Two-neutron Separation Energies Research Articles

Investigation of the magicity in some even–even Ca isotopes by using shell model and Hartree–Fock–Bogoliubov method

In the present work, the bulk nuclear properties and features of some of the excited states in the neutron-rich even–even 46−54Ca isotopes have been investigated. In order to identify the magicity and the existence of new magic numbers in these isotopes, the shell model and Hartree–Fock–Bogoliubov method were implemented based on Skyrme parameterizations. In particular, root-mean-square charge radius, binding energies, one- and two-neutron separation energies, pairing gaps, reduced transition probabilities, excitation energies, energy levels, and quadrupole deformation parameters have been investigated. The calculated results were compared with available experimental data.

Study of static and dynamic properties of even-even 14–24O and 38–54Ca in the frame of Random Phase Approximation (RPA) method with different Skyrme parameterizations

The static and dynamic nuclear properties for neutron rich oxygen and calcium isotopes have been calculated using the framework of the random phase approximation method with different Skyrme parameterizations namely; SyO-, SyO+, BSk17, SLy4, SLy5, and SkX. The nuclear charge radii, the binding energy per nucleon were calculated and compared to the experimental one to choose the best Skyrme interactions used in the calculations of dynamic properties. The two-neutron separation energy for isotopes under study has been calculated and compared to experimental data. Higher modes of the excited states, energy-weighted sum rule, the centroid, constrained, and scaling energies of the resonances have been studied and illustrated together with available experimental data for comparison. For the low-lying excited states, the energy transition densities for J π = 2+ and J π = 3− are reproduced well in 18–24O and 46–54Ca isotopes. The neutron single particle states as a function of neutron number have been also presented. The results show that the random phase approximation calculations with Skyrme-type interactions is a successful method for describing nuclear structure properties of neutron rich nuclei near the drip line.

Ground-State Properties of Even–Even Nuclei from He (Z = 2) to Ds (Z = 110) in the Framework of Skyrme–Hartree–Fock–Bogoliubov Theory

The ground-state properties of 2094 even–even nuclei with $$2\le Z\le 110$$ over a wide range of isotopes have been calculated and studied in the framework of the Hartree–Fock–Bogoliubov (HFB) theory with the SKI3 Skyrme type effective nucleon–nucleon interaction. The calculated ground-state values of the binding energy per nucleon (B.E/A), quadrupole deformation parameter (β2), two-neutron separation energy (S2n), charge radii (RC), proton rms radii, neutron rms radii and neutron pairing gap have been compared with the available experimental data of the atomic mass evaluation (AME2016), the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny effective nucleon–nucleon interaction and predictions of some nuclear models such as the finite range droplet model (FRDM2012) and relativistic mean-field model. Based on the HFBTHO results, the parameters of the Skyrme SKI3-HFB method can be successfully used for describing the ground-state properties of the investigated nuclei, in particularly the neutron-rich nuclei and the exotic nuclei near the neutron drip-line.

Nuclear shape evolution and shape coexistence in Zr and Mo isotopes

The phenomena of shape evolution and shape coexistence in even–even $$^{88-114}$$ Zr and $$^{90-116}$$ Mo isotopes are studied by employing covariant density functional theory (CDFT) with density-dependent point-coupling parameter set, DD-PCX, and with separable pairing interaction. The results for the rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate–prolate shape coexistence in $$^{96-110}$$ Zr isotopes, the correlations between shape transition and discontinuity in the observables are also examined. A smooth trend of charge radii in Mo isotopes is found to be due to the manifestation of triaxiality softness. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi level of neutron and proton, respectively. The rapid shape transition in Zr isotopes near N $$\approx $$ 60 is identified to be caused by the evolution of the shell structure associated with massive proton excitations to 1 $$\pi g_{9/2}$$ orbit. The present calculations also predict a deformed semi-bubble structure in the $$^{100}$$ Zr isotope.

Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid–shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only thethree dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.

