Nuclear Density Distribution Research Articles

Exploring the Diversity of Nuclear Density through Information Entropy.

This study explores the role of information entropy in understanding nuclear density distributions, including both stable configurations and non-traditional structures such as neutron halos and α-clustering. By quantifying the uncertainty and disorder inherent in nucleon distributions in nuclear many-body systems, information entropy provides a macroscopic measure of the physical properties of the system. A more dispersed and disordered density distribution results in a higher value of information entropy. This intrinsic relationship between information entropy and system complexity allows us to quantify uncertainty and disorder in nuclear structures by analyzing various geometric parameters such as nuclear radius, diffuseness, neutron skin, and cluster structural features.

Nonlinear-Optical Analogies in Nuclear-Like Soliton Reactions: Selection Rules, Nonlinear Tunneling and Sub-Barrier Fusion–Fission

Abstract The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics, which still remain hidden from us. We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons. On the base of this model, we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton self-induced sub-barrier transparency effect. We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions. The main finding of this study concerns the conservation of total number of nucleons (or the baryon number) in nuclear-like soliton reactions. We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a “cloud” of “dressing” spectral side-bands appears in the frequency spectra of the solitons. This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter. Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors. We show that the nuclear-like reactions between well-dressed solitons are realized by “exchange” between “particle-like” side bands in their spectra.

Global prediction of nuclear charge density distributions using a deep neural network

Global prediction of nuclear charge density distributions using a deep neural network

Microscopic optical potentials for medium-mass isotopes derived at the first order of Watson multiple-scattering theory

We perform a first-principles calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with self-consistent Green's function theory with a nucleon-nucleon t matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off calcium and nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65–200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the calcium and nickel isotopic chains. Published by the American Physical Society 2024

Study of Nuclear Structure and Elastic Electron Scattering Form Factors for Neutron Halo Nuclei (22N ,23O and 24F) Using Full Correlation Functions with Two Size Parameters

The study of neutron-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for the nuclei (22N,23 O and 24F). With the use of a strong short-range effect and a strong tensor force, the nucleons distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: the first (bcore), for the inner (core) orbits, and the second (bvalence) for the outer (halo) orbits. This work demonstrated the existence of neutron halo nuclei for the nuclei (22N, 23O and 24F) in the (2s1/2) shell. The computed density distribution of neutron, proton and matter for these nuclei displayed the long tail performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is independent of the neutrons that make up the halo, but rather it results from a difference in the proton density distribution of the last proton in the nuclei. Fortran 95 power station program was used to the neutron, proton and matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei were in good agreement with the experimental data.

Analysis of Atomic Thermal Vibration of CrN Based on Rietveld Refinement Method

The crystal structure of chromium nitride (CrN) is studied by X‐Ray diffraction from 25 to 600 °C. Based on the RIETAN‐2000 program of Rietveld refinement method, the experimental results are analyzed, and the crystal structure parameters of CrN powder crystals at different temperatures are refined. Atomic thermal vibration isotropic temperature factor B is directly obtained by the Rietveld refinement method. Using the maximum entropy method analytical procedure, the 3D and planar isoheight nuclear density distribution characteristics of CrN are derived, realizing the visualization of nuclear density distribution. It can help to calculate the thermal diffuse scattering.

Impact of different components of the Skyrme nucleon–nucleon effective interaction on the nuclear density distribution

We systematically investigate the impact of the different terms of the Skyrme energy density functional of the effective nucleon-nucleon interaction, and of its associated nuclear matter (NM) properties, on the density distributions of spherical nuclei. Twenty five Skyrme force parameterizations are examined simultaneously, covering a broad range of each characteristic parameter and NM property. The diffuseness and the neutron-skin thickness are found to be the most sensitive density quantities to the force parameterization. The diffuseness is indicated to decrease with increasing the central zero-range and the effective mass terms of the effective force, and the power σ of its density dependent term, as well as with the coefficient of the NM symmetry energy (asym) and its density slope (L) at saturation density, and the incompressibility (Ko). In contrast, the proton and neutron diffuseness tend to increase with increasing the spin–orbit force and the isoscalar effective nucleon-mass (m*), and to increases slightly with the density dependence parameters other than the power σ. Opposite impacts are pointed out for the different parts of the finite-range, and J2 tensor terms on the proton and neutron density. While the neutron-skin thickness tends to increase significantly upon increasing the central zero-range and spin–orbit force terms, asym, L, and Ko, and to increase slightly with the finite-range and J2 tensor terms, and σ, it decreases with the effective-mass term, the density-dependence exchange parameter, and with the indicated isoscalar effective mass. The proton and neutron radii exhibit decreasing behavior with the central zero-range and the spin–orbit terms, and with Ko, and m*. Increasing asym and L indicate slightly less (larger) proton (neutron) radius.

