Neutron Density Distributions Research Articles

Improved evaluation of nuclear charge radii for superheavy nuclei

Although significant progress has been made in the synthesis of superheavy nuclei, the experimental knowledge of them is still very limited while the alpha decay chain is the main tool used to identify newly produced superheavy nuclei. Previously, we have extracted nuclear charge radii of superheavy nuclei via the experimental alpha decay data. As a further step, the density dependent cluster model is improved by introducing the difference between the density distributions of protons and neutrons. Besides, the important quantity, i.e., the alpha preformation factor, is connected with the microscopic correction of nuclear mass during this procedure, to perform a more reasonable description of the alpha decay process. It is found that the present deduced nuclear charge radii of heavy nuclei are in a better agreement with the measured values as compared to those in our previous evaluations. Subsequently, the nuclear radii of heavier even–even isotopes with Z = 98–116 are probed, accompanied by the consistency with the empirical evaluations. Moreover, the effect of the depressed density at the center of superheavy nucleus on the final extracted nuclear radius plus the decay lifetime is discussed, which appears to be different from the case of lighter nuclide.

Theoretical Study of Density Distributions and Size Radii of 8B and 17Ne

The proton, neutron and matter density distributions, the corresponding size radii and elastic electron scattering form factors of one-proton 8 B and two-proton 17 Ne halo nuclei are calculated. The theoretical technique used to fulfill calculations is by assuming that both nuclei under study are composed of two main parts; the first is the compact core and the second is the unstable halo part. The single-particle radial wavefunctions of harmonic-oscillator (HO) and Woods-Saxon (WS) potentials are used to study core and halo parts, respectively. And other approach is studied by using HO potential for both core and halo parts, but using two HO size parameters for both supposed parts. The long tail behavior which is the main characteristic of halo nuclei are well produced for both 8 B and 17 Ne. The calculated size radii are in general in good agreement with the available experimental data. The electron scattering form factors of the C0+C2 and C0 components are also calculated for 8 B and 17 Ne, respectively and compared with corresponding stable 10 B and 20 Ne nuclei. For 8 B calculations, the core-polarization (CP) effects are taken into account by using Tassie and Bohr-Mottelson models. The contribution from model-space (MS) part C2 component is taken through pwt interaction. The results of the calculated charge form factors are left for the planned electron-radioactive ion beam colliders where the study of skin or halo on the charge form factors are going to be studied.

Average CsI Neutron Density Distribution from COHERENT Data.

Using the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we determine for the first time the average neutron rms radius of ^{133}Cs and ^{127}I. We obtain the practically model-independent value R_{n}=5.5_{-1.1}^{+0.9} fm using the symmetrized Fermi and Helm form factors. We also point out that the COHERENT data show a 2.3σ evidence of the nuclear structure suppression of the full coherence.

Nuclear structure calculations for neutron star crusts

The goal of this paper is to investigate properties of clusterized nuclear matter which is believed to be present in crusts of neutron stars at subnuclear densities. It is assumed that the whole system can be represented by the set of Wigner-Seitz cells, each containing a nucleus and an electron background under the condition of electroneutrality. The nuclear structure calculations are performed within the relativistic mean-field model with the NL3 parametrization. The first set of calculations is performed assuming the constant electron background. The evolution of neutron and proton density distributions was systematically studied along isotopic chains until very neutron-rich system beyond the neutron dripline. Then we have replaced the uniform electron background with the realistic electron distributions, obtained within the Thomas-Fermi approximation in a self-consistent way with the proton distributions. Finally, we have investigated the evolution of the $\beta$-stability valley as well as neutron and proton driplines with the electron density.

