Skyrme Parameters Research Articles

Investigate Cross-sections for (α, γ) reactions on p-nuclei 90Zr, 121Sb, 151Eu, and 162Er using Different Models of Radiative Strength Functions

In this work, we examine cross sections for (α, γ) reactions on p-nuclei, including 90Zr, 121Sb, 151Eu, and 162Er at astrophysically relevant energies. By using our recently developed α optical model potential (α-OMP), the (α, γ) cross sections were calculated within six models of radiative strength functions (RSF) which consisted of the microscopic HFB-QRPA model based on the BSk-14 Skyrme force, the HF-BCS theory using Skyrme parameters, the EGLO model, SMLO model, the empirical SMLO (SMLOg) and global semi-microscopic (D1M-QRPAg) models. The numerical results is then compared to the measured data of (α, γ) cross sections. For the considered (α, γ) reactions, the EGLO, SMLO, and HFB results are typically greater than the measured data. In addition, the comparison has indicated that the RSF models of SMLOg and D1M-QRPAg best fit the measured data with rms smaller than 0.2 within our proposed α-OMP. Therefore, for the (α, γ) reactions on the selected targets, RSF models of SMLOg and D1M-QRPAg are strongly recommended. The results are significant for a further systematic examination to evaluate which RSF model is most appropriate for studying (α, γ) reactions on p-nuclei in general.

Development of a more accurate Geant4 quantum molecular dynamics model for hadron therapy

Objective. Although in heavy-ion therapy, the quantum molecular dynamics (QMD) model is one of the most fundamental physics models providing an accurate daughter-ion production yield in the final state, there are still non-negligible differences with the experimental results. The aim of this study is to improve fragment production in water phantoms by developing a more accurate QMD model in Geant4. Approach. A QMD model was developed by implementing modern Skyrme interaction parameter sets, as well as by incorporating with an ad hoc α-cluster model in the initial nuclear state. Two adjusting parameters were selected that can significantly affect the fragment productions in the QMD model: the radius to discriminate a cluster to which nucleons belong after the nucleus–nucleus reaction, denoted by R, and the squared standard deviation of the Gaussian packet, denoted by L. Squared Mahalanobis’s distance of fragment yields and angular distributions with 1, 2, and the higher atomic number for the produced fragments were employed as objective functions, and multi-objective optimization (MOO), which make it possible to compare quantitatively the simulated production yields with the reference experimental data, was performed. Main results. The MOO analysis showed that the QMD model with modern Skyrme parameters coupled with the proposed α-cluster model, denoted as SkM* α, can drastically improve light fragments yields in water. In addition, the proposed model reproduced the kinetic energy distribution of the fragments accurately. The optimized L in SkM* α was confirmed to be realistic by the charge radii analysis in the ground state formation. Significance. The proposed framework using MOO was demonstrated to be very useful in judging the superiority of the proposed nuclear model. The optimized QMD model is expected to improve the accuracy of heavy-ion therapy dosimetry.

Systematic study of proton radioactivity half-lives based on the relationship between Skyrme-Hartree-Fock and the macroscopic quantities of nuclear matter* *Supported in part by the National Natural Science Foundation of China (12175100), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Natural Science Foundation of Hunan Province, China

In this study, we systematically investigate the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and the macroscopic quantities is analyzed. Moreover, we obtain a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with the Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical proton radioactivity half-life calculated using the new Skyrme parameter set can better reproduce the experimental data.

A Skyrme force for 𝚵− hypernuclei

Experimental data for the cascade hypernuclei 15ΞC, 12ΞBe, and 13ΞB are analyzed within a Skyrme-Hartree-Fock theoretical approach and optimal Skyrme parameters are determined. The important role of deformation for 13ΞB is pointed out. Predictions for 7ΞH and 10ΞLi are made.

