Nucleon Density Distributions Research Articles

A systematic study of the ground state properties of gold nuclei near the neutron drip line using HFB formalism

In this theoretical work, the ground state properties like binding energy per nucleon, two-neutron separation energy, two-neutron shell gap, neutron-pairing gap, neutron rms radii, proton rms radii, charge radii, neutron skin thickness and nucleon density distributions of odd-even and odd-odd gold isotopes (A165−265u) were systematically studied. Computations were performed for a wide mass range of gold nuclei, spanned from the proton-rich side to the neutron-rich side, following the Hartree-Fock-Bogoliubov theory. Based on this approach, the nuclear structure of gold isotopes lying up to the exotic neutron rich region where the experimental data are not available, was also investigated. Calculations, taking into account the UNEDF0 Skyrme effective interaction, reproduce the available experimental data and results of other nuclear model based estimations, such as the Relativistic-Continuum-Hartree-Bogoliubov theory and the Finite Range Droplet Models, reasonably well.

Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. V. Improved parametrization of the nucleon density distributions

Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. V. Improved parametrization of the nucleon density distributions

Перерізи пружного розсіяння реакцій 16,18O + 120Sn, одержані на основі потенціалу модифікованого методу Томаса - Фермі з урахуванням кора

Nucleon density distributions and nucleus-nucleus interaction potentials for the reactions 16,18O + 120Sn were obtained within the framework of the modified Thomas - Fermi method. In the calculations, all terms up to the second order in ћ in the quasi-classical distribution of kinetic energy were taken into account. Density-dependent Skyrme forces were used as nucleon-nucleon interaction. Using the found potentials, cross-sections of elastic scattering were calculated, which well describe the corresponding experimental data.

Size Isomers at Threshold States

An overview is provided for a new class of states, which we have named as the size isomers. Such states are weakly bound and have an exotic structure (cluster states, halo/‘‘skin’’). The development of methods for measuring the radii of nuclei in their short-lived excited states led to the discovery of new classes of states. The size of a nucleus defined by the radius of its nucleon (proton and neutron) density distribution and the proton charge distribution is one of the most fundamental and important nuclear characteristics. Nuclear radius determines the basic properties of nuclei and is a consequence of the fundamental features of the strong interaction. Up to now two groups of the size isomers were identified: the excited states with halos (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{9}$$\\end{document}Be, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}Be, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}N) and some specific alpha-cluster states (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}B, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{12}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C). All the observed states are dilute, however, some indication to possible existence of more compact than the ground states was obtained as well (in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C). The phenomenon of size isomerism occurred to be not a rare one especially if we take into account rotational bands based on some of such states. The structure of size isomers is related with some new features, e.g., rotating halos, halos in continuum, different types of quasimolecular configurations. Some rudimentary signs of alpha-particle condensation (a ‘‘ghost’’ of condensate) were observed in the Hoyle state of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{12}$$\\end{document}C, however, we cannot speak about confirmation of this ambitious theory. Analogs to the Hoyle state, expected in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}B, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{16}$$\\end{document}O, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{20}$$\\end{document}Ne near the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-emission thresholds, are considered.

Study of6,8He+p elastic scattering using the BHF formalism with three-body forces

In the present work, we have analyzed the elastic scattering data of6He+p at 25.6, 38.6, 40.9, and 71 MeV/A and8He+p at 15.6, 25.6, 32.5, 66, and 72 MeV/A, using the microscopic local optical potential calculated within the framework of the Brueckner–Hartree–Fock (BHF) formalism. The calculation requires mainly two inputs: (1) the nucleon–nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. In the present work, realistic internucleon (NN) potential from Argonne v18 (AV18) and the Urbana IX (UVIX) model of three-body forces with several nucleon density distributions are used for generating the nucleon–nucleus optical potential. We have used the exact method for calculating both the direct and the exchange parts of the spin–orbit potential. We confirm the earlier results that the spin–orbit potential for these neutron-rich nuclei is diffused and extended. Our results show that the different density distributions reproduce rather well the experimental differential cross sections for both isotopes, while the phenomenological density with a two-neutron halo gives satisfactory results for6He-p analyzing power data. None of the densities used for8He can reproduce the experimentally analyzed power data. Our analysis reveals that the calculated microscopic optical potentials, with and without three-body forces using the BHF approach, provide satisfactory agreement with the elastic scattering data for6,8He+p.

