the ultimate aim of these studies is the determination of the probability of two- and three-nucleon correlations in nuclei. To this end, we have studied the possibility to extract these probabilities from a novel analysis of inclusive A(e, e')X pr…
A brief overview is given of the properties of spectral functions in finite nuclei as obtained from (e,e'p) experiments. Based on recent experimental data from this reaction it is argued that the empirical value of the saturation density of nuclear matter is dominated by short-range correlations. This observation and the observed fragmentation and depletion of the single-particle strength in nuclei provide the motivation for attempting a self-consistent description of the nucleon spectral functions with full inclusion of short-range and tensor correlations in nuclear matter. Results for these …
Realistic NN interactions and many-body approaches have been used to calculate ground-state properties of nuclei with A=3, 4, 12, 16, 40, with particular emphasis on various kinds of momentum distributions. It is shown that at proper values of the relative (rel) and center-of-mass (c.m.) momenta, the two-nucleon momentum distribution n_A^{N_1N_2} (k_{rel}, K_{c.m.}, θ) exhibits the property of factorization, namely n_A^{N_1N_2} (k_{rel}, K_{c.m.}, θ) \simeq n_{rel}(k_{rel}) n_(c.m.)( K{c.m.}). The factorization of the momentum distributions , bearing a universal character, results from a gener…
Effects of three-nucleon forces arising from the exchange of a pion and a scalar-isoscalar object among three nucleons on nucleon-deuteron scattering observables are studied.
The EMC effect in deuterium and helium-3 is studied using a convolution formalism that allows isolating the impact of high-momentum nucleons in short-ranged correlated (SRC) pairs. We assume that the modification of the structure function of bound nucleons is given by a universal (i.e. nucleus independent) function of their virtuality, and find that the effect of such modifications is dominated by nucleons in SRC pairs. This SRC-dominance of nucleon modifications is observed despite the fact that the bulk of the nuclear inelastic scattering cross-section comes from interacting with low-momentu…
We decompose the tribaryon configuration in terms of SU(3) flavor and spin state and analyse their color-spin-flavor wave function following Pauli principle. By comparing the color-color and color-spin interactions of compact tribaryon configuration against the lowest three nucleon threshold within a constituent quark model, we show that the three nucleon forces have to be repulsive at short distance for all possible quantum numbers and all values of the SU(3) symmetry breaking parameter. Our work identifies the origin of the repulsive nuclear three body forces including the hyperons at short …
We investigate the short distance behavior of 3 nucleon forces (3NF) defined through Nambu--Bethe--Salpeter wave functions, using the operator product expansion(OPE) and calculating anomalous dimensions of 9--quark operators in perturbative QCD. As is the case of NN forces previously considered, we show that 3NF have repulsions at short distance at 1--loop, which becomes exact in the short distance limit thanks to the asymptotic freedom of QCD. Moreover these behaviors are universal in the sense that they do not depend on the energy of the NBS wave function for 3 nucleons.
We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is $\mid s^4p^2[42]_O [51]_{FS}>$ due to its specific flavour-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both $^3S_1$ and $^1S_0$ channels. The symmetry structure of the highl…
The role played by nucleon-nucleon short-range correlations in photon- and electron-nucleus reactions is analyzed with a model which includes all the diagrams containing a single correlation function. The excitation of low-lying high-spin states, the reactions (e,e'), (e,e'N) and ($γ$,N) and the two-proton emission by both electrons and real photons are investigated. The results obtained for doubly-closed shell nuclei show that ($γ$,pp) appears to be the most adequate process to identify short-range correlations in the clearer way.