New insight into α clustering of heavy nuclei via their α decay

Based on the available experimental data of nuclear charge radii and neutron skin thickness, we have renewed the two-parameter Fermi (2pF) form of nucleon density distributions in heavy nuclei. Subsequently, we focus on the α clustering phenomenon of heavy nuclei in terms of the preformation probability of α cluster before its penetration in α decay. Through the experimental decay data, the α preformation factor Pα is extracted for a large range of nuclei above the N=126 shell, leading to the interesting recognition on the behavior of α cluster formation factor. It is found that the present α preformation factor varies more smoothly towards the large neutron–proton ratio, as compared to those from the previous evaluations. This may be explained by the fact that we have separately considered proton and neutron density distributions of related nuclei, while they are treated as the same form in our previous studies. Meanwhile, the presence of the Z=92 subshell is somewhat revealed by the picture of α formation factor in this study. Moreover, the similarity between the Pα value and the pairing gap is clearly demonstrated, indicating the crucial role of pairing correlation involved in the α decay process.

Abinitio Calculations of the Isotopic Dependence of Nuclear Clustering.

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (^{4}He nuclei) within the interior of a larger nucleus. In this Letter, we present lattice MonteCarlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field MonteCarlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in ^{12}C, ^{14}C, and ^{16}C. The structural similarities among the carbon isotopes suggest that ^{14}C and ^{16}C have excitations analogous to the well-known Hoyle state resonance in ^{12}C.

The isovector nuclear density and improved description of cluster decay half-lives using isospin-dependent NN interaction

The sensitivity of cluster-decay half-life time to the isospin effect of the nucleon–nucleon (NN) interaction and the neutron-skin thickness is explored in the framework of the Wentzel–Kramers–Brillouin approximation. Within the generalized double-folding model, the cluster-daughter potential is calculated in terms of the isoscalar and isovector parts using the explicit proton and neutron density distributions. Realistic density-dependent Michigan-three-Yukawa (CDM3Y1 and CDM3Y6) NN interactions with the finite-range exchange NN force are considered in the present work. The calculated cluster-decay half-lives including the isospin effect and the differences between neutron and proton density distributions are found to be in somewhat better agreement with the experimental data as compared without these effects. This may indicate the necessity of considering the isospin effect and the neutron–proton differences of the density distributions in cluster-decay, especially for extremely neutron-rich nuclei. Predictions of cluster decay half-lives from possible cluster emitters are presented which may be helpful for future experiments. The present study could be a significant step forward in improving the description of cluster decay half-lives.

DFMDEF18: A C-code for the double folding interaction potential of a spherical nucleus with deformed nucleus

DFMDEF18: A C-code for the double folding interaction potential of a spherical nucleus with deformed nucleus

Neutron-skin thickness determines the surface tension of a compressible nuclear droplet

We systematically investigate the neutron-skin thickness of neutron-rich nuclei within a compressible droplet model, which includes several parameters characterizing the surface tension and the equation of state (EOS) of asymmetric nuclear matter as well as corrections due to the surface diffuseness. Such a systematic analysis helps towards constraining the EOS parameters of asymmetric nuclear matter and the poorly known density dependence of the surface tension; the latter is estimated with help of available experimental data for the neutron and proton density distributions and the nuclear masses. Validity of the present approach is confirmed by calculating realistic density distributions of Ca, Ni, Zr, Sn, Yb, and Pb isotopes within a microscopic Skyrme-Hartree-Fock+BCS method for various sets of the effective nuclear force. Our macroscopic model accompanied by the diffuseness corrections works well in the sense that it well reproduces the evolution of the microscopically deduced neutron-skin thickness with respect to the neutron number for selected sets of the effective nuclear force. We find that the surface tension of the compressible nuclear droplet is a key to bridging a gap between microscopic and macroscopic approaches.

High-Temperature Neutron Diffraction Study on PbWO4 and CaWO4-Based Oxide Ion Conductors with Different Defect Structure