Перерізи пружного розсіяння, одержані на основі потенціалу модифікованого методу Томаса–Фермі з урахуванням кора

Густини розподiлу нуклонiв та потенцiали взаємодiї мiж ядрами для реакцiй 16O + 40Ca, 16O + 56Fe та 16O + 90Zr було розраховано в рамках модифiкованого методу Томаса–Фермi, з урахуванням усiх доданкiв до членiв другого порядку по ~ у квазикласичному розкладi кiнетичної енергiї. В якостi нуклон-нуклонної взаємодiї використовувалися сили Скiрма, залежнi вiд густини нуклонiв. Знайдено параметризацiю потенцiалу взаємодiї мiж ядрами, яка добре описує величину потенцiалу, розрахованого у рамках модифiкованого пiдходу Томаса–Фермi з залежними вiд густини силами Скiрма. На основi одержаних потенцiалiв було обраховано перерiзи пружного розсiяння, що добре узгоджуються з експериментальними даними.

Потенціали взаємодії ізотопів 10,11,12,13В з ядром 12С

A comparative analysis of calculations for the 12С(10В,10В)12С elastic scattering at Еlab(10B) = 41.3 MeV, the 12С(11В,11В)12С elastic scattering at Еlab(11B) = 40.0 MeV, transfer reactions 13С(11В,12С)12В and 14С(11В,12С)13В at Еlab(11B) = 45.0 МеВ was performed within the coupled-reaction-channels method (CRC) using previously deduced Woods-Saxon potentials for the interaction of 10,11,12,13В + 12С nuclei in the exit reaction channels, as well as potentials for these systems of nuclei generated by means of the double-folding method using theoretically modeled shapes for the distributions of protons and neutrons in 10,11,12,13В and 12С. The relationship of isotopic effects (differences of the calculated CRC cross sections when replacing the potential for a given pair of nuclei by interaction potential for one nucleus with the isotope of another nucleus) with the internal structure, e.g. the shapes of nucleon density distributions in the interacting nuclei, is investigated. The shapes (radial dependence) of recently deduced Woods-Saxon potentials and potentials calculated by means of the double-folding methods for the systems of 10,11,12,13В + 12С nuclei are compared. Based on the results of the analysis of experimental data, an assumption is made about the possible differences in the shapes of surface nucleon density distributions from the ones modeled theoretically in 10,11B isotopes.

Favored α -decay half-lives of odd- A and odd-odd nuclei using an improved density-dependent cluster model with anisotropic surface diffuseness

We extend the improved density-dependent cluster model (DDCM+) of our recent work [Wang et al., Phys. Rev. C 105, 024327 (2022)] to study the favored $\ensuremath{\alpha}$ decays of odd-$A$ and odd-odd nuclei with $Z\ensuremath{\geqslant}82$. In this work, the effective $\ensuremath{\alpha}$-core interactions are determined using the double-folding potential with a realistic M3Y-Reid nucleon-nucleon interaction plus proton-proton Coulomb interaction, in which a deformation-dependent diffuseness correction is validated to address the surface anisotropy and polarization effects in nucleon density distribution. It is found that calculations within the anisotropic diffuseness would yield longer calculated $\ensuremath{\alpha}$ decay half-lives and suggest larger estimated $\ensuremath{\alpha}$-preformation factors, which is quite consistent with the conclusions obtained for the even-even $\ensuremath{\alpha}$ emitters. Meanwhile, the theoretical half-lives agree very well with the experimental data for the favored $\ensuremath{\alpha}$ decays of the odd-$A$ and odd-odd nuclei with a mean factor of 1.94 and 1.61, respectively. Remarkably, the experimental $\ensuremath{\alpha}$-decay half-life of the new thorium isotope $^{207}\mathrm{Th}$ [Yang et al., Phys. Rev. C 105, L051302 (2022)] is also well reproduced with a factor of about 2.50. Furthermore, we present the quantitative predictions on the favored $\ensuremath{\alpha}$-decay half-lives of $^{293,294}119$ and $^{294,295}120\phantom{\rule{4pt}{0ex}}\ensuremath{\alpha}$-decay chains in this work, which are expected to serve as useful references for the synthesis of new isotopes in the future.