Skyrme ve Gogny Modelleriyle Bakır İzotoplarının Yoğunluk Hesabı

The ground state properties of the nuclei are generally calculated using two different methods, namely Skyrme and Gogny force methods. We have calculated nucleon densities of Copper isotopes by using Hartree-Fock-Skyrme (using Woods-Saxon Potential) (SHF-WS), Hartree-Fock-Skyrme (using Harmonic Oscillator Potential) (SHF-HO), Hartree-Fock-Bogolyubov-Skyrme (HFB-S) and the Hartree-Fock-Bogolyubov-Gogny (HFB-G) methods. In the first two methods, the densities and rms (root mean square) radii for both proton and neutron of copper isotopes were calculated by different Skyrme parameters set. Theoretical calculated charge density was compared with experimental data of Angeli and Marinova to determine the best parameter set for each copper isotope. Then all evaluated nucleon densities via four different methods were compared each other. All methods gave similar results for all copper isotopes.

Constraints on Skyrme equations of state from doubly magic nuclei, ab initio calculations of low-density neutron matter, and neutron stars

We use properties of doubly-magic nuclei, ab-initio calculations of low-density neutron matter, and of neutron stars to constrain the parameters of the Skyrme energy-density functional. We find all of these properties can be reproduced within a constrained family of Skyrme parameters. The maximum mass of a neutron star is found to be sensitive to the neutron effective mass. A value of [$ m^{*}_{\rm n}/m](\rho_0) = 0.60-0.65 $ is required to obtain a maximum neutron star mass of 2.1 solar masses. Using the constrained Skyrme functional with the aforementioned effective mass, the predicted radius for a neutron star of 1.4 solar masses is 12.4(1) km and $\Lambda$ = 423(40).

Systematic Study of the Nuclear Structure for Some Exotic Nuclei Using Skyrme–Hartree–Fock Method

The ground state charge, neutron, proton and matter densities, the associated nuclear radii and the binding energy per nucleon of 8B, 17Ne, 23Al and 27P halo nuclei have been investigated using the Skyrme–Hartree–Fock (SHF) model with the new SKxs25 parameters. According to the calculated results, it is found that the SHF model with these Skyrme parameters provides a good description on the nuclear structure of above proton-rich halo nuclei. The elastic charge form factors of 8B and 17Ne halo nuclei and those of their stable isotopes 10B and 20Ne are calculated using plane-wave Born approximation with the charge density distributions obtained by SHF model to investigate the effect of the extended charge distributions of proton-rich nuclei on the elastic electron scattering. Calculations show that the major difference between the elastic charge form factors of halo nuclei and those of their stable isotopes is caused by the variation in the charge density distributions, especially the details of the outer parts.

Influence of the tensor interaction on heavy-ion fusion cross sections

[Background] While the tensor interaction has been shown to significantly affect the nuclear structure of exotic nuclei, its influence on nuclear reactions has only recently been investigated. The primary reason for this neglect is the fact that most studies of nuclear dynamics do not include the tensor force at all in their models. Indeed, only a few Skyrme parametrizations consider the tensor interaction in parameter determination. With modern research facilities extending our ability to probe exotic nuclei, a correct description of nuclear dynamics and heavy-ion fusion is vital to both supporting and leading experimental efforts. [Method] Fusion cross sections are calculated using ion-ion potentials generated by the fully microscopic density-constrained time-dependent Hartree-Fock (DC-TDHF) method with the complete Skyrme tensor interaction. [Results] For light nuclei, the tensor force only slightly changes the sub-barrier fusion cross sections at very low energies. Heavier nuclei, however, begin to exhibit a substantial hindrance effect in the sub-barrier region. This effect is strongest in spin-unsaturated systems, though can manifest in other configurations as well. Static, ground state deformation effects of the tensor force can also affect cross sections by shifting the fusion barrier. [Conclusions] The tensor interaction has a measurable effect on the fusion cross sections of nuclei spanning the nuclear chart. The effect comes from both static effects present in the ground state and dynamic processes arising from the time evolution of the system. This motivates the development of a modern Skyrme parameter set that includes all time-odd and tensor terms and that studies moving forward should include the tensor force to ensure a more robust and complete description of nuclei.