Introduction Oxide ion conductors have been attracted great interests for the application of electrolytes of solid oxide fuel cells (SOFC). Most of the oxide ion conductors employ oxide ion vacancies to perform ionic conduction, while very few possess oxide ion interstitials for the oxide ion migration. When lanthanum ions are partly substituted into lead site in scheelite-type structured PbWO4, oxide ion conduction appears at elevated temperatures [1,2]. In that case, oxide ion interstitials are formed as Pb1-xLaxWO4+x/2 for the oxide ion conduction. On the other hand, CaWO4 with the isostructure with PbWO4 does not show such an oxide ion conduction enhancement due to the lanthanum substation. Recently, we have reported that alkaline-ion substituted CaWO4 also exhibit high oxide ion conduction [3]. Although the defect structure of the latter system is oxide ion vacancy as Ca1-xKxWO4-x/2, activation energies of the oxide ion conduction for both systems are relatively close at high-temperature. In this study, oxide ion conduction paths of these two systems, Pb1-xLaxWO4+x/2 and Ca1-xKxWO4-x/2, are evaluated by means of high-temperature neutron diffraction experiments coupled with maximum entropy method and compared based on the defect structure. Experimental Pb1-xLaxWO4+x/2 and Ca1-xKxWO4-x/2 (x = 0.2 for both systems) were prepared by solid state reaction method from the starting oxides. Calcining and sintering temperatures are selected as 800oC and 900oC, respectively for Pb1-xLaxWO4+x/2, and 800oC and 1000oC for Ca1-xKxWO4-x/2. The phase singularities of the obtained compounds are confirmed by X-ray diffraction. About 10 g of the sample pellets were inserted into a vanadium holder through a thin quartz tube and neutron powder diffraction experiments were performed in the temperature range between 200°C and 800°C by using SHRPD diffractometer in J-PARC. After the Rietveld refinements using Z-Rietveld code, oxide ion conduction paths at high temperatures were estimated by using maximum entropy method (MEM) using Z-MEM. Typically, 50 reflections are served for the MEM analyses. Results and Discussions Figs.1 and 2 represent the nuclear density distribution for Pb1-xLaxWO4+x/2 and Ca1-xKxWO4-x/2, respectively, obtained by MEM based on the neutron diffraction data collected at 800oC. Regular atomic positions obtained by the Rietveld analysis are indicated by spheres in the figures. For Pb1-xLaxWO4+x/2, nuclear density seems to extend from regular site to interstitial ones, suggesting the oxide ion diffusion path occurs parallel to the a-b plane. On the other hand, Ca1-xKxWO4-x/2 without oxide ion interstitials did not show such diffusion path parallel to the a-b plane, but the neutron density distribution extends toward c-directions. Defect structure would largely attribute to the diffusion mechanism in these two scheelite systems.

Matter density distributions and elastic form factors of some two-neutron halo nuclei

The Skyrme–Hartree–Fock (SHF) method with MSK7 Skyrme parameter has been used to investigate the ground-state properties for two-neutron halo nuclei \(^{6}\hbox {He}\), \(^{11}\hbox {Li}\), \(^{12}\hbox {Be}\) and \(^{14}\hbox {Be}\). These ground-state properties include the proton, neutron and matter density distributions, the corresponding rms radii, the binding energy per nucleon and the charge form factors. These calculations clearly reveal the long tail characterizing the halo nuclei as a distinctive feature.

Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions

We report results of the first systematic simulation of proton and neutron density distributions in central heavy-ion collisions within the beam energy range of $ E_{\rm beam} \leq 800 \, \text{MeV/nucl}$ using pBUU and TDHF models. The symmetric $^\text{40}$Ca +$^\text{40}$Ca, $^\text{48}$Ca +$^\text{48}$Ca, $^\text{100}$Sn +$^\text{100}$Sn and $^\text{120}$Sn + $^\text{120}$Sn and asymmetric $^\text{40}$Ca +$^\text{48}$Ca and $^\text{100}$Sn +$^\text{120}$Sn systems were chosen for the simulations. We find limits on the maximum proton and neutron densities and the related proton-neutron asymmetry $\delta$ as a function of the initial state, beam energy, system size and a symmetry energy model. While the maximum densities are almost independent of these parameters, our simulation reveals, for the first time, their subtle impact on the proton-neutron asymmetry. Most importantly, we find that variations in the proton-neutron asymmetry at maximum densities are related at most at 50\% level to the details in the symmetry energy at supranormal density. The reminder is due to the details in the symmetry energy at subnormal densities and its impact on proton and neutron distributions in the initial state. This result puts to forefront the need of a proper initialization of the nuclei in the simulation, but also brings up the question of microscopy, such as shell effects, that affect initial proton and neutron densities, but cannot be consistently incorporated into semiclassical transport models.

