Short-range Nucleon-nucleon Correlations Research Articles

Short-range correlations in dynamical intranuclear cascade models for describing nucleon knockout reactions

Spallation and fragmentation reactions at incident energies above the Fermi momentum are considered to be the main mechanism for the production of neutron-rich nuclei at worldwide nuclear physics facilities, such as RIBF, FRIB, and GSI-FAIR. Although it is widely known that dynamical reaction models give a rather good prediction of cross sections for nuclear residues produced in spallation and fragmentation reactions, these reaction models fail in the description of peripheral collisions involving short-range nucleon-nucleon correlations (SRCs). Here, we present state-of-the-art dynamical reaction calculations based on the intranuclear cascade approach to describe spallation and fragmentation reactions. The new version of our dynamical model, including SRCs, successfully describes isotopic cross sections of neutron-rich nuclear residues and inclusive single-neutron and single-proton knockout cross sections for various stable and exotic nuclei. Finally, the results show that the systematic strong dependency of the single-knockout cross section reduction factor on the neutron-proton separation energy asymmetry parameter (ΔS) obtained by Tostevin and Gade disappears when SRCs are taken into account.

Diquark induced short-range nucleon-nucleon correlations & the EMC effect

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 3C⊗3C→3¯C channel of SU(3)C acting on valence quarks from highly overlapping nucleon wavefunctions. The most energetically favorable diquark is a valence u quark from one nucleon with a valence d quark from the other in a spin-0 state bound together via continual single gluon exchange and an attractive quantum chromodynamics short-range potential. Formation of a new scalar isospin-singlet [ud] diquark across a NN pair is proposed as the primary QCD-level theoretical foundation for SRC models of distorted structure functions in A≥3 nuclei. Contributions from the higher mass spin-1 isospin triplet states (ud), (uu) and (dd) are possible, with the spin-1 (ud) diquark proposed as a higher mass but viable structure function distortion mechanism for the spin-1 ground state deuteron. Predictions are made for lepton scattering experiments on H3 and He3 nuclear targets, with implications for the coefficients of the 3-valence quark Fock states in the nucleon wavefunction.

Universality test of short range nucleon-nucleon correlations in nuclei with strange and charmed probes

Understanding the EMC effect and its relation to the short-range nucleon-nucleon correlations (SRC) in nuclei is a major challenge for modern nuclear physics. One of the key aspects of the connection between these phenomena is the universality. The universality states that the SRC is responsible for the EMC effect and that the modification of the partonic structure of the SRC is the same in different nuclei. The flavor dependence of the universality is one of the unanswered questions. The investigations conducted to date have demonstrated the existence and universality of the SRC for light and quarks. Recently, it was suggested that the universality for heavy flavors can be studied through their deep subthreshold production in and eA collisions. In this paper, we discuss an alternative possibility to access the strange and gluon high-X structure of the SRC and to establish universality for heavy flavors using nuclear semi-inclusive deep inelastic scattering (nSIDIS), which probes different quark flavor combinations depending on the final state hadron. The specific reaction can be "tagged" by observation of a strange or charmed particle registered in coincidence with the scattering lepton. The universality of the SRC can be tested in the kinematic region, i.e., , where the contribution to the cross section from SRC becomes dominant. Exploring the strangeness, charmonium, and open charm will shed light on the role of quarks and gluons in nuclei, thereby developing an understanding of how nuclei emerge within QCD.

Short range nucleon correlations studied with electron and photon probes

This paper reviews experimental research into two- and three-body nucleon-nucleon interactions, carried out by the University of Glasgow Nuclear Physics research group. A key aim of these studies has been to elucidate the role of short-range nucleon-nucleon correlations (SRC). Studies of photon-induced two- and three-nucleon emission reactions from a range of light nuclei, carried out at the 840 MeV Mainz electron microtron MAMI-B, have provided detailed information on the contributing mechanisms. More recent electron scattering studies at the 6.0 GeV Jefferson Laboratory have probed SRC at high values of Q^{2}2 and x_{B}B and suggested a connection between SRC and the EMC effect.

