Skyrme Hartree Fock Bogoliubov Research Articles

Investigation of the production routes of 81,82m,83,84 Rb isotopes through proton-induced nuclear reactions on 82,83,84,86 Kr

Investigations using nuclear reaction models are significant and have considerable consequences in terms of understanding nuclear reaction processes and their nature. The nuclear data on radionuclides created by the cyclotron find application in nuclear diagnostics and therapeutic treatments. The excitation function of proton-induced nuclear reactions on 82,83,84,86 Kr for the generation of medically beneficial short-lived radioisotopes 81,82m,83,84 Rb from threshold energy to 50 MeV has been investigated using Koning–Delaroche optical model potential with nuclear level density (NLD) from both the phenomenological and microscopic nuclear models incorporated in TALYS1.96 code. The phenomenological constant temperature + Fermi gas model, back-shifted Fermi gas model, generalised superfluid model, and microscopic NLD from the Skyrme–Hartree–Fock–Bogoliubov, Gogny–Hartree–Fock–Bogoliubov, and temperature-dependent Gogny–Hartree–Fock–Bogoliubov NLD tables have been used to calculate the excitation function. The calculated excitation functions are compared with the experimental data from EXFOR and the TALYS evaluated nuclear data library (TENDL2023). An analysis is carried out by estimating the mean deviation D-value between the theoretical and experimental cross-sections, and the NLD model corresponding to the best result is used for the estimation of activity and production yield for each reaction channel.

Nuclear charge radius predictions based on eXtreme Gradient Boosting

Nuclear charge radii with 8 ≤ Z ≤ 100 are studied based on the eXtreme Gradient Boosting (XGBoost) method. Besides the proton, neutron, and mass numbers, the physical quantities related to the isospin, shell, and pairing effects are important to improve the performance of the XGBoost method by including them as the input variables. The XGBoost method describes the nuclear charge radii better than the Skyrme-Hartree–Fock-Bogoliubov (HFB)-21 model, especially for odd-Z nuclei. The root-mean-square deviation with respect to the experimental data is reduced from 0.025 fm of the HFB-21 model to 0.012 fm of the XGBoost method in the learning set. It is found that the XGBoost method has reliable extrapolation ability at least for the nuclei not far from the learning region, which is verified by comparison with the data in the newly measured experimental data. When extrapolated to the unknown region, the XGBoost predictions of charge radii are close to the HFB-21 results, and the deviations between them are generally less than 0.1 fm even within about 20 steps from the known region.

Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory

This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.

Determination of excitation function for alpha induced reactions on 237Np and 238Pu

The excitation function of the alpha particle-induced reactions on 237Np and 238Pu has been determined for the incident alpha energies ranging from threshold to 50 MeV using TALYS1.95 nuclear reaction code. In this study, the excitation function of (α,xn) reactions on 237Np and 238Pu has been determined by invoking the Jeukenne–Lejeune–Mahaux–Bruyeres Optical model potential. The microscopic nuclear level density from Hilaire’s combinatorial table is used to calculate the nuclear level density. Also, the excitation function has been evaluated by using the alpha potential of Watanabe folding approach with Koning–Delaroche spherical optical model potential and McFadden–Satchler potential. Furthermore, all the calculated cross-sections have been compared with the experimental results taken from EXFOR and the available evaluated cross-sections from TENDL2019 nuclear data library. The calculated cross sections using Jeukenne–Lejeune–Mahaux–Bruyeres Optical model potential together with microscopic nuclear level density from Hilaire’s combinatorial table incorporating the Skyrme–Hartree–Fock–Bogoliubov calculation results in good correspondence with the experimental values from EXFOR.

