Two-neutron Separation Energies Research Articles

Precision mass measurements in the zirconium region pin down the mass surface across the neutron midshell at N = 66

Precision mass measurements of 104Y, 106Zr, 104,104m,109Nb, and 111,112Mo have been performed with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility. The order of the long-lived states in 104Nb was unambiguously established. The trend in two-neutron separation energies around the N=66 neutron midshell appeared to be steeper with respect to the Atomic Mass Evaluation 2020 extrapolations for the 39Y and 40Zr isotopic chains and less steep for the 41Nb chain, indicating a possible gap opening around Z=40. The experimental results were compared to the BSkG2 model calculations performed with and without vibrational and rotational corrections. All of them predict two low-lying minima for 106Zr. While the unaltered BSkG2 model fails to predict the trend in two-neutron separation energies, selecting the more deformed minima in calculations and removing the vibrational correction, the calculations are more in line with experimental data. The same is also true for the 21+ excitation energies and differences in charge radii in the Zr isotopes. The results stress the importance of improved treatment of collective corrections in large-scale models and further development of beyond-mean-field techniques.

Nuclear shape evolution in even-even Pd isotopic chain

The covariant density functional theory is utilized to examine the evolution of shape in even–even 96−130 Pd isotopes by using the density-dependent meson-exchange DD-ME2 and the density-dependent point-coupling DD-PC1. This research is carried out by considering the evolution of the ground-state shapes derived from calculations of the axial and triaxial potential energy surfaces. The shape transition in the palladium isotopic chain is very clearly manifested. In addition, various ground-state properties, such as binding energy, charge radius, two-neutron separation energy, and two-neutron shell gap have been calculated and have been observed to adequately match the existing experimental data. Moreover, a robust shell closure is distinctly observed at the magic neutron number N = 82.

Effects of shape/phase transition regions on neutron capture cross sections

A recent study found a new, purely empirical correlation between two-neutron separation energies and neutron capture cross sections in keV neutron energy regimes. In shape/phase transition regimes, such as that near A= 150, S2n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2n}$$\\end{document} values show an anomaly—a flattening of the normal near linear decrease with neutron number. This paper addresses two questions: (1) Using this new correlation, is this anomaly in S2n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2n}$$\\end{document} values sizeable enough to produce an observable effect in capture cross sections? and (2) Can the correlation be used to quantitatively reproduce the cross sections in the transition region? It is found that the answer to both questions is in the affirmative. Possible relations to the r-process are briefly discussed.

Studying shape phase transition in even-proton nuclei via mass measurements

The transition between the spherical and deformed shapes of the nuclei (shape phase transition) is an interesting property of nuclei that enriches our understanding of the nuclear structure. One method for studying it is through measurement of a wide range of atomic masses and derivation of the two-neutron separation energies (S2n). Using a multiple-reflection time-of-flight mass spectrometer at the FRS Ion Catcher, GSI, atomic masses in the region of A ∼ 150 were measured. This allowed an wide study of phase shape transitions in this region of the nuclear chart. In addition, comparison with the Skyrme Hartree–Fock plus BCS approach are done; showing a remarkable good agreement between theory and experiment.

Structural and decay properties of even–even trans-lead nuclei

A systematic study of the ground-state properties of even–even Po, Rn, Ra and Th isotopes is conducted using the self-consistent Skyrme-Hartree–Fock–Bogoliubov (HFB) theory. Different Skyrme interactions are employed in the study. The bulk properties such as binding energy, two-neutron separation energies, two-proton separation energies and neutron skin thickness are investigated. The obtained results from the Skyrme-HFB formalism are compared with the calculated results from the Finite Range Droplet Model (FRDM) and the available experimental data. Our theoretical values were found to be consistent with their counterparts. In addition, the density-dependent cluster model is utilized to estimate [Formula: see text]-decay half-lives. A good agreement is achieved between the calculated results and the recent experimental data.

Prediction of two-neutron halos in the N = 28 isotones 40Mg and 39Na

The ground states of the nuclei Mg40 and Na39 are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective n-n and Mg38+n interactions is built for Mg40 based on the available data. We also give predictions for the low-lying spectrum of Na38=37Na+n and two-neutron separation energy of the Na39 nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in Mg40 for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for Na39. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the 2p3/2 and 1f7/2 orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

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.

Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings* *Partly supported by the National Natural Science Foundation of China (11935001, 11575001), the Natural Science Foundation of Anhui Province (2008085MA26), Anhui project (Z010118169), the Heavy Ion Research Facility in Lanzhou (HIRFL) (HIR2021PY007), and the project of Key

This study explores the ground-state characteristics of neutron-rich sodium isotopes, encompassing two-neutron separation energies, root-mean-square radii, quadrupole moments of proton and neutron distributions, single-particle levels of bound and resonant states, and neutron density distributions and shapes. Simultaneously, special attention is paid to the distinctive physical phenomena associated with these isotopes. The deformed relativistic mean field theory in complex momentum representations with BCS pairings (DRMF-CMR-BCS) employed in our research provides resonant states with real physics, offering insights into deformed halo nuclei. Four effective interactions (NL3, NL3*, PK1, and NLSH) were considered to assess the influence of continuum and deformation effects on halo structures. Calculations for odd-even nuclei 35–43Na revealed the dependence on the chosen effective interaction and number of considered resonant states. Neutron occupation patterns near the Fermi surface, particularly in orbitals and , were determined to be crucial in halo formation. The study provided detailed insights into the density distributions, shape evolution, and structure of neutron-rich sodium isotopes, contributing valuably to the field of nuclear physics.

Shape evolution and shape coexistence in even-even Mo isotopic chain

The phenomena of shape evolution and shape coexistence within the Molybdenum isotopic chain are investigated using the covariant density functional theory with the parameterizations DD-ME2 and DD-PC1. Furthermore, various ground state properties of this chain are investigated, including binding energy, two-neutron separation energy, charge radii, and two-neutron shell gap. A robust agreement is observed when comparing with the available experimental data. The ground state deformation of Mo isotopes evolves smoothly and correlates with the continuous and gradual changes observed in the physical properties. A noticeable phenomenon of shape coexistence can be observed in certain isotopes, marked by the simultaneous existence of both a triaxial and an oblate axial minimum. A pronounced and well-defined shell closure is prominently evident at the neutron magic number N=82.

High-precision Penning-trap mass measurements of Cd and In isotopes at JYFLTRAP remove the fluctuations in the two-neutron separation energies

High-precision Penning-trap mass measurements of Cd and In isotopes at JYFLTRAP remove the fluctuations in the two-neutron separation energies

Evolution of N = 20, 28, 50 shell closures in the 20 ≤ Z ≤ 30 region in deformed relativistic Hartree-Bogoliubov theory in continuum* *Supported in part by the National Natural Science Foundation of China (NSFC) (11975041, 11961141004). Xiang-Xiang Sun is supported in part by NSFC (12205308), and the Deutsche Forschungsgemeinschaft (DFG) and NSFC through the funds provided to the

Magicity, or shell closure, plays an important role in our understanding of complex nuclear phenomena. In this work, we employ one of the state-of-the-art density functional theories, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1, to investigate the evolution of the shell closures in the region. We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii, two-neutron separation energies, two-neutron gaps, quadrupole deformations, and single-particle levels. In particular, we find that in the region, the shell closure disappears or becomes quenched, mainly due to the deformation effects. Similarly, both experimental data and theoretical predictions indicate that the shell closure disappears in the Mn isotopic chain, mainly due to the deformation effects. The DRHBc theory predicts the existence of the shell closure in the Ca, Sc, and Ti isotopic chains, but the existing data for the Ti isotopes suggest the contrary, and therefore further research is needed.

