Nucleon-nucleon Correlations Research Articles

Nucleon-nucleon correlations, short-lived excitations, and the quarks within

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 there is a phenomenological relation between the EMC effect and the effects of SRC that is not an accident. The influence of strongly correlated neutron-proton pairs involving highly virtual nucleons is responsible for both effects. These correlated pairs are temporary high-density fluctuations in the nucleus in which the internal structure of the nucleons is briefly modified. This conclusion needs to be solidified by the future experiments and improved theoretical analyses that are discussed herein.

Abstract ID: 61 Validation of Geant4 nuclear reaction models for hadrontherapy and preliminary results with SMF and Blob

Reliable nuclear fragmentation models are of utmost importance in hadrontherapy, where Monte Carlo (MC) simulations are used to compute the input parameters of the treatment planning software, to validate the deposited dose calculation, to evaluate the biological effectiveness of the radiation, to correlate the β + emitters production in the patient body with the delivered dose, and to allow a non-invasive treatment verification. Despite of its large use, the models implemented in Geant4 have shown severe limitations in reproducing the measured secondaries yields in ions interaction below 100 MeV/A, in term of production rates, angular and energy distributions [1] , [2] , [3] . We will present a benchmark of the Geant4 models with double-differential cross section and angular distributions of the secondary fragments produced in the 12C fragmentation at 62 MeV/A on thin carbon target, such a benchmark includes the recently implemented model INCL++ [4] , [5] . Moreover, we will present the preliminary results, obtained in simulating the same interaction, with SMF [6] and BLOB [7] . Both, SMF and BLOB are semiclassical one-body approaches to solve the Boltzmann-Langevin equation. They include an identical treatment of the mean-field propagation, on the basis of the same effective interaction, but they differ in the way fluctuations are included. In particular, while SMF employs a Uehling-Uhlenbeck collision term and introduces fluctuations as projected on the density space, BLOB introduces fluctuations in full phase space through a modified collision term where nucleon-nucleon correlations are explicitly involved. Both of them, SMF and BLOB, have been developed to simulate the heavy ion interactions in the Fermi-energy regime. We will show their capabilities in describing 12C fragmentation foreseen their implementation in Geant4.

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.

Nucleon-nucleon correlations probed at far sub-Coulomb energies

Excitation functions of one- and two-neutron transfer channels have been measured for the closed shell 40 Ca+96 Zr and superfluid 60 Ni+116 Sn systems from the Coulomb barrier energy to energies far below. By using the unique PRISMA performance in terms of resolution and efficiency, measurements at very low bombarding energies have been performed. In the case of the 60 Ni+116 Sn system, a complementary particle-γ coincident measurements provide the ground and excited state populations.The experimental transfer probabilities have been compared with semiclasical microscopic calculations that incorporate nucleon-nucleon correlations, together with known structure information of entrance and exit channels nuclei and reaction dynamics. These calculations well reproduce, in the whole energy range, one- and two-neutron transfer channels in shape and magnitude.

“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.

Measurement of double-differential muon neutrino charged-current interactions onC8H8without pions in the final state using the T2K off-axis beam

We report the measurement of muon neutrino charged-current interactions on carbon without pions in the final state at the T2K beam energy using 5.734$\times10^{20}$ protons on target. For the first time the measurement is reported as a flux-integrated, double-differential cross-section in muon kinematic variables ($\cos\theta_\mu$, $p_\mu$), without correcting for events where a pion is produced and then absorbed by final state interactions. Two analyses are performed with different selections, background evaluations and cross-section extraction methods to demonstrate the robustness of the results against biases due to model-dependent assumptions. The measurements compare favorably with recent models which include nucleon-nucleon correlations but, given the present precision, the measurement does not solve the degeneracy between different models. The data also agree with Monte Carlo simulations which use effective parameters that are tuned to external data to describe the nuclear effects. The total cross-section in the full phase space is $\sigma = (0.417 \pm 0.047 \text{(syst)} \pm 0.005 \text{(stat)})\times 10^{-38} \text{cm}^2$ $\text{nucleon}^{-1}$ and the cross-section integrated in the region of phase space with largest efficiency and best signal-over-background ratio ($\cos\theta_\mu>0.6$ and $p_\mu > 200$ MeV) is $\sigma = (0.202 \pm 0.0359 \text{(syst)} \pm 0.0026 \text{(stat)}) \times 10^{-38} \text{cm}^2$ $\text{nucleon}^{-1}$.

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.

Exploring Nuclear Dynamics with (e, e′p) Reactions: From LNF to JLab

Proton knockout reactions, in which the scattered beam particle and the outgoing nucleon are detected in coincidence, proved to be a very powerful tool for studying the properties of bound nucleons. The first generation of (e, e′p) data—collected over more than thirty years, starting in the early 1960s—have greatly contributed to establish the validity of the nuclear shell model, showing at the same time its limitations. More recent measurements, made possible by the availability of continuous electron beams of higher energy, have unambiguously demonstrated the occurrence of significant effects of nucleon-nucleon correlations, thus providing new insight into the nature of short-range nuclear dynamics.

