Nuclear Short-range Correlations Research Articles

Nuclear short-range correlations and the zero-energy eigenstates of the Schrödinger equation

We present a systematic analysis of the nuclear two- and three-body short-range correlations and their relations to the zero-energy eigenstates of the Schr\"odinger equation. To this end we analyze the doublet and triplet coupled-cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these coupled-cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear two-body short range correlations, and they might also be helpful for general coupled-cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

Isospin-symmetry implications for nuclear two-body distributions and short-range correlations

We study the implications of isospin symmetry in nuclear systems on two-body distributions and derive relations between different densities or momentum distributions of a given nucleus or of different nuclei in the same isospin multiplet. A connection between neutrinoless double beta decay transition of mirror nuclei and two-body densities is also obtained. The relations are numerically verified by means of quantum Monte Carlo calculations. We discuss the relevance of these results to the analysis of nuclear short-range correlations and also show that isospin symmetry allows us to extract information about the spectator nucleons when a short-range correlated pair is formed.

Study of Short-Range nuclear Correlations in light nuclei using the BeAGLE event generator

Nuclear dynamics at short distances among nucleons is one of the most outstanding phenomena in nuclear physics. Understanding the role of QCD in generating nuclear forces is important for uncovering the underlying physics of Short-Range Correlations (SRCs). In recent years, SRCs has been observed from light to heavy nuclei using fixed target experiments at Jefferson lab via high energy electron-nucleus scattering. In this talk, I will talk about the opportunity of studying SRCs using light nuclei with collider experiments, e.g., the Electron-Ion Collider (EIC). The experimental technique of studying the light nuclei can be based on exclusive processes with tagging final-state particles, in order to fully control the initial state of the target wavefunction. In particular, incoherent diffractive production of J/\psiJ/ψ particle off deuteron will be presented. In addition, the spectral function in light nuclei has been recently modeled in the BeAGLE event generator, where the decay kinematics of the light nuclei and their influence on the very forward detector design at the EIC will be discussed.

Phase-space distributions of nuclear short-range correlations

Nuclear short-range correlations (SRCs) induce high-momentum/high-energy fluctuations in the nuclear medium. In order to assess their impact on nuclear bulk properties, like nuclear radii and kinetic energies, it is instrumental to determine how SRCs are distributed in phase space as this sheds light on the connection between their appearance in coordinate and momentum space. Using the lowest-order correlation operator approximation (LCA) to include SRC, we compute two-dimensional nuclear Wigner quasiprobability distributions w(r,k) to locate those (r,k) phase-space regions that are most heavily impacted by SRCs. The SRC-induced high-momentum components find their origin in a radial range that is confined to the nuclear interior. Significant SRCs strength is generated in the full momentum range 0≤k≲5fm−1 covered in this work, but below the Fermi momentum those are dwarfed by the mean-field contributions. As an application of w(r,k), we focus on the radial dependence of the kinetic energy T and the momentum dependence of the radius rrms for the symmetric nuclei C12, Ca40 and the asymmetric nucleus Ca48. The kinetic energy almost doubles after including SRCs, with the largest increase occurring in the nuclear interior r≲2 fm. The momentum dependence of the rrms teaches that the largest contributions stem from k≲2 fm−1, where the SRCs induce a slight reduction of the order of a few percent. The SRCs systematically reduce the Ca48 neutron skin by an amount that can be 10%.

Many-body factorization and position–momentum equivalence of nuclear short-range correlations

Ab-initio Quantum Monte Carlo (QMC) calculations of nuclei from deuterium to 40Ca, obtained using four different phenomenological and local chiral nuclear potentials, are analyzed using the Generalized Contact Formalism (GCF). We extract spin- and isospin-dependent "nuclear contact terms" for each interaction in both coordinate and momentum space. The extracted contact terms, that count the number of short-range correlated (SRC) pairs with different quantum numbers, are dependent on the nuclear interaction model used in the QMC calculation. However, the ratios of contact terms for a nucleus A to deuterium (for spin-1 pn pairs) or to 4He (for all NN pairs) are independent of the nuclear interaction model and are the same for both short-distance and high-momentum pairs. This implies that the relative abundance of short-range pairs in the nucleus is a long-range (mean-field) quantity that is insensitive to the short-distance nature of the nuclear force. Measurements of exclusive (e,e'NN) pair breakup processes are instead more sensitive to short-range dynamics

Effects of short-range nuclear correlations on the deformability of neutron stars