Continuum Skyrme Hartree–Fock–Bogoliubov theory with Green’s function method for neutron-rich Ca, Ni, Zr, and Sn isotopes

Continuum Skyrme Hartree–Fock–Bogoliubov theory with Green’s function method for neutron-rich Ca, Ni, Zr, and Sn isotopes

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking

Models based on nuclear energy density functionals can provide access to a multitude of observables for thousands of nuclei in a single framework with microscopic foundations. Such models can rival the accuracy of more phenomenological approaches, but doing so requires adjusting parameters to thousands of nuclear masses. To keep such large-scale fits feasible, several symmetry restrictions are typically imposed on the nuclear configurations. One such example is time-reversal invariance, which is generally enforced via the Equal Filling Approximation (EFA). Here we lift this assumption, enabling us to access the spin and current densities in the ground states of odd-mass and odd-odd nuclei, which contribute to the total energy of such nuclei through so-called ‘time-odd’ terms. We present here the Skyrme-based BSkG2 model whose parameters were adjusted to essentially all known nuclear masses without relying on the EFA, refining our earlier work [G. Scamps et al., EPJA 57, 333 (2021)]. Moving beyond ground state properties, we also incorporated information on the fission barriers of actinide nuclei in the parameter adjustment. The resulting model achieves a root-mean-square (rms) deviation of (i) 0.678 MeV on 2457 known masses, (ii) 0.027 fm on 884 measured charge radii, (iii) 0.44 MeV and 0.47 MeV, respectively, on 45 reference values for primary and secondary fission barriers of actinide nuclei, and (iv) 0.49 MeV on 28 fission isomer excitation energies. We limit ourselves here to a description of the model and the study the impact of lifting the EFA on ground state properties such as binding energies, deformation and pairing, deferring a detailed discussion of fission to a forthcoming paper.

Neutron 3s1/2 occupation change across the stable tin isotopes investigated using isotopic analysis of proton scattering at 295 MeV

The isotopic systematics of Sn isotopes in the range A=116--124 were investigated by combining the nuclear structure and reaction calculations for the analysis of Sn(p,p) reactions at 295 MeV. The Sn(p,p) reactions were calculated employing relativistic impulse approximation (RIA) with theoretical densities obtained for the Sn isotopes from relativistic Hartree-Bogoliubov (RHB) calculations with the DD-ME2 interaction and nonrelativistic Skyrme Hartree-Fock-Bogoliubov (SHFB) calculations with the SKM* interaction. Calculation using the DD-ME2 density reproduced the experimental data for $^{122}$Sn(p,p) but overestimated the $^{116}$Sn(p,p) and $^{118}$Sn(p,p) cross sections at backward angles. In the isotopic analysis of the cross section ratio $R(\sigma)$ of $^{122}$Sn to $^{116}$Sn, a calculation using the SKM* density reproduced the peak amplitudes of $R(\sigma)$ obtained from the experimental cross sections, whereas a calculation using the DD-ME2 density did not. The ratio $R(\sigma)$ was found to be sensitive to the isotopic change of the neutron $3s_{1/2}$ occupation through the isotopic difference of the surface neutron density around r=4--5 fm. Isotopic analysis indicated that a rapid increase of the $3s_{1/2}$ occupation from $^{116}$Sn to $^{122}$Sn obtained by the DD-ME2 calculation is unlikely. This result derived from the 295 MeV Sn(p,p) cross section data is consistent with the direct measurement of the neutron occupations in Sn isotopes by neutron transfer and pick-up reactions.

Semi-bubble structure of superheavy nuclei

The nuclear structure properties of heavy and superheavy nuclei lying at the extremes of charge, especially [Formula: see text], and their density profiles have been explored using the relativistic Hartree–Bogoliubov in axial symmetry and the Skyrme–Hartree–Fock–Bogoliubov framework in transformed harmonic oscillator basis. In this study, we found that the semi-bubble (reduced central density) structure is mainly driven by Coulomb repulsion which stabilizes the nuclei either by pushing the nuclear matter in the surface region or by shape deformation. The shell effect is found maximum in spherical symmetric nuclei as the vanishing fission barrier in Liquid Drop formula indicates that the shell correction energy is responsible for the stabilization of these nuclei.