Microscopic study of shape evolution and ground-state properties of Iodine isotopes

In this paper, we investigated the shape evolution and ground-state properties of 108−144I isotopes using Hartree–Fock-Bogoliubov Model while employing the axially deformed single-particle harmonic oscillator basis for the expansion of quasiparticle wave functions. We have used SKP and UNEDF2 models to perform the theoretical calculations. We have presented the shape evolution and final values of the quadrupole deformation parameter β 2 of iodine isotopes. We have used the final values of the β 2 for studying the ground-state properties of the iodine isotopic chain. The investigated ground-state properties are the nuclear electric quadrupole moment, single-particle energy levels, the binding energy per nucleon, pairing energy, one-neutron separation energy, two-neutron separation energy, nuclear charge radius, neutron rms radius, proton rms radius, and neutron skin thickness. After using the SKP parameterization on 109I, we have observed the shape coexistence of prolate and oblate shape. Similarly, after using the UNEDF2 parameterization on 110I, 112I, 114I, 115I, 116I, 117I, 118I, and 119I, we discover the shape coexistence of prolate and oblate shape.

Shell evolution in neutron-rich Ge, Se, Kr and Sr nuclei within RHB approach

The exotic even–even isotopic chains from [Formula: see text] to [Formula: see text] are investigated by means of the relativistic Hartree–Bogoliubov (RHB) approach with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density-Dependent Point-Coupling (DD-PC1) models. The classic magic number [Formula: see text] is reproduced and the new number [Formula: see text] is predicted to be a robust shell closure by analysing several calculated quantities such as: two-neutron separation energies, two-neutron shell gap, neutron pairing energy, potential energy surface and neutron single particle energies. The obtained results are compared with the predictions of finite range droplet model (FRDM) and with the available experimental data. A reasonable and satisfactory agreement between the theoretical models and experiment is established.

Estimate of the location of the neutron drip line for calcium isotopes from an exact Hamiltonian with continuum pair correlations

The eastern region of the calcium isotope chain of the nuclei chart is, nowadays, of great activity. The experimental assessment of the limit of stability is of interest to confirm or improve microscopic theoretical models. The goal of this work is to provide the drip line of the calcium isotopes from the exact solution of the pairing Hamiltonian which incorporates explicitly the correlations with the continuum spectrum of energy. The modified Richardson equations, which include correlations with the continuum spectrum of energy modeled by the continuum single particle level density, is used to solve the many-body system. Three models are used, two isospin independent models with core 40Ca and 48Ca, and one isospin dependent model. One and two-neutron separation energies and occupation probabilities for bound and continuum states are calculated from the solution of the Richardson equations. The one particle drip line is found at the nucleus 57Ca, while the two neutron drip line is found at the nucleus 60Ca from the isospin independent model and at 66Ca from the isospin dependent one.

Shell-model study of calcium isotopes toward their drip line

We report in this paper a study in terms of the nuclear shell model about the location of the calcium isotopes drip line. The starting point is considering the realistic two-body potential derived by Entem and Machleidt within chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO), as well as a chiral three-body force at next-to-next-to-leading order (N2LO) whose structure and low-energy constants are consistent with the two-body potential. Then we construct the effective single-particle energies and residual interaction needed to diagonalize the shell-model Hamiltonian. The calculated two-neutron separation energies agree nicely with experiment until 56Ca, which is the heaviest isotope whose mass has been measured, and do not show any sign of two-neutron emission until 70Ca. We discuss the role of the choice of the model space in determining the neutron drip line, and also the dependence of the results on the parameters of the shell-model Hamiltonian.

Charge radii of exotic neon and magnesium isotopes

We compute the charge radii of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include delta isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data and the dripline in neon is accurate. The computed charge radii have an estimated uncertainty of about 2-3% and are accurate for many isotopes where data exist. Finer details such as isotope shifts, however, are not accurately reproduced. Chiral potentials correctly yield the subshell closure at N = 14 and also a decrease in charge radii at N = 8 (observed in neon and predicted for magnesium). They yield a continued increase of charge radii as neutrons are added beyond N = 14 yet underestimate the large increase at N = 20 in magnesium.

Microscopic description of structural, surface, and decay properties of Z=124, 126 superheavy nuclei

A systematic investigation has been carried out for even-even isotopic series of two superheavy nuclei with Z=124 and Z=126 in the region 160≤N≤220, and 162≤N≤218, respectively, within the framework of covariant density functional theory (CDFT). Based on the potential energy curves calculated using the explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models, many sensitive observables have been analyzed to understand the structural evolution, shape coexistence, and to predict the possible candidates for neutron shell-closure within the isotopic series of Z=124 and Z=126. The shell correction energy and nuclear symmetry energy have been evaluated within the Strutinsky shell correction approach and the Coherent Density Fluctuation Model (CDFM), respectively. All the sensitive observables i.e. two-neutron separation energy, its differential, neutron-pairing energy, single-particle energy levels, and total shell-correction energy reproduce known spherical neutron magic numbers, and present evidence on new deformed neutron magic numbers at N=168, 174 and 178. The symmetry energy shows a direct correlation with the shape of the system. The α-decay chain of four isotopes 124298,302 and 126300,304 have been studied within three different semi-empirical approaches named UNIV2, SemFIS2 and ImSahu, and compared with the available experimental data, FRDM2012 and the WS4 mass model. All the models, DD-ME2, DD-PC1, FRDM2012, and WS4 have predicted around 8α to 10α decay before spontaneous fission (SF) can start.