In the present work, we investigate the effects of short-range correlations (SRC) on the dimensionless deformability of the binary neutron system related to the GW170817 event. We implemented phenomenological SRC in a relativistic mean-field model in which the bulk parameters, namely, incompressibility ($K_0$), effective nucleon mass ratio ($m^*$), symmetry energy ($J$) and its slope ($J_0$), are independently controlled. Our results point out that the SRC favor the model to pass through the constraints, established by the LIGO/Virgo Collaboration, on the values of $\Lambda_{1.4}$ and on the $\Lambda_1\times\Lambda_2$ region. We also found a clear linear correlation between $\Lambda_{1.4}$ with $K_0$ and $L_0$ (increasing dependence), and with $m^*$ and $J$ (decreasing dependence). Finally, we also obtained compatible numbers for $R_{1.4}$ (model with and without SRC) in comparison with recent data from the neutron star interior composition explorer mission.

The isospin and neutron-to-proton excess dependence of short-range correlations

We provide a systematic study of the isospin composition and neutron-to-proton (NZ) ratio dependence of nuclear short-range correlations (SRC) across the nuclear mass table. We use the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distributions for 14 different nuclei from A=4 to A=208. Ten asymmetric nuclei are included for which the neutrons outnumber the protons by a factor of up to 1.54. The computed momentum distributions are used to extract the pair composition of the SRC. We find that there is a comprehensive picture for the isospin composition of SRC and their evolution with nucleon momentum. We also compute the non-relativistic kinetic energy of neutrons and protons and its evolution with nuclear mass A and NZ. Confirming the conclusions from alternate studies it is shown that the minority species (protons) become increasingly more short-range correlated as the neutron-to-proton ratio increases. We forge connections between measured nucleon-knockout quantities sensitive to SRC and single-nucleon momentum distributions. It is shown that the LCA can account for the observed trends in the data, like the fact that in neutron-rich nuclei the protons are responsible for an unexpectedly large fraction of the high-momentum components.

Energy and momentum dependence of nuclear short-range correlations - Spectral function, exclusive scattering experiments and the contact formalism

Results of electron-induced one- and two-nucleon hard knockout reactions, A(e,e′p) and A(e,e′pN), in kinematics sensitive to nuclear short-range correlations, are studied using the nuclear contact formalism. A relation between the spectral function and the nuclear contacts is derived and used to analyze the dependence of the data on the initial energy and momentum of the knocked-out proton. The ratio between the number of emitted proton-proton pairs and proton-neutron pairs is shown to depend predominantly on a single ratio of contacts. This ratio is expected to present deep minima in the initial energy and momentum plane, associated with the node in the proton-proton wave function.The formalism is applied to analyze data from recent 4He and 12C electron-scattering experiments performed at Jefferson laboratory. Different nucleon-nucleon potentials were used to assess the model-dependence of the results. For the ratio of proton-proton to proton-neutron pairs in 4He, a fair agreement with the experimental data is obtained using the two potentials, whereas for the ratio of proton-proton pairs to the total knocked-out protons in 12C, some of the features of the theory are not seen in the experimental data. Several possible explanations for this disagreement are discussed. It is also observed that the spectral function at specific domains of the momentum-energy plane is sensitive to the nucleon-nucleon interaction. Based on this sensitivity, it might be possible to constrain the short range part of the nuclear potential using such experimental data.

Short-range correlations and the charge density

Sophisticated high-energy and large momentum-transfer scattering experiments combined with ab-initio calculations can reveal the short-distance behavior of nucleon pairs in nuclei. On an opposite energy and resolution scale, elastic electron scattering experiments are used to extract the charge density and charge radius of different nuclei. We show that even though the charge density has no obvious connection with nuclear short-range correlations, it can be used to extract properties of such correlations. This is accomplished by using the nuclear contact formalism to derive a relation between the charge density and the proton–proton nuclear contacts that describe the probability of two protons being at close proximity. With this relation, the values of the proton–proton contacts are extracted for various nuclei using only the nuclear charge density and a solution of the two-nucleon Schroedinger equation as inputs. For symmetric nuclei, the proton–neutron contacts can also be extracted from the charge density. Good agreement is obtained with previous extractions of the nuclear contacts. These results imply that one can predict (with reasonably good accuracy) the results of high-energy and large momentum-transfer electron-scattering experiments and ab-initio calculations of high momentum tails using only experimental data of elastic scattering experiments.

Hierarchy of Azimuthal Anisotropy Harmonics in Collisions of Small Systems from the Color Glass Condensate.