Response functions in nuclear matter at finite temperature are considered beyond the usual Hartree-Fock (HF) plus Random Phase Approximation (RPA) scheme. The contributions due to the propagator for the dressed nucleons and the corresponding vertex corrections are treated in a consistent way. For that purpose a semi-realistic Hamiltonian is developed with parameters adjusted to reproduce the nucleon self-energy as derived from realistic nucleon-nucleon interactions. For a scalar residual interaction the resulting response functions are very close to the RPA response functions. However, the col…
We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory ($χ$EFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as $χ$EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $χ$EFT expansion. This produce…
The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the two-nucleon momentum distribution into the product of the two single nucleon distributions shows up in an analogous property of the spectral function. The correlated model yields a two-hole contribution quenched whith respect to Fermi gas model, while the peaks acquire a quasiparticle width that vanishes as the two momenta approach $k_F$. In addition, three-hole one-…
We derive a novel chiral power counting scheme for in-medium chiral perturbation theory with explicit nucleonic and pionic degrees of freedom coupled to external sources. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of non-perturbative diagrams that require a resummation. Within this scheme, the pion self-energy in asymmetric nuclear matter is analyzed and calculated up-to-and-including next-to-leading order (NLO). It is shown that the corrections involving in-medium nu…
We summarize recent progress in the studies of the short-rang correlations (SRC) in nuclei in high energy electron and hadron nucleus scattering and suggest directions for the future high energy studies aimed at establishing detailed structure of two-nucleon SRCs, revealing structure of three nucleon SRC correlations and discovering non-nucleonic degrees of freedom in nuclei.
Diquark formation across a short-range nucleon-nucleon pair is proposed as the underlying QCD physics of short-range correlations (SRC) in nuclei. SRC pairs have been proposed as the cause of distorted quark behavior in nuclei; experimentally observed quark momentum distribution distortions termed the EMC effect. The strong spatial overlap of SRC pairs brings nucleon constituents within range of inter-nucleon QCD potentials and any bonds formed - such as the diquark bond - affects their distributions. In this SRC model, diquarks form in the $\rm 3_C \otimes 3_C \rightarrow \bar{3}_C$ channel o…
We consider the spin-isospin-independent central part of the residual nucleon-nucleon potential in finite spherical nuclei taking into account the deformation effects of the nucleons within the surrounding nuclear environment. It is shown that inside the nucleus the short-range repulsive contribution of the potential is increased and the intermediate attraction is decreased. We identify the growth of the radial component of the spin-isospin independent short-range part of the in-medium nucleon-nucleon interaction as the responsible agent that prevents the radial collapse of the nucleus.
We discuss a number of constraints on the effects of zero-range potentials in quantum mechanics. We show that for such a potential $p \cot(δ)$, where $p$ is the momentum of the nucleon in the center of mass frame and $δ$ is the S-wave phase shift, must be a monotonically decreasing function of energy. This implies that the effective range of the potential is non-positive. We also examine scattering from the sum of two potentials, one of which is a short-range interaction. We find that if the short-range interaction is of zero-range then it must be attractive, and the logarithmic derivative of …
We develop a theoretical approach for nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation~(SRC) model. The approach is based on the effective Feynman diagrammatic method which allows to account for the relativistic effects important in the SRC domain. In addition to two-nucleon SRC with center of mass motion we derive also the contribution of three-nucleon SRCs to the nuclear spectral functions. The latter is modeled based on the assumption that 3N SRCs are a product of two sequential short range NN interactions. This appro…
Instead of the Yukawa mechanism for intermediate- and short-range interaction some new approach based on formation of the symmetric six-quark bag in the state $|(0s)^6[6]_X,L=0>$ dressed due to strong coupling to $π$, $σ$ and $ρ$ fields are suggested. This new mechanism offers both a strong intermediate-range attraction which replaces the effective $σ$-exchange (or excitation of two isobars in the intermediate state) in traditional force models and also short-range repulsion. Simple illustrative model is developed which demonstrates clearly how well the suggested new mechanism can reproduce $N…
Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence that arises can be renormalised using an order-Q^2 counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.
Talk given at the "International Workshop on (e,e'p) Processes", July 2-6, 2017, Bled, Slovenia. Various many-body calculations are compared and the results provided by the Normalization Conserving Linked Cluster Expansion with realistic NN interactions are reviewed and analyzed in detail, as far as ground state energies, momentum distributions and spectral functions of few-nucleon system and complex nuclei are concerned.
We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order cor…
