Skyrme Hartree-Fock Research Articles

Determining the radii of single-particle potentials with Skyrme Hartree-Fock calculations

Determining the radii of single-particle potentials with Skyrme Hartree-Fock calculations

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.

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.

Properties of glitching pulsars in the Skyrme–Hartree–Fock framework

Properties of glitching pulsars in the Skyrme–Hartree–Fock framework

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.

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

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

The Magnetic Form Factors for Some Nuclei 51V, 59Co, 93Nb, 115In by using Valence with and Without Core Polarization Effects Models

The magnetic electron scattering form factor with glekpn, d3f7, ho models space for 51V , 59Co, 93Nb, and 115In nuclei are discussed with and without core polarization effects(CP). The calculations are done with the help of NuShellX@MUS code. The radial wave function for the single-particle matrix elements have been calculated with the SKyrme-Hartree Fock (SKX), Wood-Saxon(WS), and harmonic oscillator (HO) potentials. valence model(Vm) used in these calculation to calculate form factors with core-polarization effects. The results give a good agreement with available experimental data.

The difference between charge polarizations of fission fragments deduced by the static theoretical model and in the current data library

In this paper, we propose a theoretical method to deduce the charge polarization (CP) and most probable charge for fission fragments for the selected range of mass numbers based on a quantum many-body framework, namely, a constrained Skyrme Hartree–Fock+BCS model. We investigate the CP on the low energy neutron-induced fission of [Formula: see text]U as a representative reaction. We have found that the calculated CP has a noticeable dip that is clearly affected by the spherical shell structure around [Formula: see text]Sn and deformed one around [Formula: see text]144 and a peak for their counterparts, which are common features to those of widely-used Wahl’s systematics, but otherwise, our CP values converge to zero. Especially, we could not see a deep valley and a big hump in the region of symmetric fission at [Formula: see text]112 and 124 present in Wahl’s systematics. The gradient of our CP near the symmetric fission is negative concerning the mass number of fission fragments, which is consistent with other previous theoretical studies; however, that is the opposite of the gradient in Wahl’s systematics. This paper shows the difference between the charge distribution of fission fragments, which has been used practically so far, in comparison with the calculation by microscopic nuclear theory.

Comparative study on charge radii and their kinks at magic numbers

Isotope dependences of charge radii, i.e., isotope shifts, calculated by the Skyrme Hartree-Fock, the relativistic mean-field, and the relativistic Hartree-Fock calculations are compared against the experimental data of magic and semimagic nuclei. It is found that the tensor interaction plays a role in reproducing the ``kink'' behavior, irregularity of isotope shifts at the neutron magic number, in the relativistic Hartree-Fock approach. With several Skyrme models, it is found that the kink behavior can be reproduced with the spin-orbit interaction having nonzero isovector channel. The single-particle orbitals near the Fermi energy are crucial to determine the kink size. The effects of the symmetry energy and the pairing interaction are also discussed in relation to the kink behavior.

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

Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme–Hartree–Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

Proton s -resonance states of C12 and O14,15 within the Skyrme Hartree-Fock mean-field framework

The excitation functions of proton elastic scattering on $^{12}\mathrm{C}$ and $^{14,15}\mathrm{O}$ nuclei at the energies near the proton-emission threshold are calculated using the Skyrme Hartree-Fock (SHF) in continuum approach. For each excitation function, the first resonance is identified as the $s$-state resonance of the mean-field theory. For $^{15}\mathrm{O}$, whose ground-state spin is nonzero, the $s$-state resonance splits into two resonances via the spin-spin component of the optical potential. With a slight adjustment of the strength of the central potential, which is obtained from the SHF in continuum approach, the excitation functions of proton elastic scattering for the three nuclei can be explained with high accuracy. The proposed framework can provide a practical method to explain nuclear scattering at the energies near the proton-emission threshold with minimal experimental input.

Role of hexadecapole deformation in fission potential energy surfaces of 240Pu

In this work, the multipole deformation-constrained Skyrme Hartree-Fock+BCS (SHF-BCS) calculations are implemented to obtain microscopic multi-dimensional potential energy surfaces for descriptions of fission of 240Pu. The SHF-BCS equation is solved in the axial-symmetric lattice space. The results show that the hexadecapole deformation is important at large deformations, and is related to issues of multiple solutions and discontinuities in potential energy surfaces. With a suitable disturbation of hexadecapole deformation β4, we can obtain a smooth 2-dimensional potential energy surface in (β2, β3) by parallel calculations. The constrained SHF-BCS calculation in the 3-dimensional deformation space of (β2, β3, β4) is also developed.

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.

Single-particle properties of the near-threshold proton-emitting resonance in B11

The excitation function of proton elastic scattering from $^{10}\mathrm{Be}$ at keV energy is calculated using the method of self-consistent Skyrme Hartree-Fock in the continuum. The calculation successfully reproduces the narrow near-threshold proton-emitting resonance (${E}_{x}=11.4$ MeV, $\mathrm{\ensuremath{\Gamma}}=6$ keV, and quantum number ${J}^{\ensuremath{\pi}}=1/{2}^{+}$) in $^{11}\mathrm{B}$ relevant to the $\ensuremath{\beta}$-delayed proton emission of $^{11}\mathrm{Be}$. This supports the recent experimental result of Ayyad et al. at the ReA3 reaccelerator facility of the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The resonance is interpreted as the ${s}_{1/2}$ single-proton resonance state in the Skyrme Hartree-Fock mean-field theory.

Electromagnetic moments and magnetic form factors of the ground states of odd-A nuclei in the vicinity of Z = 20 closure

Magnetic dipole and electric quadrupole moments are calculated for odd-[Formula: see text] nuclei in the vicinity of [Formula: see text] closure. Also, elastic magnetic electron scattering form factors are calculated for some of these nuclei, for which there are available experimental data. Excitation out of major shell space is taken into account through a microscopic theory which allows particle–hole excitation from the core and model-space orbits to all higher orbits with [Formula: see text] excitations, with [Formula: see text] as the number of shells that gives convergence to core-polarization matrix elements. Effective charges are obtained for each isotope. Core polarization (CP) is essential for obtaining a reasonable description of the electric quadrupole moments, but has no effect on the magnetic dipole moments but squeezes the magnetic form factors, and describes the data very well. For nuclei where there are data for large momentum transfer values, Skyrme–Hartree–Fock (SHF) method is used to generate from it a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. Those with high momentum transfer data which give evidence of the structure of the different multipoles, are more well described using SHF formalism than the harmonic oscillator (HO) single-particle matrix elements.