Studies of Deformed Halo Structures of 39Na and 42Mg

Background: The recent experimental discovery of drip-line nucleus 39Na has attracted great interest in theoretical studies of exotic nuclear structures in this mass region. Methods: We solve the Skyrme–Hartree–Fock–Bogoliubov (Skyrme-HFB) equation within deformed coordinate-spaces. The present approach is suitable for descriptions of weakly bound deformed nuclei with continuum effects and deformed halo structures. Results: The systematical two-neutron separation energies are obtained with the SkMext1* and UNEDF0ext1 forces for Na and Mg isotopes close to the neutron drip line. The density distributions show that 39Na and 42Mg have deformed halo structures. Furthermore, there are significant influences of various pairing interactions on halo shapes at large distances. Conclusions: Both 39Na and 42Mg are very weakly bound with well prolate deformed cores. However, their surface halo structures are dependent on the choices of pairing interactions. The volume-type pairing interaction tends to predict a prolate deformed halo, while the halo deformations at large distances are reduced by adopting the surface pairing. We demonstrate that 39Na and 42Mg are promising candidates for two-neutron deformed halo nuclei.

Skyrme–Hartree–Fock–Bogoliubov Calculations of Even and Odd Neutron-Rich Mg Isotopes

Using the Skyrme functional with SIII, SKM*, SLy4, and UNE0 sets of parameters and the Hartree–Fock–Bogoliubov mean-field method; the ground-state properties of even-even and even-odd neutron-rich Mg isotopes have been investigated. The results of calculations of the binding energy per nucleon (B/A), the one- and two-neutron separation energies (Sn and S2n), proton and neutron rms radii, neutron pairing gap, and quadrupole deformation parameter (B2) have been compared with the available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny force, and predictions of some nuclear models such as the Finite Range Droplet Model (FRDM) and Relativistic Mean-Field (RMF) model. Our results show good agreements in comparison with the experimental data and the results of the mentioned models.

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.

Proximity effect of pair correlation in the inner crust of neutron stars

Abstract We study the proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme–Hartree–Fock–Bogoliubov theory formulated in coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superfluid confined in a spherical box. Using a density-dependent effective pairing interaction that reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in a neutron superfluid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of the neutron superfluid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density $5 \times 10^{-4}$ fm$^{-3} \mathop < \limits_ \sim \ \rho_b \mathop < \limits_ \sim \ 2\times 10^{-2}$ fm$^{-3}$, the proximity effect is strongly limited in the vicinity of the nuclear cluster, i.e., in a sufficiently smaller area than the Wigner–Seitz cell. In contrast, the proximity effect is predicted to extend to the whole volume of the Wigner–Seitz cell in shallow layers of the inner crust with $\rho_b \mathop < \limits_ \sim \ 2 \times 10^{-4}$ fm$^{-3}$, and in deep layers with $\rho_b \mathop > \limits_ \sim \ 5 \times 10^{-2}$ fm$^{-3}$.

Nuclear properties of Z = 114 isotopes and shell structure of 298114

The two-neutron separation energies (S2n) and α-decay energies (Qα) of the Z = 114 isotopes are calculated by the deformed Skyrme–Hartree–Fock–Bogoliubov (SHFB) approach with the SLy5, T22, T32 and T43 interactions. It is found that the tensor force effect on the bulk properties is weak and the shell closure at N = 184 is seen evidently with these interactions by analyzing the S2n and Qα evolutions with neutron number N . Meanwhile, the single-particle energy spectra of 298114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus 298114. It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions. Finally, by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of 298114, it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.

A systematic study of the ground state properties of W, Os and Pt isotopes using HFB theory

A systematic study of the ground state properties of transitional nuclei W, Os and Pt is conducted with the help of Skyrme–Hartree–Fock–Bogoliubov theory. Different Skyrme interactions are employed in the study. Two different bases, harmonic oscillator and transformed harmonic oscillator, are used in our investigation. 2[Formula: see text]-separation energy, charge radii, neutron and proton rms radii, neutron skin thickness and deformation parameter have been estimated. The results obtained are in good agreement with the available experimental values.

Pairing Effects on Bubble Nuclei**Supported by the National Natural Science Foundation of China under Grant Nos U1832120 and 11675265, the State Scholarship Fund of China Scholarship Council under Grant No 201708130035, and the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China under Grant No A2018210146.