Coarse-grained short-range correlations

We develop a scheme to take into account the effects of short-range nucleon-nucleon correlations in the nucleon-pair wave function by solving the Bethe-Goldstone equation for a coarse grained delta shell potential in S-wave configuration. The S-wave delta shell potential has been adjusted to reproduce the $^1$S$_0$ phase shifts of the AV18 potential for this partial wave up to 2 GeV in the laboratory kinetic energy. We show that a coarse grained potential can describe the high momentum tail of the back-to-back correlated pairs and the $G$-matrix in momentum space. We discuss the easiness and robustness of the calculation in coordinate space and the future improvements and utilities of this model. This work suggests the possibility of using perturbation theory for describing the short-range correlations, and related to this, to substitute the $G$-matrix by an appropriate coarse-grained potential.

“Hammer” events, neutrino energies, and nucleon-nucleon correlations

Neutrino oscillation measurements depend on a difference between the rate of neutrino-nucleus interactions at different neutrino energies or different distances from the source. Knowledge of the neutrino energy spectrum and neutrino-detector interactions are crucial for these experiments. Short range nucleon-nucleon correlations in nuclei (SRC) affect properties of nuclei. The ArgoNeut liquid Argon Time Projection Chamber (lArTPC) observed neutrino-argon scattering events with two protons back-to-back in the final state ("hammer" events) which they associated with SRC pairs. The MicroBoone lArTPC will measure far more of these events. We simulate hammer events using two simple models. We use the well-known electron-nucleon cross section to calculate e-argon interactions where the e- scatters from a proton, ejecting a pi+, and the pi+ is then absorbed on a moving deuteron-like $np$ pair. We also use a model where the electron excites a nucleon to a Delta, which then deexcites by interacting with a second nucleon. The pion production model results in two protons very similar to those of the hammer events. These distributions are insensitive to the momentum of the $np$ pair that absorbed the $\pi$. The incident neutrino energy can be reconstructed from just the outgoing lepton. The Delta process results in two protons that are less similar to the observed events. ArgoNeut hammer events can be described by a simple pion production and reabsorption model. These hammer events in MicroBooNE can be used to determine the incident neutrino energy but not to learn about SRC. We suggest that this reaction channel could be used for neutrino oscillation experiments to complement other channels with higher statistics but different systematic uncertainties.

Differential cross section measurement of the 12C(e,e’pp)10Beg.s. reaction

The differential cross section was measured for the 12C(e,e’pp)10Beg.s. reaction at energy and momentum transfers of 163MeV and 198MeV/c, respectively. The measurement was performed at the Mainz Microtron by using two high-resolution magnetic spectrometers of the A1 Collaboration and a newly developed silicon detector telescope. The overall resolution of the detector system was sufficient to distinguish the ground state from the first excited state in 10 Be. We chose a super-parallel geometry that minimizes the effect of two-body currents and emphasizes the effect of nucleon-nucleon correlations. The obtained differential cross section is compared to the theoretical results of the Pavia reaction code in which different processes leading to two-nucleon knockout are accounted for microscopically. The comparison shows a strong sensitivity to nuclear-structure input and the measured cross section is seen to be dominated by the interplay between long- and short-range nucleon-nucleon correlations. Microscopic calculations based on the ab initio self-consistent Green’s function method give a reasonable description of the experimental cross section.

Some universal properties of density matrices for finite nuclei (bound systems)

The properties of one-body and two-body density matrices of a nucleus as a nonrelativistic system are studied. Unlike the usual procedure applied in the theory of infinite systems, for a nucleus of A nucleons these quantities are determined as the expectation values of A-body multiplicative operators that depend on the relative coordinates and momenta (Jacobi variables) and affect the intrinsic wave functions. The translational invariance of these operators is thus ensured. An algebraic technique based on the Cartesian representation is developed for handling such operators. Within this technique, the coordinate and momentum operators are linear combinations of production and annihilation operators \(\hat \vec a^ + \) and \(\hat \vec a\) with commutation relations for bosons (oscillators). Each of the multiplicative operators reduces to the normally ordered product of two exponents, one of which depends on set \(\left\{ {\hat \vec a^ + } \right\}\) only and is located to the left of the second, which depends on \(\left\{ {\hat \vec a} \right\}\) only. This procedure offers a new view of the origin of the so-called Tassie–Barker factors and other model-independent results. In addition, the proposed method yields a fair description of the available experimental data and can easily be extended to investigate the role of short-range nucleon-nucleon correlations within these translationally invariant calculations of nucleon density and momentum distributions in light nuclei.