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Study of Matter Density Distributions, Elastic Electron Scattering Form factors and Root Mean Square Radii of 9C, 12N, 23Al, 11Be and 15C Exotic Nuclei

The ground state densities of neutron-rich (11Be,15C) and proton-rich (9C,12N,23Al) exotic nuclei are investigated using a two-body nucleon density distribution (2BNDD) with two frequency shells model (TFSM). The structure of the valence one-neutron of 11Be is in pure (1p1/2) and of 15C in pure (1d5/2) configuration, while the structure of valence one-proton configuration is in 9C,12N are to be in a pure (1p1/2) and 23Al in a pure (2s1/2) . For our studied nuclei, an efficient (2BNDD) operator for point nucleon system folded with two-body correlation operator's functions is used to investigate nuclear matter density distributions, elastic electron scattering form factors, and root-mean square (rms) radii. The effect of the strong tensor force (TC) in nucleon-nucleon forces is taken into account in the correlation. The wave functions of a single particle harmonic oscillator are used with two different oscillator size parameters, βc and βv, the former for core (inner) orbits and the latter for valence (halo) orbits. The measured matter density distributions of these nuclei clearly show the long tail results. The plane wave born approximation (PWBA) is used to investigate the elastic electron scattering form factors for these exotic nuclei.

Subbarrier fusion and elastic scattering cross-sections based on modified Thomas-Fermi method potentials

The nucleon density distributions and nucleus-nucleus interaction potentials for the reactions 16O+92Zr and 16O+116Sn were calculated using the modified Thomas-Fermi method, taking into account all terms up to members of the second order by ħ in the quasiclassical decomposition of the kinetic energy. As a nucleon-nucleon interaction, density depended Skyrme forces were used. Based on the obtained potentials, the cross-sections of subbarrier fusion and elastic scattering were calculated. It is shown that the obtained cross-sections of the reactions agree well with the latest experimental data.

Taming nucleon density distributions with deep neural network

With the datasets of the density distributions calculated by Skyrme density functional theories, we elaborated deep neural networks to generate the density profile and provide a table of related hyperparameters set for similar applications of other structural models. In the process of machine learning with the objective/target functions that normalized mean square error and Kullback–Leibler divergence (cross entropy), there is a turning point showing the transition from the Fermi-like distribution to the realistic Skyrme distribution, while this property is transcended when Pearson χ2 divergence is employed. A training program of about 35 minutes with only about 5%−10% nuclei (200−300) is sufficient to describe the nucleon density distributions of all the nuclear chart within 2% relative error. We obtain similar results employing different datasets calculated by different Skyrme density functional theories. We further investigate the extrapolation properties, which show that an addition of 15 nucleons is acceptable. Based on the results, we propose a mixed dataset approach and a retraining approach in order to go beyond a single physical structure model.

Matter Density Distributions, Root-mean Square Radii and Elastic Electron Scattering Form Factors of Some Exotic Nuclei (17B, 11Li, 8He)

The two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of the effect for the strong tensor force (TC's). The wave functions of single particle harmonic oscillator are used with two different oscillator size parameters βc and βv, where the former is for the core (inner) orbits and the latter is for the valence (halo) orbits. The measured matter density distributions of these nuclei clearly showed long tail results. To investigate elastic electron scattering form factors the plane wave born approximation (PWBA) with two body nucleon density distribution (2BNDD's) was use.

Structural properties of nuclei with semi-magic number N(Z) = 40

In this paper, various ground state properties are explored for full isotonic(isotopic) chain of neutron number N [Formula: see text]proton number [Formula: see text] using different families of Relativistic Mean-Field theory. Several properties, such as nucleon separation energies, pairing energies, deformation, radii and nucleon density distributions, are evaluated and compared with the experimental data as well as those from other microscopic and macroscopic models. [Formula: see text] isotonic chain presents ample of support for the neutron magicity and articulates double magicity in recently discovered [Formula: see text]Ca and [Formula: see text]Ni. Our results are in close conformity with the recently measured value of charge radius of [Formula: see text]Ni [S. Kaufmann et al., Phys. Rev. Lett. 124 (2020) 132502] which supports the [Formula: see text] magicity. Contrarily, Zr isotopes ([Formula: see text]) display variety of shapes leading to the phenomenon of shape transitions and shape co-existence. The role of 3s[Formula: see text] state, which leads to central depletion if unoccupied, is also investigated. [Formula: see text]S and [Formula: see text]Zr are found to be doubly bubble nuclei.