In the framework of the Skyrme–Hartree–Fock–Bogoliubov approach with the SkT interaction, the pairing effects on the proton bubble structures of 46Ar and 206Hg are discussed. In calculations, three kinds of pairing forces (volume, surface and mixed pairing interactions) are used. For 46Ar, it is shown that the bubble structure with the volume pairing is almost the same as that with the mixed pairing. The bubble with the surface pairing is less pronounced than those with the volume and mixed pairings. Analyzing the density distributions and occupation probabilities of the proton s states and the quasi-degeneracy between the proton 2s1/2 and 1d3/2 orbitals, we explain the difference between the bubble structure with the surface pairing and those with the volume and mixed pairings. For 206Hg, it is seen that the proton density distribution with the surface pairing is different from those with the volume and mixed pairings in the whole region of the radial distance. In addition, it is found that the bubbles with the three pairing forces are different from each other and the least pronounced bubble is obtained with the surface pairing. Thus the selection of the pairing force is important for the study of the nuclear bubble structure.

A systematic study of alpha and cluster decay in Platinum isotopes

The feasibility of alpha and cluster decay from Pt isotopes has been investigated within the framework of Skyrme Hartree–Fock–Bogoliubov (HFB) theory. Calculations have been carried out for various Skyrme forces. Harmonic oscillator and transformed harmonic oscillator basis are used to solve HFB equations. The role played by shell closure is analyzed. Half-lives are estimated with the help of Universal Decay Law (UDL). Geiger–Nuttal plots are also drawn and their linear nature is successfully reproduced.

A study of nuclear structure properties of even and odd 103–140Sb, 105–143Te, 107–145I, 109–148Xe and 112–151Cs nuclei in the axial deformation

We investigated ground-state nuclear structure properties of even and odd [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] nuclei via the axially deformed solution of Skyrme Hartree–Fock Bogoliubov (HFB) based on the transformed harmonic oscillator (THO) and the harmonic oscillator. In the calculations, different Skyrme force parameters were used to obtain wide nuclear data of the nuclei. The calculated results were compared with the results of the experimental data and theoretical models, i.e., the finite-range liquid-drop model (FRDM) and relativistic mean-field theory (RMFT). Additionally, the deformation regions of neutron rich Sb, Te, I, Xe and Cs nuclei have also been discussed. Moreover, in addition to the binding energy per particle, charge, proton and neutron density radii, one-neutron [Formula: see text], and two-neutron separation energies [Formula: see text], the quadropule deformation parameter [Formula: see text], the neutron skin thicknesses (NST), the quadrupole moments [Formula: see text] and the pairing gap energies of the nuclei were determined by HFBTHO 2.00 code.

Properties of nuclear matter from macroscopic–microscopic mass formulas

Based on the standard Skyrme energy density functionals together with the extended Thomas–Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic–microscopic mass formulas: Lublin–Strasbourg nuclear drop energy (LSD) formula and Weizsäcker–Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are K∞=230±11 MeV and 235±11 MeV, respectively. The slope parameter of symmetry energy at saturation density is L=41.6±7.6 MeV for LSD and 51.5±9.6 MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [4]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron–proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrme Hartree–Fock–Bogoliubov calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of the mean-field potential.

Investigation of nuclear structure of 30–44S isotopes using spherical and deformed Skyrme–Hartree–Fock method

Nuclear many-body system is usually described by a mean-field built upon a nucleon–nucleon effective interaction. In this work, we investigate ground state properties of the sulfur isotopes covering a wide range from the line of stability up to the dripline region (30–44S). For this purpose the Hartree–Fock mean field theory in coordinate space with a Skyrme parameterization SkM* has been utilized. In particular, we calculate the nuclear charge, neutrons, protons, mass densities, the associated radii, neutron skin thickness and binding energy. The charge form factors have been also investigated using SkM*, SkO, SkE, SLy4 and Skxs15 Skyrme parameterizations and the results obtained using the theoretical approach are compared with the available experimental data. To investigate the potential energy surface as a function of the quadrupole deformation for isotopic sulfur chains, Skyrme–Hartree–Fock–Bogoliubov theory has been adopted with SLy4 parameterization.