Nucleus probing for short-range correlations using neutrino-nucleon interactions

Short-range nucleon-nucleon correlations (NN SRC) contain important information about nuclear structure and dynamics within the nuclei. It has been extensively studied through two-nucleon knockout reactions, in both pion and electron scattering experiments. A very recent approach is to probe NN SRC using neutrino scattering, however, with limited results due to the intrinsic uncertainty of the four-momentum transfer. Here, we present one of the latest attempts to reconstruct this information.

Measurement of the EMC effect in the deuteron

We have determined the structure function ratio $R^d_{\rm EMC}=F_2^d/(F_2^n+F_2^p)$ from recently published $F_2^n/F_2^d$ data taken by the BONuS experiment using CLAS at Jefferson Lab. This ratio deviates from unity, with a slope $dR_{\rm EMC}^{d}/dx= -0.10\pm 0.05$ in the range of Bjorken $x$ from 0.35 to 0.7, for invariant mass $W>1.4$ GeV and $Q^2>1$ GeV$^2$. The observed EMC effect for these kinematics is consistent with conventional nuclear physics models that include off-shell corrections, as well as with empirical analyses that find the EMC effect proportional to the probability of short-range nucleon-nucleon correlations.

Detection of back-to-back proton pairs in charged-current neutrino interactions with the ArgoNeuT detector in the NuMI low energy beam line

Short range nucleon-nucleon correlations in nuclei (NN SRC) carry important information on nuclear structure and dynamics. NN SRC have been extensively probed through two-nucleon knock- out reactions in both pion and electron scattering experiments. We report here on the detection of two-nucleon knock-out events from neutrino interactions and discuss their topological features as possibly involving NN SRC content in the target argon nuclei. The ArgoNeuT detector in the Main Injector neutrino beam at Fermilab has recorded a sample of 30 fully reconstructed charged current events where the leading muon is accompanied by a pair of protons at the interaction vertex, 19 of which have both protons above the Fermi momentum of the Ar nucleus. Out of these 19 events, four are found with the two protons in a strictly back-to-back high momenta configuration directly observed in the final state and can be associated to nucleon Resonance pionless mechanisms involving a pre-existing short range correlated np pair in the nucleus. Another fraction (four events) of the remaining 15 events have a reconstructed back-to-back configuration of a np pair in the initial state, a signature compatible with one-body Quasi Elastic interaction on a neutron in a SRC pair. The detection of these two subsamples of the collected (mu- + 2p) events suggests that mechanisms directly involving nucleon-nucleon SRC pairs in the nucleus are active and can be efficiently explored in neutrino-argon interactions with the LAr TPC technology.

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei (4He and 16O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own “Tassie-Barker” factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of 4He and 16O evaluated by using the well-known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.

High-Momentum components of the nuclear wave function: short range correlations, EMC effect, and the tensor parts of the N-N Interaction

The combination of inclusive and exclusive electron scattering data from JLab in kinematic regimes that were not reachable before, together with the analysis and interpretation of older data from hadronic reactions at BNL is finally revealing the details of short-range nucleon-nucleon correlations in nuclei. The most significant result is the demonstration of the dominance of correlated np pairs over pp and nn pairs. I will review these results, discuss them in terms of short-range tensor-force dominance and also discuss the connection to the EMC effect.

Universality of Short-Range Nucleon-Nucleon Correlations in Nuclei

We investigate the short-range correlations in light nuclei. The highly correlated many-body states are obtained with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrodinger equation for a realistic interaction. We show two-body density distributions for the different spin-isospin channels calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in high momentum components of the two-body momentum distributions.

Studying hadrons in matter with PANDA

With the PANDA experiment at the FAIR facility in Darmstadt, Germany it will be possible to investigate antiproton-nucleus reactions in an energy range not explored so far. This provides opportunities for unique measurements of which some are outlined in this article. Possible modifications of hadron properties in nuclear matter is subject of extensive theoretical and experimental studies. With PANDA it will be possible to extend this kind of studies to the charm sector. A study of particular interest will be to measure the J/Ψ-nucleon dissociation cross-section. This cross-section is relevant for the interpretation of the J/Ψ suppression observed in high energy heavy ion reactions. Further topics include the study of antibaryons in nuclei and short-range nucleon-nucleon correlations.