Systematic analysis of 17,19F and 16,17O elastic scattering on 208Pb just below the coulomb barrier

The 17F, 17O + 208Pb elastic scattering at 90.4 and 78 MeV (just below coulomb barrier), respectively, are analyzed within the framework of the double folding approach. The folded potentials are constructed by folding the density independent M3Y effective nucleon-nucleon interaction over the nucleon density distribution of 17F and its mirror 17O nuclei. Gaussian oscillator (GO) density distribution is considered to represent the (core16O+nucleon) structure for 17F and 17O. The knock-on exchange potentials are introduced to construct the real semi-microscopic potentials. The imaginary potentials are supplemented to derive potentials in two forms: either phenomenological Woods-Saxon (WS) or the same form as real folded potentials and different strengths. Moreover, the analysis of 19F, 16O + 208Pb elastic scattering at 91, 78 MeV energies, in that order, is applied in comparison to the 17F, 17O + 208Pb systems in an endeavor to investigate the behavior and properties of 17F and 17O projectiles.

Effects of QCD critical point on light nuclei production

Using the nucleon coalescence model, which can naturally take into account the correlations in the nucleon density distribution, we study the effects of QCD critical point on light nuclei production in relativistic heavy-ion collisions. We find that the yield ratio NtNp/Nd2 of proton (p), deuteron (d) and triton (t) increases monotonically with the nucleon density correlation length, which is expected to increase significantly near the critical point in the QCD phase diagram. Our study thus demonstrates that the yield ratio NtNp/Nd2 can be used as a sensitive probe of the QCD critical phenomenon. We further discuss the relation between the QCD phase transitions in heavy-ion collisions and the possible non-monotonic behavior of NtNp/Nd2 in its collision energy dependence.

Impact of strong magnetic fields on the inner crust of neutron stars

We study the impact of strong magnetic fields on the pasta phases that are expected to exist in the inner crust of neutron stars. We employ the relativistic mean field model to describe the nucleon interaction and use the self-consistent Thomas-Fermi approximation to calculate the nonuniform matter in neutron star crust. The properties of pasta phases and crust-core transition are examined. It is found that as the magnetic field strength $B$ is less than ${10}^{17}$ G, the effects of magnetic field are not evident comparing with the results without magnetic field. As $B$ is stronger than ${10}^{18}$ G, the onset densities of pasta phases and crust-core transition density decrease significantly, and the density distributions of nucleons and electrons are also changed obviously.

Probing the Neutron Skin with Ultrarelativistic Isobaric Collisions.

Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.

Nucleon density distribution in description of nuclear decays

A correlation is demonstrated between the diffuseness of the self-consistent nucleon distribution and the nucleon-nucleon attraction on nuclear surface. The last two values determine the nucleus-nucleus interaction potential. Because the half-lives of alpha-decay, cluster radioactivity, and spontaneous fission are sensitive to the nucleus-nucleus interaction potential, we try to verify the self-consistent nucleon-nucleon attraction on nuclear surface. Based on the dinuclear system model, the unified approach is proposed for calculating half-lives of different nuclear decay modes using the phenomenological and self-consistent nucleon distributions.

Microscopic study of 7Li-nucleus potential * * Supported by National Natural Science Foundation of China (11705009, 11575291) and Science Challenge Project (TZ2018005)

A microscopic approach is employed to study the optical potential for the 7Li-nucleus interaction system without any free parameters. It is obtained by folding the microscopic optical potentials of the constituent nucleons of 7Li over their density distributions. We employ an isospin-dependent nucleon microscopic optical potential, which is based on the Skyrme nucleon-nucleon effective interaction and derived using the Green's function method, as the nucleon optical potential. The harmonic oscillator shell model is used to describe the internal wave function of 7Li and obtain the nucleon density distribution. The 7Li microscopic optical potential is used to predict the reaction cross-sections and elastic scattering angular distributions for the target range from 27Al to 208Pb and energy range below 450 MeV. Generally, the results can reproduce the measured data reasonably well. In addition, the microscopic optical potential is comparable to a global phenomenological optical potential by fitting the presently existing measured data.