Nucleon Momentum Distribution Research Articles

Modern numerical differentiation technique for extracting nucleon momentum distributions

Modern numerical differentiation technique for extracting nucleon momentum distributions

High-resolution momentum distributions from low-resolution wave functions

Nucleon momentum distributions calculated with a common one-body operator vary with the resolution scale (and scheme) of the Hamiltonian used. For high-resolution potentials such as Argonne v18 (AV18) there is a high-momentum tail, reflecting short-range correlations in the nuclear wave function, which is reduced or absent for softer, lower-resolution interactions. We explore if the similarity renormalization group (SRG) can be used to quantitatively reproduce the high-resolution distributions from variational Monte Carlo at all momenta using SRG-evolved operators and empirically fit single-particle orbitals rather than a full RG evolution of many-body wave functions. The goal of this approach is to enable calculations of high-resolution distributions for a wider range of nuclei as well as for other interactions, and provides connections to phenomenological analyses of experiments.

Probing high-momentum component in nucleon momentum distribution by neutron-proton bremsstrahlung γ-rays in heavy ion reactions

The high momentum tail (HMT) of nucleons, as a signature of the short-range correlations in nuclei, has been investigated by the high-energy bremsstrahlung γ rays produced in 86Kr+124Sn at 25 MeV/nucleon. The energetic photons are measured by a CsI(Tl) hodoscope mounted on the spectrometer CSHINE. The energy spectrum ≥35 MeV can be reproduced by the Isospin- and Momentum-Dependent Boltzmann-Uehling-Uhlenbeck model calculations incorporating the photon production channel from np process in which the HMTs of nucleons is considered. A non-zero HMT ratio of about 15% is favored by the data. The effect of the capture channel np→dγ is demonstrated.

Influence of single-particle energy on inclusive electron scattering

Extensive studies have been carried out over the past decades to explore the impacts of nucleon momentum distributions (NMDs) on the inclusive electron scattering process. Nevertheless, there remains limited research about the effects of the single-particle energy level distributions E s.p.(β) on reaction. For a given nucleus, the E s.p.(β) of different deformations exhibits distinct changes. In this paper, we investigate the influences of the E s.p.(β) of distinct deformations on process. Using the plane-wave impulse approximation method, we calculate the cross sections of different deformed configurations. The corresponding E s.p.(β) and NMDs are obtained from the deformed relativistic mean-field model. It is found that the theoretical cross sections show moderate dependence on the E s.p.(β) of distinct deformations. This is due to the conservation of energy, which restricts the number of nucleons participating in the process of diverse deformed configurations. The studies in this paper can provide useful guides for future lepton-nucleus scattering experiments.

Nucleon momentum distributions from inclusive electron scattering with superscaling analysis

Nucleon momentum distributions are crucial windows to probe nuclear structures. They provide valuable information not only on mean-field structures but also on short-range correlations. The $y$ scaling analysis generally serves as a tool to extract the nucleon momentum distribution from inclusive quasielastic electron cross sections. In this paper, we report new nucleon momentum distributions for deuteron, ${}^{3,4}\mathrm{He}$, $^{9}\mathrm{Be}$, and $^{12}\mathrm{C}$, extracted, based on ${\ensuremath{\psi}}^{\ensuremath{'}}$ scaling, directly from the latest high-precision experimental data. It is found that, for deuteron, ${}^{3,4}\mathrm{He}$, $^{9}\mathrm{Be}$, and $^{12}\mathrm{C}$, the ${\ensuremath{\psi}}^{\ensuremath{'}}$-scaling method provides reasonable results in agreement with state-of-the-art ab initio calculations up to 3.5 ${\mathrm{fm}}^{\ensuremath{-}1}$. These new nucleon momentum distributions can be helpful references for future studies of nuclear structures.