Shape evolution of nuclei in the region of (A≈30) using covariant density functional theory

Shape evolution of even–even isotopes of Ne, Mg, Si, S, Ar and Ca in the vicinity of [Formula: see text] mass region of the nuclear chart is studied using covariant density functional theory. It will be studied based on finite range NN-interaction force represented by NL3∗ and DD-ME2 and zero finite range NN-interaction force represented by DD-PC1. Both [Formula: see text]Mg and [Formula: see text]Si exhibit shape coexistence and the ground state shape which is found to be both oblate and prolate. The spherical shape is obtained for the Ca isotopes, and for nuclei that have magic neutron numbers [Formula: see text] and 20. The rest of the isotopic chain has only one minimum and alternates between prolate and oblate shapes. Physical properties are calculated at the location of ground state deformation with neutron number ([Formula: see text]) and proton number ([Formula: see text]), such as the binding energy, two-neutron separation energies, proton, neutron and charge radii. In general, a smooth change in these properties is found, except near [Formula: see text] and 20 one can see a sharp change, which reflects the sudden change in the ground state deformation in the neighboring nuclei. A very good agreement is found with the available experimental data, HF and FRDM models

Level structures of 56,58Ca cast doubt on a doubly magic 60Ca

Gamma decays were observed in 56Ca and 58Ca following quasi-free one-proton knockout reactions from 57,59Sc beams at ≈200 MeV/nucleon. For 56Ca, a γ ray transition was measured to be 1456(12) keV, while for 58Ca an indication for a transition was observed at 1115(34) keV. Both transitions were tentatively assigned as the 21+→0gs+ decays, and were compared to results from ab initio and conventional shell-model approaches. A shell-model calculation in a wide model space with a marginally modified effective nucleon-nucleon interaction depicts excellent agreement with experiment for 21+ level energies, two-neutron separation energies, and reaction cross sections, corroborating the formation of a new nuclear shell above the N = 34 shell. Its constituents, the 0f5/2 and 0g9/2 orbitals, are almost degenerate. This degeneracy precludes the possibility for a doubly magic 60Ca and potentially drives the dripline of Ca isotopes to 70Ca or even beyond.

Nuclear mass predictions with multi-hidden-layer feedforward neural network

Based on Keras deep learning framework, the feedforward neural network (FNN) model is employed to improve the predictions of the liquid drop model (LDM). It is shown that the prediction ability of FNN can be significantly improved if multiple hidden layers are used with only four input parameters. The root-mean-square deviation (RMSD) of nuclear mass predicted by LDM can be reduced from 2.38 MeV to 196 keV with the multi-hidden-layer FNN model, which is only one third of the single-hidden-layer FNN model. The predictions of two-neutron separation energies (S2n) and single-neutron separation energies (Sn) indicate that the multi-hidden-layer FNN model gives a better description of the shell structure. In addition, the extrapolation capability of the model in the super-heavy nuclear region is studied, the results show that better extrapolation capability can be achieved if multiple hidden layers are employed.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation, pairing correlations and continuum in a unified way. In order to consider the triaxial deformation, the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space. In order to take the pairing correlations into account and treat the continuum properly, by using the Dirac Woods–Saxon basis, which has correct asymptotic behavior, the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved. The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented. Taking an axially deformed nucleus 24Ne and a triaxially deformed nucleus 76Ge as examples, the numerical checks are performed. A weakly bound nucleus 112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters. In addition, the ground-state properties of even–even germanium isotopes are investigated. The evolutions of two-neutron separation energy, deformation, root-mean-square radii and density distribution with mass number are analyzed. The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed. It is found that the neutron drip line is extended from 114Ge to 118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Scaling of the B19 two-neutron halo properties close to unitarity

We explore the description of the bound $^{19}\mathrm{B}$ isotope in terms of a $^{17}\mathrm{B}+n+n$ three-body system where the two-body subsystems $^{17}\mathrm{B}+n$ and neutron-neutron ($nn$) have virtual states close to the continuum. Dimensionless scaling functions for the root-mean-square (rms) radii are defined and studied for different parameters of the neutron-core potential and considering three different models for neutron-neutron interaction. The scaling functions for the radii are rooted in the universal behavior of three-body systems close to the Efimov limit and depend only on dimensionless quantities formed by the two-neutron separation energies and scattering lengths. Our results show in practice the model independence of these scaling functions close to unitarity. We provide an estimation of the different rms relative separation distances between the constituents, as well as of the proton and matter radii.

Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional. II. Examples of odd Nd isotopes

Background: One fascinating frontier in nuclear physics is the study of exotic nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which simultaneously includes the nuclear superfluidity, deformation, and continuum effects, can provide proper descriptions for both stable and exotic nuclei. In a previous work [Zhang et al., Phys. Rev. C 102, 024314 (2020)], the DRHBc theory based on the point-coupling density functionals was developed and the DRHBc calculation, previously accessible only for light nuclei, was extended for all even-even nuclei in the nuclear chart. The ground-state properties for the even-even nuclei with 8≤Z≤120 from the DRHBc calculations have been summarized [Zhang et al., At. Data Nucl. Data Tables 144, 101488 (2022)]. Purpose: The aim of this paper is to extend the point-coupling DRHBc theory to odd-A and odd-odd nuclei and examine its applicability by taking odd-A Nd isotopes as examples. Method: In the DRHBc theory, the densities and potentials with axial deformation are expanded in terms of Legendre polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a Dirac Woods-Saxon basis to include the continuum effects. For an odd-A or odd-odd nucleus, the blocking effect of the unpaired nucleon(s) is taken into account with the equal filling approximation. To determine its ground state, an automatic blocking procedure is adopted, in which the orbital with the lowest quasiparticle energy is blocked during the iteration. This procedure is justified by comparing with the results from the orbital-fixed blocking calculations, in which the blocked orbital near the Fermi surface is fixed during the iteration. The ground states for both light and heavy nuclei can be provided by the automatic blocking procedure as the orbital-fixed blocking procedure, but with considerably reduced computational cost. Results: The numerical details for even-even nuclei, including the convergence on the energy cutoff, angular momentum cutoff, and Legendre expansion, are found to be valid for odd-A and odd-odd nuclei as well. The ground-state properties of odd-A Nd isotopes are calculated with the density functional PC-PK1. The calculated physical observables, such as binding energies, two-neutron and one-neutron separation energies, and charge radii, are in good agreement with the available experimental data for the whole Nd isotopic chain. Conclusions: The point-coupling DRHBc theory is extended to odd-A and odd-odd nuclei by including the blocking effect. Taking Nd isotopes including both even-even and odd-A ones as examples, the calculated ground-state properties with PC-PK1 are in good agreement with the available experimental data. This paper paves the way to construct the DRHBc mass table including all even-even, odd-A, and odd-odd nuclei in the nuclear chart.6 MoreReceived 4 May 2022Accepted 12 July 2022DOI:https://doi.org/10.1103/PhysRevC.106.014316©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesEnergy levels & level densitiesNuclear bindingNuclear charge distributionNuclear many-body theoryNuclear spin & parityNuclear structure & decaysNucleon distributionNuclear Physics

Structure and decay chain of fermium isotopes using relativistic mean-field approach

In this paper, we have analyzed the ground state structural properties of fermium-isotopes in the mass range [Formula: see text] within the relativistic mean-field with NL3[Formula: see text] and Relativistic Hartree–Bogoliubov approach with DD-ME2 parameter sets. The bulk properties, such as binding energy, root mean-square charge radius, quadruple deformation parameter, chemical potentials, two-neutron separation energy and differential two- neutron separation energy, are estimated for the above Fm- isotopic chain. All the calculated observables are compared with finite range droplet model (FRDM) predictions and experimental data wherever available. The analysis predicts the existence of shell closure in the neutron-rich region of the isotopic chain at [Formula: see text]. The decay properties such as the [Formula: see text]-decay energy and corresponding half-life for three decay chains i.e. [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are studied. Six different empirical formulae, namely; Viola-Seaborg, Royer, modified B. Alex Brown, Parkhomenko–Sobiczewski, Universal decay law and modified universal decay law are employed to ascertain the numerical dependency of the half-life for each decay energy. A comparative study of [Formula: see text]-values and half-lives for these decay chains gives a good signature of the calculated results. The half-life calculations of three decay chains suggest that [Formula: see text]Pu, [Formula: see text]Pu, [Formula: see text]Pu are shell closure nuclei having maximum half-lives, whereas [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are shell stabilized with lower half-lives.