Study of P+10,11Be elastic scattering using different potentials at low energies

A microscopic approach was used to analyze the elastic scattering of protons on [Formula: see text]Be at incident energies of 9.1, 15.1, 39.1, and 59.3[Formula: see text]MeV/nucleon for [Formula: see text]Be and [Formula: see text]Be (38.4[Formula: see text]MeV/nucleon and 49.3[Formula: see text]MeV/nucleon) within the framework of single folding (SF) and São-Paulo (SP) potentials. Also, the energy dependence of the reaction cross-sections of the considered reactions is investigated. The study was performed using FRESCO code on the free parameters ([Formula: see text] and [Formula: see text]). The DFPOT code was used to compute the SF and SP potentials microscopically for the real and imaginary parts of the optical potential (OP), respectively. The OP was derived using two different nuclear density distributions since [Formula: see text]Be as Gaussian–Gaussian (GG) [Formula: see text] and Gaussian–Oscillator (GO) [Formula: see text], and the effective N–N interactions were represented in the Gaussian form. The resulting differential cross-sections agreed well with the given experimental data.

Calibration of nuclear charge density distribution by back-propagation neural networks

Calibration of nuclear charge density distribution by back-propagation neural networks

Spatial distribution and influencing factors of high-quality tourist attractions in Shandong Province, China.

Optimizing the spatial layout of high-quality tourist attractions is of great significance in the sustainable development of the tourism industry. This work employs the ArcGIS spatial analysis tool to study the form, equality, and density of the spatial distribution of the 892 3A+ tourist attractions (high-quality tourist attractions hereafter) in Shandong Province, China. It also examines the factors influencing the spatial distribution of tourist attractions from the perspectives of geographic features and landscapes, culture and heritage, socioeconomic development, and transportation. We therefore find the following: 1) High-quality tourist attractions in Shandong Province have obvious clustering in spatial distribution with the high-density areas mainly concentrated in Qingdao, Jining, Jinan, Tai'an and other cities. Influenced by resource endowment and economic development, the two major geographical areas in Central Shandong and Jiaodong Peninsula have the most concentrated distribution of high-quality tourist attractions. 2) The distribution of high-quality tourist attractions shows a southwest‒northeast clustering direction; Qingdao is a high-high clustering area, and Heze is a low-high clustering area with low uniformity of spatial distribution and obvious spatial divergence. 3) Tourist attractions show an obvious "N" type high-density distribution belt and nuclear density distribution across the three existing agglomeration centers in the Jining-Tai'an intersection, Binzhou-Dongying intersection, and Qingdao Jiaozhou Bay coast. 4) Topography, climate conditions, history and culture are intrinsic factors affecting the spatial distribution of tourist attractions, while socioeconomic and transportation conditions are external requirements for the development thereof; collectively, they constrain the spatial distribution of high-quality tourist attractions.