A study of nuclear structure for 244Cm, 241Am, 238Pu, 210Po, 147Pm, 137Cs, 90Sr and 63Ni nuclei used in nuclear battery

In this paper, we intend to extend the nuclear data of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] nuclei used in nuclear battery technology, because, these nuclei are quite important for space investigations in radioisotope thermoelectric generator (RTG) and for microelectronic technologies in betavoltaic batteries. Therefore, the nuclear structure properties of nuclei such as separation energies, neutron skin thicknesses, proton, charge and neutron density distributions as a function of radius, the root mean square (rms) proton, charge and neutron radii, binding energies per particle, have been investigated by Hartree–Fock with eight different Skyrme forces. The obtained results have been compared with the experimental data in literature and relativistic mean field theory (RMFT) results.

Nuclear structure investigation of some neutron-rich halo nuclei

The ground state proton, neutron and matter densities, the corresponding rms radii and charge form factors of a dripline nuclei 6He, [Formula: see text]Li, [Formula: see text]Be and [Formula: see text]Be have been studied via a three–body model of [Formula: see text]. The core–neutron interaction takes the form of Woods-Saxon (WS) potential. The two valence neutrons of 6He, [Formula: see text]Li and [Formula: see text]Be interact by the realistic interaction of ZBMII while those of [Formula: see text]Be interact via the realistic interaction of VPNP. The core and valence (halo) density distributions are described by the single-particle wave functions of the WS potential. The calculated results are discussed and compared with the experimental data. The long tail performance is clearly noticed in the calculated neutron and matter density distributions of these nuclei. The structure of the two valence neutrons in 6He, [Formula: see text]Li and [Formula: see text]Be is found to be mixed configurations with dominant [Formula: see text] while that for [Formula: see text]Be is mixed configurations with dominant ([Formula: see text]. The analysis of the present study supports the halo structure of these nuclei.

Relativistic effects and three-nucleon forces in nuclear matter and nuclei

We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac–Brueckner–Hartree–Fock approach to nuclear matter and finite nuclei. The success of this method has been largely related to its ability to take into account important three-body effects. Therefore, the overarching theme of this paper is the interpretation of the so-called “Dirac effects” as an effective three-nucleon force. We address the equation of state (EoS) of isospin symmetric and asymmetric nucleonic matter and related issues, ranging from proton and neutron density distributions to momentum distributions and short-range correlations. A central part of the discussion is devoted to the optical model potential for nucleon–nucleus scattering. We also take the opportunity to explore similarities and differences with predictions based on the increasingly popular chiral effective field theory.

Investigation of constraints on few-neutron forces in neutron matter by empirical information on the neutron skin of Ca48 and Pb208

The neutron matter equation of state is calculated from two-neutron forces up to fifth order of the chiral expansion and the order-by-order convergence of the predictions is investigated. Based on these equations of state, the binding energies and the neutron and proton density distributions in 208Pb and 48Ca are derived, with particular attention to the neutron skins, the focal point of this paper. Anticipating future experiments which will provide reliable information on the weak charge density in nuclei, the theoretical uncertainties and the possibility of constraining the size of few-neutron forces in neutron matter are discussed.

Spherical nuclei near the stability line and far from it

Results of microscopic and semiphenomenological calculations of features of spherical nuclei lying near the stability line and far from it are presented. The reason why the nuclei being considered are spherical is that they are magic at least in one nucleon sort. The present analysis is performed for Z = 50 and Z = 28 isotopes and for N = 50 isotones, the region extending from neutron-rich to neutron-deficient nuclei being covered. The isotopic dependence of the mean-field spin–orbit nuclear potential is revealed; systematics of energies of levels and probabilities for electromagnetic transitions is examined; and root-mean-square radii of nuclei are calculated, along with the proton- and neutron-density distributions in them. Nuclei in the vicinity of closed shells are considered in detail, and the axial-vector weak coupling constant in nuclei is evaluated. A systematic comparison of the results of calculations with experimental data is performed.