Insights on Skyrme parameters from GW170817

The binary neutron-star merger event, GW170817, has cast a new light on nuclear physics research. Using a neutron-star model that includes a crust equation of state (EoS), we calculate the properties of a 1.4 solar-mass neutron star. The model incorporates more than 200 Skyrme energy density functionals, which describe nuclear matter properties, in the outer liquid core region of the neutron star. We find a power-law relation between the neutron-star tidal deformability, Λ, and the neutron-star radius, R. Without an explicit crust EoS, the model predicts a smaller R and the difference becomes significant for stars with large radii. To connect the neutron star properties with nuclear matter properties, we confront the predicted values for Λ against the Taylor expansion coefficients of the Skyrme interactions. There is no pronounced correlation between Skyrme parameters relevant to symmetric nuclear matter and neutron star properties. However, we find the strongest correlation between Λ and Ksym, the curvature of the density dependence of the symmetry energy at saturation density. At twice the saturation density, our calculations show a strong correlation between Λ and total pressure, providing guidance to laboratory nucleus-nucleus collision experiments.

Nuclear structure investigation of neutron-rich Mn isotopes

Structural evolution of odd-even and odd-odd Mn isotopes from the valley of stability up to neutron dripline is studied in the framework of the self-consistent mean-field theory of Hartree–Fock–Bogoliubov. Three Skyrme effective interactions, namely, SLy4, SLy5 and SLy5T, are employed to investigate the tensor force effect on the ground-state properties. It is shown that the calculated quantities with the SLy4 interaction correctly reproduce the available experimental data and agree well with finite range droplet model and relativistic mean-field predictions. An inconsistency has been observed between the curves of the separation energies and that of the charge radius around N = 40. It is explained by the flatness of the potential energy curves in this region. The SLy5 and SLy5T results point to the necessity to refit all the Skyrme parameters after including the tensor terms.

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

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

Self-consistent Hartree–Fock RPA calculations in 208Pb

The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree–Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even–even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

Microscopic method for E0 transition matrix elements

We present a microscopic model for electric monopole ($E0$) transition matrix elements by combining a configuration interaction model for orbital occupations with an energy-density functional model for the single-particle potential and radial wave functions. The configuration interaction model is used to constrain the orbital occupations for the diagonal and off-diagonal matrix elements. These are used in an energy-density functional calculation to obtain a self-consistent transition density. This density contains the valence contribution, as well as the polarization of the protons by the valence protons and neutrons. We show connections between $E0$ matrix elements and isomer and isotope shifts of the charge radius. The spin-orbit correction to the charge density is important in some cases. This model accounts for a large part of the data over a wide region of the nuclear chart. It also accounts for the shape of the observed electron scattering form factors. The results depend on the Skyrme parameters used for the energy-density functional and might be used to provide new constraints for them.

Uncertainty quantification of effective nuclear interactions

We give a brief review on the development of phenomenological NN interactions and the corresponding quantification of statistical uncertainties. We look into the uncertainty of effective interactions broadly used in mean field calculations through the Skyrme parameters and effective field theory counterterms by estimating both statistical and systematic uncertainties stemming from the NN interaction. We also comment on the role played by different fitting strategies on the light of recent developments.

Shape evolution and energy spectra of Pt isotopes

The shapes and low-energy spectra of [Formula: see text]Pt isotopes are discussed by a nonrelativistic Skyrme–Hartree–Fock (SHF) approach plus a density-dependent pairing in the BCS approximation. Two different Skyrme parameters SLy5 and SGII are used to perform constrained triaxial mean-field calculations of energy surface. The calculations beyond mean field are introduced by a projection of mean-field intrinsic wave functions onto good angular momentum. Theoretical calculations exhibit the evolution of shapes from triaxial in light Pt isotopes to [Formula: see text] soft for medium Pt isotopes, and finally oblate shapes in heavy isotopes. In particular, the calculated excitation spectra are in good agreement with available data and the trend of experimental [Formula: see text] is reproduced. The mean-field calculations indicate a stable shape evolution with SLy5 and SGII interactions, respectively. In the present SHF approach, the lighter nuclei Pt isotopes present a slightly triaxial shapes.