Effects of high-momentum tail of nucleon momentum distribution on initiation of cluster production in heavy-ion collisions at intermediate energies

Based on the transport model isospin-dependent Boltzmann-Uehling-Uhlenbeck coupled with a phase-space coalescence afterburner, we studied the effects of the high-momentum tail (HMT) of nucleon momentum distribution in initialization in 197Au+197Au reactions at a beam energy of 400 MeV/nucleon with different impact parameters.We found remarkable impact parameter-dependent HMT effects on the fragment multiplicity distribution. The average neutron to proton ratio of produced isotopes is also affected by the HMT. The rapidity distributions of triton and 3He and their elliptic flows are all evidently affected by the HMT. All the effects of the HMT on the cluster production in heavy-ion collisions are centrality dependent.

Neutron-neutron short-range correlations and their impacts on neutron stars

Due to the very nature of the nucleon-nucleon interactions, some nucleons form strongly correlated nucleon-nucleon pairs. This paper focuses on the significance of nn pairs for neutron star matter. Inspired by recent numerical and experimental advances in SRCs, we propose density-dependent nucleon momentum distributions with the isospin-asymmetry scaling parameter. We also analyze the impacts of nn pairs on the physical properties of neutron stars. Our numerical results find that nn pairs, plus np pairs, could stiffen the equation of state of neutron star matter and consequently cause a significant increase in the maximum mass of neutron stars. This work might generate a fresh viewpoint on confronting the upper limit on the maximum mass of neutron stars.

Nucleon momentum distribution of 56Fe from the axially deformed relativistic mean-field model with nucleon-nucleon correlations

Nucleon momentum distribution (NMD), particularly its high-momentum components, is essential for understanding the nucleon--nucleon ($ NN $) correlations in nuclei. Herein, we develop the studies of NMD of $^{56}\text{Fe}$ from the axially deformed relativistic mean-field (RMF) model. Moreover, we introduce the effects of $ NN $ correlation into the RMF model from phenomenological models based on deuteron and nuclear matter. For the region $ k<k_{\text{F}} $, the effects of deformation on the NMD of the RMF model are investigated using the total and single-particle NMDs. For the region $ k>k_{\text{F}} $, the high-momentum components of the RMF model are modified by the effects of $ NN $ correlation, which agree with the experimental data. Comparing the NMD of relativistic and non-relativistic mean-field models, the relativistic effects on nuclear structures in momentum space are analyzed. Finally, by analogizing the tensor correlations in deuteron and Jastrow-type correlations in nuclear matter, the behaviors and contributions of $ NN $ correlations in $^{56}\text{Fe}$ are further analyzed, which helps clarify the effects of the tensor force on the NMD of heavy nuclei.

Stable15N and Neutron Halo 16N Nuclei Structure Study by Elastic Electron Scattering Form Factors and Nucleon Momentum Distributions

In this manuscript, the elastic electron scattering form factors and the nucleon momentum distributions (NMD) for stable 15N and neutron halo 16N at the ground state were reported. This was accomplished by utilizing the well-known Coherent Density Fluctuation Model (CDFM) via the employment of fluctuation function (|F(q)|2) which is coupled with the density distributions nuclei. The long-tail performance in the NMD at high momentum region was further determined via experimental and theoretical fluctuation functions. The evaluated elastic electron scattering form factors were evaluated on the bases of the density distributions as well as the root mean square (RMS) radii for each measured nucleon. The proposed study provides a robust correlation between the theoretical formation factors and the practical results of 15N and 16N nuclei.

Impacts of nucleon-nucleon short-range correlations on neutron stars

Nucleon-nucleon short-range correlations (SRCs) are inevitable consequences of realistic nucleon-nucleon interactions. The corresponding SRC pairs, characterized by high relative momenta, have been verified experimentally to be important in finite nuclei. In this work, we study the impacts of nucleon-nucleon SRCs on the physical properties of neutron stars. Considering the small center-of-mass momenta of SRC pairs, new nucleon momentum distributions with high-momentum tails (HMTs) are proposed by extrapolating well-established experimental results of SRCs in finite nuclei to neutron star matter. HMTs with different shapes are adopted to estimate theoretical uncertainties. It is found that nucleon-nucleon SRCs generally stiffen the equation of state of neutron star matter and increase the maximum mass of neutron stars.

Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tagging

Background: DIS on the polarized deuteron with detection of a proton in the nuclear breakup region (spectator tagging) represents a unique method for extracting the neutron spin structure functions and studying nuclear modifications. The tagged proton momentum controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. Such measurements could be performed with the future electron-ion collider (EIC) and forward proton detectors if deuteron beam polarization could be achieved. Purpose: Develop theoretical framework for polarized deuteron DIS with spectator tagging. Formulate procedures for neutron spin structure extraction. Methods: A covariant spin density matrix formalism is used to describe general deuteron polarization in collider experiments (vector/tensor, pure/mixed). Light-front (LF) quantum mechanics is employed to factorize nuclear and nucleonic structure in the DIS process. A 4-dimensional representation of LF spin structure is used to construct the polarized deuteron LF wave function and efficiently evaluate the spin sums. Free neutron structure is extracted using the impulse approximation and analyticity in the tagged proton momentum (pole extrapolation). Results: General expressions of the polarized tagged DIS observables in collider experiments. Analytic and numerical study of the polarized deuteron LF spectral function and nucleon momentum distributions. Practical procedures for neutron spin structure extraction from the tagged deuteron spin asymmetries. Conclusions: Spectator tagging provides new tools for precise neutron spin structure measurements. D-wave depolarization and nuclear binding effects can be eliminated through the tagged proton momentum dependence. The methods can be extended to tensor-polarized observables, spin-orbit effects, and diffractive processes.

Novel observation of isospin structure of short-range correlations in calcium isotopes

Short Range Correlations (SRCs) have been identified as being responsible for the high momentum tail of the nucleon momentum distribution, n(k). Hard, short-range interactions of nucleon pairs generate the high momentum tail and imprint a universal character on n(k) for all nuclei at large momentum. Triple coincidence experiments have shown a strong dominance of np pairs, but these measurements involve large final state interactions. This paper presents the results from Jefferson Lab experiment E08014 which measured inclusive electron scattering cross-section from Ca isotopes. By comparing the inclusive cross section from 48Ca to 40Ca in a kinematic region dominated by SRCs we provide a new way to study the isospin structure of SRCs.

Properties of dibaryons in nuclear medium

Properties of six-quark dibaryons in nuclear medium are considered by example of $A=6$ nuclei within the three-cluster $\alpha+2N$ model. Dibaryon production in nuclei leads to the appearance of a three-body force between the dibaryon and nuclear core. This non-conventional scalar force is shown to provide an additional attractive contribution to the three-body binding energy. This three-body contribution improves noticeably agreement between theoretical results and experimental data for the majority of observables. The most serious difference between the traditional $NN$-force models and the dibaryon-induced model is found for the nucleon momentum distribution, the latter model providing a strong enrichment of the high-momentum components both for $^6$Li and $^6$He cases.

Nucleon momentum distribution extracted from the experimental scaling function

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum (q) and the scaling variable (y), is taken into account, and the analysis is extended to both, positive and negative y-values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parameterizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.

Direct photon emission and influence of dynamical wave packets in an extended quantum molecular dynamics model

Direct photon produced from first proton-neutron ($p$-$n$) collision during the early stage of heavy ion reaction is a sensitive probe to reflect energy and momentum distribution of nucleons. In this work, we embedded the hard photon production channel in an extended quantum molecular dynamics (EQMD) model, and took the direct photon as a possible probe to improve namely the Fermi motion in the EQMD model. A possible scheme is offered to handle the dynamical wave packet width within incoherent bremsstrahlung process. Direct photons calculated by our modified EQMD were compared with data of $^{14}$N + $^{12}$C at beam energies $E/A$ = 20, 30 and 40 MeV, and it is found that the yield, inverse slope and angular distribution of direct photons could be reasonably reproduced. In addition, asymmetric reaction systems of $^{4}$He + C and $^{4}$He + Zn at $E/A$ = 53 MeV are also simulated in this work. It is found that the symmetric angular distribution in the nucleon-nucleon ($N$-$N$) center-of-mass (c.m.) frame and the velocity of $ the \gamma$-emission source can be reasonably obtained from our method although there is some quantitative differences.