A Hartree-Fock-Bogoliubov Study on the Pairing Correlations of the Isotopes of Cobalt

Background: The phenomena of nucleon pairing could be outlined from the Bethe-Weizäcker semi-empirical formula, from which the nuclear properties, viz. the binding energy, stability, shape etc. could be clearly sketched. Though the pairing correlation seems to be a small correction to the binding energy term, it plays a determinative role in defining the structure of nuclear systems. The addition to the binding energy in turn affects the position of the isotope on the dripline and hence increases the stability.
 Purpose: To study the effects of pairing on the ground state properties of the isotopes of Cobalt.
 Methods: We use Hartree-Fock-Bogoliubov (HFB) theory for the study. The general wave functions for the HFB approach are determined from variational principle. The eigen functions for the Hamiltonian are connected with the particle operators through the Bogoliubov transformations. The Hartree-Fock energy is obtained through the minimization of the variational parameter and the HFB equation is solved by iterative diagonalization by restoring the particle number symmetry.
 Results: The HFB analysis substantiates the effect of pairing correlation on binding energies, neutron and proton pairing energies, neutron and proton pairing gaps and one- and two-neutron separation energies of the Cobalt isotopes. The binding energies and one and two-neutron separation energies match with the experimental values and for pairing energies and pairing gaps, the regions where pairing is significant and the effects of shell closure at the vicinity of magic configuration of neutrons could be recognized.
 Conclusion: The Hartree-Fock-Bogoliubov calculations of the effects of pairing could be used as an efficient tool to study the nuclear structure. It can be ascertained that pairing plays an important role in determining the ground state properties of atomic nuclei.

Isospin dependent properties of the isotopic chains of Scandium and Titanium nuclei within the relativistic mean-field formalism * *Supported by Science and Engineering Research Board (SERB) (CRG/2021/001229), FOSTECT (FOSTECT. 2019B.04), FAPESP (2017/05660-0)

Density-dependent nuclear symmetry energy is directly related to isospin asymmetry for finite and infinite nuclear systems. It is critical to determine the coefficients of symmetry energy and their related observables because they hold great importance in different areas of nuclear physics, such as the analysis of the structure of ground state exotic nuclei and neutron star studies. The ground state bulk properties of Scandium (Z = 21) and Titanium (Z = 22) nuclei are calculated, such as their nuclear binding energy ( ), quadrupole deformation ( ), two-neutron separation energy ( ), differential variation in the two-neutron separation energy ( ), and root-mean-square charge radius ( ). The isospin properties, namely the coefficient of nuclear symmetry energy and its components, such as the surface and volume symmetry energy of a finite isotopic chain, from the corresponding quantities of infinite nuclear matter, are also estimated. Finally, we correlate the neutron-skin thickness with the coefficient of symmetry energy and the related observables corresponding to the isotopic chains of these nuclei. The coherent density fluctuation model (CDFM) is used to estimate the isospin-dependent properties of finite nuclei, such as symmetry energy, surface symmetry energy, and volume symmetry energy, from their corresponding component in infinite nuclear matter. The relativistic mean-field (RMF) formalism with non-linear NL3 and relativistic-Hartree-Bogoliubov theory with density-dependent DD-ME2 interaction parameters are employed in the analysis. The weight function is estimated using the total density of each nucleus, which in turn is used with the nuclear matter quantities to obtain the effective symmetry energy and its components in finite nuclei. We calculate the ground state bulk properties, such as nuclear binding energy, quadrupole deformation, two-neutron separation energy, differential variation in the two-neutron separation energy, and root-mean-square charge radius, for the Sc- and Ti- isotopic chains using the non-linear NL3 and density-dependent DD-ME2 parameter sets. Furthermore, the ground state density distributions are used within the CDFM to obtain the effective surface properties, such as symmetry energy and its components, namely volume and surface symmetry energy, for both the parameter sets. The calculated quantities are used to understand the isospin dependent structural properties of finite nuclei near and beyond the drip line, which broadens the scope of discovering new magicity along the isotopic chains. A shape transition is observed from spherical to prolate near 44 and 40 for the Sc- and Ti- isotopic chains, respectively. Notable signatures of shell and/or sub-shell closures are found for the magic neutron numbers N = 20 and 28 for both isotopic chains using the nuclear bulk and isospin quantities. In addition to these, a few shell/sub-shell closure signatures are observed near the drip-line region at N = 34 and 50 by following the surface/isospin dependent observables, namely symmetry energy and its component, for both the isotopic chain of odd-A Sc- and even-even Ti- nuclei.