DFMSPH14: A C-code for the double folding interaction potential of two spherical nuclei

This is a new version of the DFMSPH code designed to obtain the nucleus–nucleus potential by using the double folding model (DFM) and in particular to find the Coulomb barrier. The new version uses the charge, proton, and neutron density distributions provided by the user. Also we added an option for fitting the DFM potential by the Gross–Kalinowski profile. The main functionalities of the original code (e.g. the nucleus–nucleus potential as a function of the distance between the centers of mass of colliding nuclei, the Coulomb barrier characteristics, etc.) have not been modified. New version program summaryProgram title: DFMSPH14Catalog identifier: AEFH_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFH_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland.Licensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 7211No. of bytes in distributed program, including test data, etc.: 114404Distribution format: tar.gzProgramming language: CComputer: PC and MacOperation system: Windows XP and higher, MacOS, Unix/LinuxMemory required to execute with typical data: below 10 MbyteClassification: 17.9Catalog identifier of previous version: AEFH_v1_0Journal reference of previous version: Comp. Phys. Comm. 181 (2010) 168Does the new version supersede the previous version?: YesNature of physical problem: The code calculates in a semimicroscopic way the bare interaction potential between two colliding spherical nuclei as a function of the center of mass distance. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by an analytical profile (Woods–Saxon or Gross–Kalinowski) near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g. the range of the exchange part of the nuclear term) can be investigated.Method of solution: The nucleus–nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts, the density matrix expansion method is applied.Typical running time: less than 1 minute.Reason for new version: Many users asked us how to implement their own density distributions in the DFMSPH. Now this option has been added. Also we found that the calculated Double-Folding Potential (DFP) is approximated more accurately by the Gross–Kalinowski (GK) profile. This option has been also added.

Investigation ofBe10and its cluster dynamics with the nonlocalized clustering approach

We extend the new concept of nonlocalized clustering to the nucleus 10Be with proton number Z=4 and neutron number N=6 (N=Z+2). The Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function is formulated for the description of different structures of 10Be. Physical properties such as energy spectrum and root-mean-square radii are calculated for the first two 0+ states and corresponding rotational bands. With only one single THSR wave function, the calculated results show good agreement with other models and experimental values. We apply, for the first time, the THSR wave function on the chain orbit ({\sigma}-orbit) structure in the 0^+_2 state of 10Be. The ring orbit ({\pi}-orbit) and {\sigma}-orbit structures are further illustrated by calculating the density distribution of the valence neutrons. We also investigate the dynamics of ff-clusters and the correlations of two valence neutrons in 10Be.

Study of the neon interaction cross section using the Glauber model

Working within the framework of the Coulomb-modified correlation expansion for the Glauber model S-matrix, we calculate the interaction cross section ( $\sigma_{I}$ ) of neon isotopes, 17-32Ne, on 12C at 240 MeV/nucleon. The calculations involve i) up to the two-body density term in the correlation expansion, and ii) the single Gaussian approximation for the nucleon-nucleon amplitude. The colliding nuclei are described with Slater determinants consisting of the harmonic oscillator single-particle wave functions. The sole input of the density of each colliding nucleus, the oscillator constant, is fixed from the respective root-mean-square (rms) radius calculated using the relativistic mean-field approach. It is found that the calculated results for $\sigma_{I}$ generally provide fairly good agreement with the experimental data except for 31Ne, for which the required rms neutron radius comes closer to the one obtained earlier using the extended (halo-like) neutron density distribution. This finding is also supported by our predicted differential cross section of 31Ne on 12C at 240 MeV/nucleon. However, as expected, the results of the present analysis are unable to discriminate between the halo and non-halo structure of 31Ne. In conclusion, our results suggest that the present calculations can be considered as a good starting point to predict the rms matter radii of exotic neutron-rich nuclei.