We demonstrate that the striking systematics of two-particle azimuthal Fourier harmonics v_{2} and v_{3} in ultrarelativistic collisions of protons, deuterons, and helium-3 ions off gold nuclei measured by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC) is reproduced in the color glass condensate effective field theory. This contradicts the claim in C. Aidala etal. (PHENIX Collaboration), arXiv:1805.02973, that their data rule out initial state-based explanations. The underlying systematics of the effect, as discussed previously in K. Dusling, M. Mace, R. Venugopalan, Phys. Rev. D 97, 016014 (2018)PRVDAQ2470-001010.1103/PhysRevD.97.016014; Phys. Rev. Lett. 120, 042002 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.042002; Proc. Sci., QCDEV2017 (2018) 039, arise from the differing structure of strong color correlations between gluon domains of size 1/Q_{S} at fine (p_{⊥}⪆Q_{S}) or coarser (p_{⊥}⪅Q_{S}) transverse momentum resolution. Further tests of the limits of validity of this framework can be carried out in light-heavy ion collisions at both RHIC and the Large Hadron Collider. Such measurements also offer novel opportunities for further exploration of the role of the surprisingly large short-range nuclear correlations measured at Jefferson Lab.

Effects of the initialization of nucleon momentum in heavy-ion collisions at medium energies

Based on the Isospin-dependent transport model Boltzmann-Uehling-Uhlenbeck (IBUU), effects of the difference of the high momentum tails (HMTs) of nucleon momentum distribution in colliding nuclei on some isospin-sensitive observables are studied in the $^{197}\rm {Au}+^{197}\rm {Au}$ reactions at incident beam energy of 400 MeV/nucleon. It is found that the nucleon transverse and elliptic flows, the free neutron to proton ratio at low momenta are all less sensitive to the specific form of the HMT, while the free neutron to proton ratio at high momenta and the yields of $\pi^{-}$ and $\pi^{+}$ as well as the $\pi^{-}/\pi^{+}$ ratio around the Coulomb peak are sensitive to the specific form of the HMT. Combining the present studies with the experimental measurements at rare-isotope reaction facilities worldwide, one may get more insights into the nuclear short-range correlations in heavy nuclei or nuclear matter.

Probing short-range correlations in asymmetric nuclei with quasi-free pair knockout reactions

Short-range correlations (SRC) in asymmetric nuclei with an unusual neutron-to-proton ratio can be studied with quasi-free two-nucleon knockout processes following the collision between accelerated ions and a proton target. We derive an approximate factorized cross section for those SRC-driven p(A,p′N1N2) reactions. Our reaction model hinges on the factorization properties of SRC-driven A(e,e′N1N2) reactions for which strong indications are found in theory-experiment comparisons. In order to put our model to the test we compare its predictions with results of C12(p,p′pn) measurements conducted at Brookhaven National Laboratory (BNL) and find a fair agreement. The model can also reproduce characteristic features of SRC-driven two-nucleon knockout reactions, like back-to-back emission of the correlated nucleons. We study the asymmetry dependence of nuclear SRC by providing predictions for the ratio of proton–proton to proton–neutron knockout cross sections for the carbon isotopes 9−15C thereby covering neutron excess values (N−Z)/Z between −0.5 and +0.5.

QCD corrections and long-range mechanisms of neutrinoless double beta decay

Recently it has been demonstrated that QCD corrections are numerically important for short-range mechanisms (SRM) of neutrinoless double beta decay ($0\nu\beta\beta$) mediated by heavy particle exchange. This is due to the effect of color mismatch for certain effective operators, which leads to mixing between different operators with vastly different nuclear matrix elements (NMEs). In this note we analyze the QCD corrections for long-range mechanisms (LRM), due to diagrams with light-neutrino exchange between a Standard Model (V-A)$\times$(V-A) and a beyond the SM lepton number violating vertex. We argue that in contrast to the SRM in the LRM case, there is no operator mixing from color-mismatched operators. This is due to a combined effect of the nuclear short-range correlations and color invariance. As a result, the QCD corrections to the LRM amount to an effect no more than 60%, depending on the operator in question. Although less crucial, taken into account QCD running makes theoretical predictions for $0\nu\beta\beta$-decay more robust also for LRM diagrams. We derive the current experimental constraints on the Wilson coefficients for all LRM effective operators.

Influence of short-range correlations in neutrino-nucleus scattering

Background: Nuclear short-range correlations (SRCs) are corrections to mean-field wave functions connected with the short-distance behavior of the nucleon-nucleon interaction. These SRCs provide corrections to lepton- nucleus cross sections as computed in the impulse approximation (IA). Purpose: We want to investigate the influence of SRCs on the one-nucleon (1N) and two-nucleon (2N) knockout channel for muon-neutrino induced processes on a $^{12}$C target at energies relevant for contemporary measurements. Method: The model adopted in this work, corrects the impulse approximation for SRCs by shifting the com- plexity induced by the SRCs from the wave functions to the operators. Due to the local character of the SRCs, it is argued that the expansion of these operators can be truncated at a low order. Results: The model is compared with electron-scattering data, and two-particle two-hole responses are presented for neutrino scattering. The contributions from the vector and axial-vector parts of the nuclear current as well as the central, tensor and spin-isospin part of the SRCs are studied. Conclusions: Nuclear SRCs affect the 1N knockout channel and give rise to 2N knockout. The exclusive neutrino-induced 2N knockout cross section of SRC pairs is shown and the 2N knockout contribution to the QE signal is calculated. The strength occurs as a broad background which extends into the dip region.