Universality of short-range nucleon-nucleon correlations

Short-range correlations between nucleon pairs in different spin-isospin channels are investigated for light nuclei using the Argonne V8' interaction. At distances below 1 fm a universal behavior is found for the deuteron, 3H, 3He and for ground and first excited states in 4He. This behavior in coordinate space is reflected by a universal behavior for the high-momentum components in momentum space. The universality indicates that a pairwise renormalization is possible in order to obtain a universal effective two-body interaction that does not scatter to high momentum states. The exact two-body densities are compared with those obtained using the unitary correlation operator method with simple trial wave functions. The effect of three-body correlations due to the tensor force on the two-body densities is discussed.

Effects of ground-state correlations on high energy scattering off nuclei: The case of the total neutron-nucleus cross section

With the aim at quantitatively investigating the longstanding problem concerning the effect of short-range nucleon-nucleon correlations on scattering processes at high energies, the total neutron-nucleus cross section is calculated within a parameter-free approach which, for the first time, takes into account, simultaneously, central, spin, isospin, spin-isospin, and tensor nucleon-nucleon correlations, and Glauber elastic and Gribov inelastic shadowing corrections. Nuclei ranging from $^{4}\mathrm{He}$ to $^{208}\mathrm{Pb}$ and incident neutron momenta in the range 3 GeV/$c$--300 GeV/$c$ are considered; the commonly used approach which approximates the square of the nuclear wave function by a product of one-body densities is carefully analyzed, showing that $\mathit{NN}$ correlations can play a non-negligible role in high energy scattering off nuclei

Investigation of Proton-Proton Short-Range Correlations via theC12(e,e′pp)Reaction

We investigated simultaneously the 12C(e,e'p) and 12C(e,e'pp) reactions at Q2=2 (GeV/c)2, xB=1.2, and in an (e, e'p) missing-momentum range from 300 to 600 MeV/c. At these kinematics, with a missing momentum greater than the Fermi momentum of nucleons in a nucleus and far from the delta excitation, short-range nucleon-nucleon correlations are predicted to dominate the reaction. For (9.5+/-2)% of the 12C(e,e'p) events, a recoiling partner proton was observed back-to-back to the 12C(e,e'p) missing-momentum vector, an experimental signature of correlations.

Probing short-range nucleon-nucleon correlations with virtual photons at MAMI

Nucleon-nucleon correlations were studied in two ( e, e′ pp) experiments. The first one, on 12 C, was performed in close to 4π geometry at E beam = 705 MeV, ω = 225 MeV, and q = 412 MeV/c. The electrons were observed in a large-acceptance magnetic spectrometer in coincidence with protons detected in a BGO crystal ball. Missing energy and momentum, relative momentum and angular distributions were derived and compared with a facorised two-nucleon emision model. A G-matrix correlation function is favoured by the data. The second experiment was a high resolution study of the reaction 16 O( e, e′ pp) 14 C in super-parallel kinematics. Three magnetic spectrometers were used in coincidence at E beam = 855 MeV, ω = 215 MeV, q = 316 MeV/c. A missing momentum (pair momentum) range −100 MeV/c ≤ P m ≤ 450 MeV/c was sampled. Two-hole states were preferentially excited, with an energy resolution of 500 keV. Their momentum distributions are compared with unfactorised model calculations which make use of realistic NN potentials.

Investigation of short-range nucleon-nucleon correlations using the reaction [formula omitted] in close to 4 π geometry

Two-proton correlations were studied in close to 4 π geometry using the reaction 12 C(e,e′pp) . The beam energy was 705 MeV, the energy transfer 225 MeV, and the three-momentum transfer 412 MeV/c. The electrons were observed in a large-acceptance magnetic spectrometer in coincidence with protons observed in a BGO crystal ball. Missing energy and momentum, relative momentum and angular distributions were derived and compared with a factorized two-nucleon emission model. Soft-core correlation functions are favoured by the data.