Skyrme Interaction Research Articles

Bayesian inference of the dense matter equation of state built upon extended Skyrme interactions

Bayesian inference of the dense matter equation of state built upon extended Skyrme interactions

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.

Bayesian Survey of the Dense Matter Equation of State Built upon Skyrme Effective Interactions

The nonrelativistic model of nuclear matter (NM) with zero-range Skyrme interactions is employed within a Bayesian approach in order to study the behavior of the neutron star (NS) equation of state (EOS). A minimal number of constraints from nuclear physics and ab initio calculations of pure neutron matter (PNM) are imposed together with causality and a lower limit on the maximum mass of an NS to all our models. Our key result is that accounting for correlations among the values that the energy per neutron in PNM takes at various densities and that are typically disregarded efficiently constrains the behavior of the EOS at high densities. A series of global NS properties, e.g., maximum mass, central density of the maximum mass configuration, minimum NS mass that allows for direct URCA, and radii of intermediate and massive NSs, appear to be correlated with the value of effective neutron mass in PNM at 0.16 fm−3. Together with similar studies in the literature our work contributes to a better understanding of the NS EOS as well as its link with the properties of dense NM.

Tensor force impact on shell evolution in neutron-rich Si and Ni isotopes* *This study was supported by the Interdisciplinary Scientific and Educational School of Moscow University's "Fundamental and Applied Space Research." Sidorov S.V. expresses his gratitude for the support provided by the Foundation for the Development of Theoretical Physics and Mathematics "BASIS."

The influence of the tensor interaction of nucleons on the characteristics of neutron-rich silicon and nickel isotopes was studied in this work. Tensor forces are considered within the framework of the Hartree-Fock approach with the Skyrme interaction. The addition of a tensor component of interaction is shown to improve the description of the splittings between different single-particle states and decrease nucleon-nucleon pairing correlations in silicon and nickel nuclei. Special attention was directed toward the role of isovector tensor forces relevant to the interaction of like nucleons.

Coulomb and symmetry-energy effects on proton and neutron density-distributions in central heavy-ion collisions, across beam energies and system masses

In this contribution, we review our current and previous investigations of total, proton, and neutron particle number densities and the asymmetry of proton and neutron density distributions achievable in central heavy-ion collisions at beam energy below 800 MeV/nucleon. Furthermore, the effects of the Coulomb interaction and the dependence on a system size in three representative symmetric and asymmetric Ca, Sn and Pb systems are studied. The Boltzmann-Uhlenbeck-Uehling (pBUU) transport and Time-Dependent Hartree-Fock (TDHF) models, employing the SVbas, SkT3 and SVsym Skyrme interactions, are used in these simulations. We find that (i) the highest total densities predicted at Ebeam = 800 MeV/nucleon are on the order of ∼ 2.5ρ0 (ρ0 = 0.16 fm−3), (ii) the proton-neutron asymmetry for maximal densities, δ = (ρnmax−ρpmax)/(ρnmax+ρpmax) do not generally exceed the asymmetry in the initial state of the collision at all beam energies and tend to decrease during the reaction, and (iii) a significant portion of this asymmetry has its microscopic origin in Coulomb forces, masking the pure nuclear contribution. In addition, the evolution of normalized maximal proton, neutron, and total nucleon number density with increasing beam energy, the impact of correlations in the reaction, and the time evolution of the proton and neutron density distributions in the plane transverse to the beam direction are illustrated and discussed.

Isoscalar monopole response in the neutron-rich molybdenum isotopes using self-consistent QRPA

The isoscalar giant monopole resonance (ISGMR) of even molybdenum isotopes 92,94,96,98,100Mo has been studied within the Skyrme self-consistent Hartree - Fock - Bardeen, Cooper, and Schrieffer and quasi-particle random phase approximation. Ten sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM are used in the calculations. The calculated strength distributions, centroid energies Ecen, scaled energies Es and constrained energies Econ of ISGMR are compared with available experimental data. Due to the appropriate value of the nuclear matter incompressibility KNM, several types of Skyrme interactions were successful in describing the ISGMR strength distribution in the 92,94,96,98,100Mo isotopes. As a result, high correlations between Ecen and KNM were found.

HYPERNUCLEI AND NEUTRON STARS WITH CHARGE SYMMETRY BREAKING HYPERONIC POTENTIAL

In this paper, we propose a method of taking charge symmetry breaking (CSB) in hypernuclei and neutron stars into account within the framework of the Hartree-Fock approach with Skyrme interaction. The parameters of the contribution of Λ𝑁-Skyrme force leading to CSB are derived from the corresponding parameters of the hyperon-nucleon interaction in the meson exchange models. Based on the obtained parameters, the effect of charge symmetry breaking on the hyperon binding energy in carbon hypernuclei is analyzed. The effect of charge symmetry breaking on the characteristics of neutron stars, such as their maximum mass and radii, is considered for the first time.