Probing nucleon-nucleon correlations in heavy-ion transfer reactions

The γ-particle coincident measurements, performed by coupling of the PRISMA spectrometer to the large γ arrays (CLARA and AGATA), demonstrate a strong interplay between single-particle and collective degrees of freedom that is pertinent to the reaction dynamics. By using the unique PRISMA performance in terms of both resolution and efficiency, measurements at very low bombarding energies have been performed. Via transfer of nucleon pairs, valuable information on the component responsible for particle correlations has been derived.

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.

Probing nucleon-nucleon correlations in heavy-ion transfer reactions

The γ -particle coincident measurements, performed by coupling of the PRISMA spectrometer to the large γ arrays (CLARA and AGATA), demonstrate a strong interplay between single-particle and collective degrees of freedom that is pertinent to the reaction dynamics. By using the unique PRISMA performance in terms of both resolution and efficiency, measurements at very low bombarding energies have been performed. Via transfer of nucleon pairs, valuable information on the component responsible for particle correlations has been derived.

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.

轻核α团簇结构理论和实验研究进展

The degree of freedom of α cluster exists widely in light α conjugate nuclei, which not only plays essential roles in the synthesis of elements and abandance of elements in nuclear astrophysics but also serves as the natural laboratory to test various new many-body theories and nuclear force due to the available high precision data. This article briefly summarizes the different theoretical approaches for alpha-cluster and compares the results of 12C Hoyle state with these approaches. All the theories support the structure of Hoyle state with a more extended size compared with ground state. However, a consensus has not be reached about how α clusters stay inside Hoyle state, where several candidate states are possible, such as a condensate state, a gas or crystalline arrangements of the α-particles. Further more, we also introduce the new experimental measurements of a decay and collective excitation of rotational band. In order to pin down the existence form of a in Hoyle state, a deeper knowledge of the collective excitation of cluster is needed. The essential progress can only be possible by high combination of new data with high precision and new many-body theory, where the roles of nucleon-nucleon correlation, cluster-cluster correlation and continuum are needed to be included reasonably.

Neutral current quasielastic (anti)neutrino scattering beyond the Fermi gas model at MiniBooNE and BNL kinematics

Neutral current quasielastic (anti)neutrino scattering cross sections on a $^{12}$C target are analyzed using a realistic spectral function $S(p,E)$ that gives a scaling function in accordance with the ($e,e'$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations by using natural orbitals (NOs) from the Jastrow correlation method and has a realistic energy dependence. The standard value of the axial mass $M_A= 1.032$ GeV is used in all calculations. The role of the final-state interaction (FSI) on the spectral and scaling functions, as well as on the cross sections is accounted for. A comparison of the calculations with the empirical data of the MiniBooNE and BNL experiments is performed. Our results are analyzed in comparison with those when NN correlations are not included, and also with results from other theoretical approaches, such as the relativistic Fermi gas (RFG), the relativistic mean field (RMF), the relativistic Green's function (RGF), as well as with the SuperScaling Approach (SuSA) based on the analysis of quasielastic electron scattering.

Transfer reaction studies in inverse kinematics with the magnetic spectrometer PRISMA

The large solid angle magnetic spectrometers, in combination with large gamma arrays, allowed to perform reaction mechanism and nuclear structure studies in different regions of the nuclear chart, especially in the neutron-rich direction. By studying transfer of multiple pairs valuable information on nucleon-nucleon correlations can be derived, especially from measurements performed below the Coulomb barrier. There is growing interest in the study of the properties of the heavy binary partner, in the Pb and in the actinides regions, crucial also for astrophysics.

Probing nucleon-nucleon correlations via heavy ion transfer reactions

The revival of transfer reaction studies benefited from the construction of the new generation large solid angle spectrometers, coupled to large arrays. The recent results of -particle coincident measurements demonstrate a strong interplay between single-particle and collective degrees of freedom that is pertinent to the reaction dynam- ics. Via transfer of pairs, valuable information on the component responsible for particle correlations has been derived.

Short-range correlation effects on the nuclear matrix element of neutrinoless double-βdecay

We report the results of a calculation of the nuclear matrix element of neutrinoless double-$\ensuremath{\beta}$ decay of $^{48}\mathrm{Ca}$, carried out taking into account nucleon-nucleon correlations in both coordinate and spin space. Our numerical results, obtained using nuclear matter correlation functions, suggest that inclusion of correlations may lead to a $\ensuremath{\sim}20$% decrease of the matrix element, with respect to the shell-model prediction. This conclusion is supported by the results of an independent calculation, in which correlation effects are taken into account using the spectroscopic factors of $^{48}\mathrm{Ca}$, obtained from an ab initio many-body approach, to renormalize the shell-model states.

Correlations in the Monte Carlo Glauber model

Event-by-event fluctuations of observables are often modeled using the Monte Carlo Glauber model, in which the energy is initially deposited in sources associated with wounded nucleons. In this paper, we analyze in detail the correlations between these sources in proton-nucleus and nucleus-nucleus collisions. There are correlations arising from nucleon-nucleon correlations within each nucleus, and correlations due to the collision mechanism, which we dub twin correlations. We investigate this new phenomenon in detail. At the Brookhaven Relativistic Heavy Ion Collider and CERN Large Hadron Collider energies, correlations are found to have modest effects on size and eccentricity fluctuations, such that the Glauber model produces to a good approximation a collection of independent sources.

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.