Analysis of the nuclear loads on Chromium monoblock divertor target for DEMO

The Plasma Facing Components (PFCs) of DEMO divertor play a fundamental role for the heat removal and particle exhaust functions, during fusion plasma. This implies a very harsh operation environment characterized by the combination of complex loading and stress conditions, intense particle bombardment, high heat flux deposition and a significant neutron irradiation. In the framework of the European DEMO divertor project (WPDIV), several target design concepts alternative to the baseline ITER-like technology are under evaluation, such as Chromium block design. It consists of chromium block, tungsten armor tile and copper alloy cooling pipe, and it is very attractive from an activation reduction, waste management and safety point of view. Therefore, the assessment of the most impacting nuclear loads for the PFC design is a pivotal aspect for DEMO divertor R&D program and this study is fully devoted to the comprehension of the spatial distributions of the main nuclear quantities (radiation damage, He-production and nuclear heating density) on the overall divertor targets. Neutronics analyses have been performed with MCNP5 Monte Carlo code using both DEMO MCNP Water Cooled Lithium Lead (WCLL) and Helium Cooled Pebble Bed (HCPB) blanket models, with a fully heterogeneous representation of the divertor cassette and Chromium PFCs geometry. The results of this analysis show that nuclear heating density and radiation damage distributions are higher with WCLL blanket than HCPB, except for He-production which seems not significantly affected by the blanket configuration. For each nuclear quantity, the peak values are achieved in correspondence of the baffle region and especially on the external units of the targets, as expected, being this region the most exposed to irradiation.

Theoretical Study of Proton Halo Structure and Elastic Electron Scattering Form Factor for 23Al and 27P Nuclei by Using Full Correlation Functions (Tensor Force and Short Range)

The study of proton-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for nuclei (23Al and 27P), use two body charge density distributions (2BCDD's). With the effects of the strong tensor force and short range, the nucleon distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: bc for the inner (core) orbits and bv for the outer (halo) orbitals. This work demonstrated the existence of proton halo nuclei for the nuclei (23Al and 27P) in the shell (2s1/2), and the computed proton, neutron, and matter density distributions for these nuclei both displayed the long tail of the performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is dependent on the difference in the proton density distribution of the last proton in the nucleus. The Fortran 95 power station program was used to calculate the neutrons, protons, matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei agree well with the experimental data.

Theoretical Study of Matter Density Distributions, and Elastic Electron Scattering Form Factors of Exotic Nuclei (26F and 9C)

Abstract: The distributions of nuclear density, root mean square radii, and elastic electron scattering form factor are calculated for nuclei (9C) (core +2p) and (26F) (core +2n) with the two different nuclear potential parameters for (bc) and (bv), were correlations for both the (effects tensor force and short-range) are used, and the appearance of the long extension is observed in Nuclear density distributions for these nuclei. Fortran 95 power station was used to program nuclear properties such as nucleon density (matter, neutron, and proton), elastic electron scattering form factor, and rms radii. The computed results for these exotic nuclei are determined to correspond pretty well with the experimental data.

Properties of Ground-State of 17,19,20,24,26F using the Wave Functions of Harmonic-Oscillator and Spherical Hankel Functions

The nuclear size radii, density distributions and elastic electron scattering charge form factors for Fluorine isotopes (17,19,20,24,26F) were studied using the radial wave functions (WF) of harmonic-oscillator (HO) potential and free mean field described by spherical Hankel functions (SHF) for the core and the valence parts, respectively for all aforementioned isotopes. The parameters for HO potential (size parameter ) and SHF were chosen to regenerate the available experimental size radii. It was found that using spherical Hankel functions in our work improved the calculated results quantities in comparison with empirical data.

Study of the Nuclear Structure for Some Nuclei Using Self-Consistent RPA Calculations with Skyrme-Type Interaction

In the present research, some static and dynamic nuclear properties of the closed-shell nuclei; 58Ni, 90Zr, 116Sn, and 144Sm nuclei have been studied using the Random Phase Approximation (RPA) method framework and different Skyrme parameterizations, particularly SyO-, Sk255, SyO+, SLy4, BSk17, and SLy5. In particular, in studies of static properties such as nuclear densities for neutrons, protons, mass, and charge densities with their corresponding rms radii, the single-particle nuclear density distributions All the obtained results agreed well with the relevant experimental data. Concerning the dynamic properties, the excitation energy, transition density, and giant resonance modes for the excitation to the low-lying negative partite excited states 1–, 3–, 5–, and 7– have also been studied. The findings indicate that estimates of RPA with Skyrme-type interactions are a good way to describe the properties of the structure of even-even, closed-shell nuclei.