A search for neutron magicity in the isotopic series of Z = 122, 128 superheavy nuclei

The superheavy nuclei have been examined systematically in the region 158 ⩽ N ⩽ 218, 162 ⩽ N ⩽ 212 for Z = 122 and 128, respectively. The explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models within the framework of covariant density functional theory (CDFT) have been used to study the structural and decay properties of the isotopic series which includes the separable form of a finite range of pairing interaction. From the potential energy curves, the ground state properties of nuclei are predicted. Due to the importance of the shell effect in the superheavy region, the Strutinsky shell correction method has been employed for a better understanding of the extra stability of nuclei. The results from neutron pairing energy, two-neutron separation energy (S 2n ), single-particle energy levels, and total shell-correction energy strongly support N = 168, 174, and 178 as deformed neutron-magic numbers from both the force parameter, in both the isotopic series. N = 172 and 184 are predicted as spherical magic with DD-ME2 interaction in the Z = 122 isotopic series. Using three different semi-empirical approaches named UNIV2, SemFIS2, and ImSahu, the α-decay properties are studied and compared with available experimental data, FRDM2012 and the WS4 mass model. The stability of synthesized superheavy nuclei can be determined by comparing spontaneous fission half-lives with α-decay half-lives.

Exploring the α-decay chain of 302122 within relativistic mean-field formalism

The ground and first excited state structural properties, like binding energy, charge radius, deformation parameter, pairing energy, and two-neutron separation energy, for the isotopic chain of Z = 122 are analysed. The axially deformed relativistic mean-field formalism with NL3* force parameter is used for the present analysis. Based on the analysis of binding energy per particle, chemical potential, and single-particle spacing, we predict the isotopes of Z = 122 with N = 180, 182, and 184 are the possible stable nuclei over the considered isotopic chain. The α-decay energies and the decay half-lives of 302122 chains are investigated using four different empirical formulae. The results of our calculations are compared with the available experimental data and finite range droplet model predictions. We also established a correlation for the decay energy with the half-lives for the considered α-decay chains for various empirical formulae.

Mapping of a New Deformation Region around ^{62}Ti.

We performed the first direct mass measurements of neutron-rich scandium, titanium, and vanadium isotopes around the neutron number 40 at the RIKEN RI Beam Factory using the time-of-flight magnetic-rigidity technique. The atomic mass excesses of ^{58-60}Sc, ^{60-62}Ti, and ^{62-64}V were measured for the first time. The experimental results show that the two-neutron separation energies in the vicinity of ^{62}Ti increase compared to neighboring nuclei. This shows that the masses of Ti isotopes near N=40 are affected by the Jahn-Teller effect. Therefore, a development of Jahn-Teller stabilization appears below the Cr isotopes, and the systematics in Sc, Ti, and V isotopes suggest that ^{62}Ti is located close to the peak of the Jahn-Teller effect.

Neutron-rich calcium isotopes within realistic Gamow shell model calculations with continuum coupling

Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in the calcium chain around neutron numbers \textit{N} = 32, 34 and 40 are understood by calculating effective single-particle energies, the excitation energies of the first $2^+$ states and two-neutron separation energies. The calculations support shell closures at $^{52}$Ca (\textit{N} = 32) and $^{54}$Ca (\textit{N} = 34) but show a weakening of shell closure at $^{60}$Ca (\textit{N} = 40). The possible shell closure at $^{70}$Ca (\textit{N} = 50) is predicted.

A study of nuclear radii and neutron skin thickness of neutron-rich nuclei near the neutron drip line

We studied the charge radius ([Formula: see text]), neutron radius ([Formula: see text]), and neutron skin-thickness ([Formula: see text]) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) and effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement is noted. We additionally assessed the two-neutron separation energy ([Formula: see text]) to mark the drip line nuclei of the considered isotopic series. In the reference of [Formula: see text], neutron magicity is also discussed. The calculated neutron radii are compared with empirical estimation made by [Formula: see text] to examine the abnormal trend of the radius for neutron drip line nuclei. In view to guide the long tails, the density distribution for some skin candidates is analyzed. Finally, neutron skin thickness is observed for the whole considered isotopic series.

Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional: Examples of even-even Nd isotopes

The aim of this work is to develop the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) theory based on the point-coupling density functionals and extend it to provide a unified description for all even-even nuclei in the nuclear chart by overcoming all possible challenges. The nuclear superfluidity is considered via Bogoliubov transformation. Densities and potentials are expanded in terms of Legendre polynomials to include the axial deformation degrees of freedom. Sophisticated relativistic Hartree-Bogoliubov equations in coordinate space are solved in the DiracWoods-Saxon basis to consider the continuum effects. Numerical checks are performed from light nuclei to heavy nuclei. The techniques to construct the DRHBc mass table for even-even nuclei are explored. The DRHBc theory is extended to study heavier nuclei beyond magnesium isotopes. Taking Nd isotopes as examples, the experimental binding energies, two-neutron separation energies, quadrupole deformations, and charge radii are reproduced rather well. The deformation and continuum play essential roles in the description of nuclear masses and prediction of drip-line nuclei. By examining the single-particle levels in the canonical basis and their contributions to the total density, the thickness of the neutron skin, the particles number in continuum, and the Coulomb barrier, the exotic structures including the neutron skin and the proton radioactivity are predicted.

Constraints on the neutron drip line with the newly observed Na39

The recently observed weakly-bound 39Na provides a stringent theoretical constraint on the neutron drip-line. We studied the properties of drip-line nuclei around 39Na with the Hartree-Fock-Bogoliubov method and various Skyrme interactions. We adopted the extended SkM*-ext1 parameterization which can properly describe two-neutron separation energies of oxygen and fluorine isotopes and deformations at the center of the "island of inversion". Systematic calculations of drip lines of O, F, Ne, Na, Mg, and Al isotopes have been performed. We infer that 42Mg is weakly bound and 45Al is less weakly bound. 44Mg and 47Al could be barely existed. We also demonstrated the deformed halo properties of 39Na. Our studies could be valuable for experimental explorations of drip-line nuclei in the forthcoming FRIB and other rare-isotope beam facilities .

Microscopic study of the shell structure evolution in isotopes of light to middle mass range nuclides

Shell structure evolution in isotopes (even Z and even N) of Silicon (Si), Sulphur (S), Argon (Ar) and Calcium (Ca) has been analysed. We have used both Relativistic Hartree-Bogoliubov theory and Non-Relativistic Hartree-Fock-Bogoliubov theory for the theoretical calculations of the physical observables of interest. We have employed the model based on Relativistic Hartree-Bogoliubov theory with the density dependent effective interactions of meson exchange and point coupling types. Calculations based on Hartree-Fock-Bogoliubov theory are carried out with different skyrme forces and their sensitivity has been tested. Physical observables of interest include binding energies, single neutron separation energies, two-neutron separation energies, shell closure parameter Dn(Z, N) and differential variation dS2n(Z, N) based on two neutron separation energy. Our theoretical results gives indication of shell closure at neutron number N =14 and neutron number N = 20 for the nuclei of Silicon (Si). Shell closures at neutron numbers N = 14, 20 and neutron number N = 28 are observed for Sulphur (S) nuclides. Argon (Ar) and Calcium (Ca) isotopes also provides the signature of shell closures at neutron numbers N = 20 and neutron number N = 28.

Ground state properties of Zn, Ge, and Se isotopic chains in covariant density functional theory

A systematic investigation of the ground state deformation, the physical properties (two-neutron separation energy and neutron, proton, and charge radii), and the possibility of nuclear shape coexistence in Zn, Ge, and Se isotopes was performed using the relativistic Hartree-Bogoliubov formalism using density-dependent zero- and finite-range $NN$ interactions. Shape coexistence does not show up clearly in Zn isotopes. However, it is clear in most of the Ge and Se isotopes; the two coexistence minima are axial and triaxial in the case of Ge, while both are axial in the case of Se. Along all these chains one can see the existence of several transition points, where the ground state shape suddenly changes. This sudden change affects the evolution of the physical properties. The density of states near the Fermi level is a key factor in determining the ground state minima. Both point-coupling and meson-exchange models give similar results with few exceptions. A very good agreement is found with the available experimental data. The SU(3) proxy provides a reasonable prediction of the deformation value in the middle of the isotopic chain.