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.

Neutron polarization analysis study of the frustrated magnetic ground state ofβ-Mn1−xAlx

We have performed a neutron polarization analysis study of the short-range nuclear and magnetic correlations present in the dilute alloy, $\ensuremath{\beta}{\text{-Mn}}_{1\ensuremath{-}x}{\text{Al}}_{x}$ with $0.03\ensuremath{\le}x\ensuremath{\le}0.16$, in order to study the evolution of the magnetic ground state of this system as it achieves static spin-glass order at concentrations $x>0.09$. To this end we have developed a reverse--Monte Carlo algorithm which has enabled us to extract Warren-Cowley nuclear short-range order parameters and magnetic spin correlations. Using conventional neutron powder diffraction, we show that the nonmagnetic Al substituents preferentially occupy the magnetic site II Wyckoff positions in the $\ensuremath{\beta}\text{-Mn}$ structure---resulting in a reduction of the magnetic topological frustration of the Mn atoms. These Al impurities are found to display strong anticlustering behavior. The magnetic spin correlations are predominantly antiferromagnetic, persisting over a short range which is similar for all the samples studied---above and below the spin-liquid-spin-glass boundary---while the observed static (disordered) moment is shown to increase with increasing Al concentration.

Chiral approach to antikaons- andp-wave interactions in dense nuclear matter

The properties of the antikaons in nuclear matter are investigated from a chiral unitary approach which incorporates the $s$- and $p$-waves of the $\overline{K}N$ interaction. To obtain the in-medium meson-baryon amplitudes we include, in a self-consistent way, Pauli blocking effects, meson self-energies corrected by nuclear short-range correlations and baryon binding potentials. We pay special attention to investigating the validity of the on-shell factorization, showing that it cannot be applied in the evaluation of the in-medium corrections to the $p$-wave amplitudes. In nuclear matter at saturation energy, the \ensuremath{\Lambda} and \ensuremath{\Sigma} develop an attractive potential of about \ensuremath{-}30 MeV, while the ${\ensuremath{\Sigma}}^{*}$ pole remains at the free space value although its width gets sensibly increased to about 80 MeV. The antikaon also develops a moderate attraction that does not support the existence of very deep and narrow bound states, confirming the findings of previous self-consistent calculations.

Nuclear Halo-Like Phenomena of 6,8He and Nuclear Short Range Correlation**The project supported in part by National Natural Science Foundation of China under Grant Nos. 10247004 and 10075081, and the Natural Science Foundation of Guangxi Province of China under Grant No. 0339008

Based on the nuclear short range correlation in a halo-like nucleus, theoretical analysis of the experimental cross sections for small-angle elastic scattering at the energy of about has been performed in the framework of Glauber multiple scattering theory. Our theoretical calculations reproduce the corresponding experimental data quite successfully. These good agreements confirm that the nuclear halo-like phenomena may originate from the short range correlation between nucleons in a halo-like nucleus.

Nuclear and magnetic short-range order in some dilute β-Mn alloys

Using full XYZ neutron polarization analysis, we have studied the nuclear and magnetic diffuse scattering of various β-Mn alloys. This has enabled the study of not only the magnetic short-range spin-correlations in isolation, but also the crucial role of the interplay between the magnetic and nuclear disorder in the lattice as the impurity atoms are introduced. Using reverse Monte-Carlo methods, we deduce the nuclear short-range order parameters and magnetic correlations of these alloys over a large number of near neighbour shells.

Nuclear Halo-Like Phenomena and Short-Range Nuclear Correlation**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19975053, 19835010, and 10075081

Based on Glauber Multiple Scattering Theory, high-energy proton elastic scattering on halo-like nucleus 13C is studied in a single nucleon wave function with low angular momentum configurations. A great agreement with experimental data is obtained and the theoretical prediction clearly shows that 13C has a neutron halo-like structure. Then, the origin and nature of nuclear halo phenomena are explained in terms of nuclear short-range correlations. Our conclusion shows that the origin of nuclear halo-like phenomena originates from short range nuclear correlation.