High-momentum components in the 4He nucleus caused by inter-nucleon correlations

High-momentum components of nuclei are essential for understanding the underlying inter-nucleon correlations in nuclei. We perform the comprehensive analysis for the origin of the high-momentum components of 4He in the framework of Tensor-optimized High-momentum Antisymmetrized Molecular Dynamics (TO-HMAMD), which is a completely variational approach as an ab initio theory starting from the bare nucleon-nucleon interaction. The analytical derivations are provided for the nucleon momentum distribution of the Antisymmetrized Momentum Dynamics (AMD) wave functions, with subtraction of center-of-mass motion. The nucleon momentum distribution for 4He is calculated by applying a new expansion technique to our ab initio wave function, and agrees with the values extracted from experimental data up to the high-momentum region. Fine-grained analysis is performed for the high-momentum components in 4He with respect to different nucleon correlations. Contributions from tensor, central with short-range, and many-body correlations are extracted from the nucleon momentum distributions. The manifestation of tensor correlation around 2 fm−1 region is explicitly confirmed by comparing the momentum distributions predicted using different types of NN interactions with and without the tensor force.

The nucleon momentum and density distribution of the 4He nucleus using the Morse potential

The nucleon momentum and density distribution of the 4He nucleus are calculated by using the Morse single-particle potential. The parameters for the momentum distribution n(fc) are determined by fitting either the charge form factor to the available experimental data of the elastic electron scattering by 4He or the momentum distribution to the corresponding "experimental" values. The calculations can be performed partly analytically and the results show a considerable overall improvement with respect to those obtained with the oscillator shell model. The r.m.s radius of the charge density distribution determined by fitting the charge form factor is in very good agreement with the vaiues obtained by means of model independent analysis.

The nucleon momentum distribution in light nuclei

The nucléon momentum distribution in light nuclei is studied by means of a single particle potential model which consists of an attractive harmonic oscillator potential Va=½mω²r² and also of a repulsive one of the form Vr=B/r², Β &gt; 0. The latter simulates to some extend effects which would result if short range correlations were included (e.g. by a Jastrow factor) in a nuclear wave function, having as uncorrelated part a Slater determinant of harmonic oscillator orbitals. The main advantage of this model is that it leads to fairly simple analytic expressions for the momentum distribution of light nuclei and also for the density distributions and the elastic form factors. These expressions are quite useful in obtaining, for example, the asymptotic form of η(k) for large k from which it is seen that the steep decrease of the nucléon momentum distribution observed with the harmonic oscillator model in this region is improved. Numerical results using various least squares fittings are obtained and discussed for a number of nuclei of the 1s, 1p shell.

Proton-proton momentum correlation function as a probe of the high momentum tail of the nucleon-momentum distribution

Within an improved transport model, we examine effects of the high momentum tail of the nucleon momentum distribution induced by short-range correlations on the proton-proton momentum correlation function in $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon. It is found that the proton-proton momentum correlation function from preequilibrium emissions responds sensitively to the presence as well as fraction of nucleons in the high momentum tail of the nucleon momentum distribution, but is almost robustly insensitive to other factors including the symmetry energy and the uncertainty of cutoff value of nucleon effective high momentum. In terms of the sensitivity and clearness, we propose that the proton-proton momentum correlation function from preequilibrium emissions can be as an effective probe of the high momentum tail of the nucleon momentum distribution.

Nucleon momentum distributions in asymmetric nuclear matter

Nucleon momentum distributions at various densities and isospin-asymmetries for nuclear matter are investigated systematically within the extended Bruecker-Hartree-Fock approach.The shapes of the normalized momentum distributions varying with $k/k_{F}$ are practically identical, while the density and isospin dependent magnitude of the distribution is directly related to the depletion of the Fermi sea. Based on these properties, a parameterized formula is proposed with the parameters calibrated to the calculated result.