Global description ofβ−decay in even-even nuclei with the axially-deformed Skyrme finite-amplitude method

We use the finite amplitude method for computing charge-changing Skyrme-QRPA transition strengths in axially-deformed nuclei together with a modern Skyrme energy-density functional to fit several previously unconstrained parameters in the charge-changing time-odd part of the functional. With the modified functional we then calculate rates of beta-minus decay for all medium-mass and heavy even-even nuclei between the valley of stability and the neutron drip line. We fit the Skyrme parameters to a limited set of beta-decay rates, a set of Gamow-Teller resonance energies, and a set of spin-dipole resonance energies, in both spherical and deformed nuclei. Comparison to available experimental beta-decay rates shows agreement at roughly the same level as in other global QRPA calculations. We estimate the uncertainty in our rates all the way to the neutron drip line through a construction that extrapolates the errors of known beta-decay rates in nuclei with intermediate Q values to less stable isotopes with higher Q values.

Error analysis of nuclear forces and effective interactions

The nucleon–nucleon (NN) interaction is the starting point for ab initio nuclear structure and nuclear reactions calculations. These are effectively carried out via effective interactions fitting scattering data up to a maximal center of mass momentum. However, NN interactions are subjected to statistical and systematic uncertainties, which are expected to propagate and have some impact on the predictive power and accuracy of theoretical calculations, regardless on the numerical accuracy of the method used to solve the many body problem. We stress the necessary conditions required for a correct and self-consistent statistical interpretation of the discrepancies between theory and experiment which enable a subsequent statistical error propagation and correlation analysis. We comprehensively discuss a stringent and recently proposed tail-sensitive normality test and provide a simple recipe to implement it. As an application, we analyze the deduced uncertainties and correlations of effective interactions in terms of Moshinsky–Skyrme parameters and effective field theory counterterms as derived from the bare NN potential containing one-pion-exchange and chiral two-pion-exchange interactions inferred from scattering data.

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of 16O+16O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.

Magicity of theCa52andCa54isotopes and tensor contribution within a mean-field approach

I investigate the magicity of the isotopes $^{52}\mathrm{Ca}$ and $^{54}\mathrm{Ca}$, which was recently confirmed by two experimental measurements, and relate it to like-particle and neutron-proton tensor effects within a mean-field description. By analyzing Ca isotopes, it is shown that the like-particle tensor contribution induces shell effects that render these nuclei more magic than would be predicted by neglecting it. In particular, such induced shell effects are stronger in the $^{52}\mathrm{Ca}$ nucleus, and the single-particle gaps are increased in both isotopes due to the tensor force. By studying $N=32$ and $N=34$ isotones, neutron-proton tensor effects may be isolated and their role analyzed. It is shown that neutron-proton tensor effects lead to increasing $N=32$ and $N=34$ gaps, when going along isotonic chains, from $^{58}\mathrm{Fe}$ to $^{52}\mathrm{Ca}$ and from $^{60}\mathrm{Fe}$ to $^{54}\mathrm{Ca}$, respectively. Mean-field calculations are perfomed by employing one Skyrme parameter set, which was introduced in a previous work by fitting the tensor parameters together with the spin-orbit strength. The signs and values of the tensor strengths are thus checked within this specific application. The obtained results indicate that the employed parameter set, even if generated with a partial adjustment of the parameters of the force, leads to the correct shell behavior and provides, in particular, a description of the magicity of $^{52}\mathrm{Ca}$ and $^{54}\mathrm{Ca}$ within a pure mean-field picture with the effective two-body Skyrme interaction.

Constraints on nucleon effective mass splitting with heavy ion collisions

A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the symmetry potential which leads to the effective mass splitting. However the sensitivity of effective mass splitting effect on the double n/p yield ratios decreases with increasing beam energy, even though high energy protons and neutrons are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100–200 MeV per nucleon.