Prediction of nuclear charge density distribution with feedback neural network

Prediction of nuclear charge density distribution with feedback neural network

Nuclear charge radii of Cr46–62 isotopes and reaction cross sections for p−Cr

The nuclear charge radii and density distributions for $^{46--62}\mathrm{Cr}$ have been calculated in the frameworks of both relativistic and nonrelativistic self-consistent mean-field models. The relativistic Hartree-Bogoliubov model with density-dependent meson-exchange functional DD-ME2 and the nonrelativistic Hartree-Fock-Bogoliubov model with the Gogny D1S interaction, hereafter referred to as DIRHB and HFB, respectively, are used to compute ground-state properties of even $^{46--62}\mathrm{Cr}$ isotopes. Both calculations for the root-mean-squared charge radii reveal the characteristic kink at the $N$ = 28 shell closure in accordance with the corresponding experimental radii. The point proton and neutron density distributions calculated from both DIRHB and HFB are used to obtain the optical potentials for $p$-Cr at an incident proton energy of 65 MeV. The elastic scattering differential and total reaction cross sections, computed from the semimicroscopic proton optical potentials, have been derived by folding each of the target matter densities with the Jeukenne-Lejeune-Mahaux-Bruye\ifmmode \acute{r}\else \'{r}\fi{}es (JLMB) energy- and density-dependent internucleon interaction. The calculated elastic scattering differential cross sections for stable even isotopes, $^{50,52,54}\mathrm{Cr}$, using the respective DIRHB and HFB densities in the folding model reproduce the corresponding cross-section data well. The correlation between root-mean-squared charge radii and nuclear reaction observables obtained from the DIRHB and HFB calculations have been used in the folding model approach to predict the reaction cross sections for $p\text{\ensuremath{-}}^{46--62}\mathrm{Cr}$ at an incident proton energy of 65 MeV.

Exploring the sensitivity of charge-exchange(p,n)reactions to the neutron density distribution

$Background:$ The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which attracted considerable attention recently, such as in the context of the PREX experiment. $Purpose:$ Our aim is to analyze the sensitivity of charge-exchange ($p, n$) reactions to the neutron density distribution $\rho_{n}$ and constrain the neutron characteristics in the nuclear structure models. $Method:$ By combing the folding and the mean-field models, the nucleon-nucleus ($NA$) potential can be obtained from the nuclear density distribution. Further, the ($p, p$) and ($p, n$) cross sections for $^{48}$Ca and $^{208}$Pb are calculated following the distorted-wave Born approximation (DWBA) method. $Results:$ Compared with the ($p, p$) cross section, the effects of $\rho_{n}$ variation on the ($p, n$) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that $^{48}$Ca and $^{208}$Pb have relatively large neutron skin thickness $\Delta R_{n p}$. $Conclusions:$ Results illustrate that the charge-exchange ($p, n$) reaction is a sensitive probe of $\rho_{n}$. The results in this paper can offer useful guides for future experiments of neutron characteristics.

Possible shape coexistence in odd-A Ne isotopes and the impurity effects of Λ hyperons * *Supported by the National Natural Science Foundation of China (U2032141), the Natural Science Foundation of Henan Province (202300410479), the Foundation of Fundamental Research for Young Teachers of Zhengzhou University (JC202041041), and the Physics Research and Development Program of Zhengzhou University (32410217)

In this study, shape evolution and possible shape coexistence are explored in odd-A Ne isotopes in the framework of the multidimensionally constrained relativistic-mean-field (MDC-RMF) model. By introducing and hyperons, the impurity effects on the nuclear shape, energy, size, and density distribution are investigated. For the interaction, the PK1 parameter set is adopted, and for the interaction, the PK1-Y1 parameter set is used. The nuclear ground state and low-lying excited states are determined by blocking the unpaired odd neutron in different orbitals around the Fermi surface. Moreover, the potential energy curves (PECs), quadrupole deformations, nuclear r.m.s. radii, binding energies, and density distributions for the core nuclei as well as the corresponding hypernuclei are analyzed. By examining the PECs, possibilities for shape coexistence in Ne and a triple shape coexistence in 31Ne are found. In terms of the impurity effects of Λ hyperons, as noted for even-even Ne hypernuclear isotopes, the hyperon exhibits a clear shrinkage effect, which reduces the nuclear size and results in a more spherical nuclear shape. The hyperon occupying the orbital is prolate, which causes the nuclear shape to be more prolate, and the hyperon occupying the orbital displays an oblate shape, which drives the nuclei to be more oblate.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.