Hot and highly magnetized neutron star matter properties with Skyrme interactions

Hot and highly magnetized neutron star matter properties with Skyrme interactions

Investigation of the relationship between mirror proton radii and neutron-skin thickness* *This study is partially Supported by the National Natural Science Foundation of China (11925502, 11935001, 11961141003, 11890714, 12147101), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030000) and the National Key R&D Program of China (2018YFA0404404)

Through systematic investigations using the axially deformed solutions of the Skyrme-Hartree-Fock-Bogoliubov equations with 132 sets of Skyrme interaction parameters, it is confirmed that the neutron-skin thickness () of a neutron-rich nucleus is proportional to the difference between the proton radii of mirror nuclei (). This indicates that may be deduced from . Compared with the results of the Skyrme-Hartree-Fock model, pairing effects are found to enhance the correlation for most mirror pairs, whereas deformation effects may weaken the correlation. Furthermore, the correlation between and is studied for isotones with and , which reveals a stronger linear correlation with increasing . This result demonstrates that it is possible to extract the neutron-skin thickness of an unstable nucleus from the proton radii difference of the mirror nuclei of its isotones.

Electroexcitation Form Factors and Deformation of 20,22Ne Isotopes Based on the Shell Model and Hartree-Fock plus BCS Calculations

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interaction was used to calculate the radial wave functions of the single-particle matrix elements, from which a one-body potential in Hartree-Fock theory with SLy4 parametrization can be generated. Furthermore, we have explored the interplays among neutron and proton density profiles in two dimensions, along with the deformations of 20,22Ne using Hartree-Fock plus BCS calculations.

Shell Model Investigation of Some p and sd-Shell Nuclei with Harmonic Oscillator and Skyrme Interactions

In this study, the longitudinal charge and form factors for the nuclei 9Be and 28Si lying in the p and sd shells are studied by employing the Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗). The C0 and C2 from factors calculated for the ground state 3/2-, the 5/2- (2.429 MeV) and 7/2- (6.380 MeV) for 9Be, while the ground state 0+ and 2+ (1.779 MeV) state for 28Si nucleus. Calculations of microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations are utilized to generate the effective charges necessary to account for the “core polarization effect”. The shell model calculations are utilized on the extended model space to include all 1s, 1p, 2s–1d, 2p‑1f orbits with truncation. Bohr-Mottelson collective model and Tassie model with properly estimated effective neutron and proton charges are taken into account to consider the effect of the core contribution. The estimated form factors were compared with the measured available data and they were in good agreement for most of the studied states. A conclusion can be drawn that truncation is very good choice to study the longitudinal form factors.
 
 The choice of Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗) is adequate for form estimation of longitudinal form factors.
 The estimation of the effective charges based on microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations is adequate.
 The truncation proves to be very successful to perform the study.

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.

Calculation of the electromagnetic moments and electroexcitation form factors for some boron isotopes using shell model with skyrme interaction

The magnetic dipole and electric quadrupole moments for some Boron isotopes were calculated using the shell model taking into account the effect of the two-body effective interactions and the single-particle potentials. These isotopes are; (8 5)B(2 +), (1 50)B(3 +), (1 51)B((3/2)−), ( 1 52)B(1 +) and (1 53)B((3/2)−). Also, the elastic and inelastic longitudinal and transverse electron scattering form factors are calculated for 10B and 11B, for which there are available experimental data. The one-body transition density matrix elements (OBDM) were calculated using the two-body effective interactions; PWT, PEWT, PKUO and CKIHE, which are carried out in the p-shell model space. Skyrme interaction was implemented to generate the single-particle matrix elements with Hartree-Fock approximation and compared with those of harmonic-oscillator and Wood-Saxon potentials. All the evaluated results were compared with available experimental data. The present work has led us to conclude that the shell model calculations with Skyrme type interaction give a good tool for nuclear structure studies. All signs for the experimental electromagnetic moments data are reproduced correctly. The longitudinal and transverse form factors for positive and negative parity states are fairly well reproduced when using a suitable model space.

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.

Effect of Incompressibility and Symmetry Energy Density on Charge Distribution and Radii of Closed-Shell Nuclei

In this work, the effect of incompressibility modulus KNM and symmetry energy density J on charge distribution and root-mean-square radii of neutron Rn and proton Rp has been investigated for light, medium and heavy closed-shell nuclei 40, 48Ca, 90Zr, 116Sn, 144Sm and 208Pb within the framework of self-consistent Hartree-Fock (HF) with 20 types of Skyrme interactions having wide range of nuclear properties such as incompressibility modulus KNM and symmetry energy density J. The nuclear charge densities have been obtained and compared with the experiment data to give us a picture about the internal structure of the investigated nuclei. Also, the sensitivity of proton and neutron root-mean-square radii to nuclear matter properties has been examined by determining and discussion the statistical Pearson linear correlation coefficient.

Spatial correlation of a particle-hole pair with a repulsive isovector interaction

We study the spatial correlation of a particle-hole pair in the isovector channel in $^{56}$Co and $^{40}$K nuclei. To this end, we employ the Hartree-Fock+Tamm-Dancoff approximation with the Skyrme interaction. We find a large concentration of the two-body density at positions where the neutron particle and the proton hole states locate on the opposite side to each other with respect to the core nucleus. This feature originates from a repulsive nature of the isovector residual interaction, which is in stark contrast to the dineutron correlation with an attractive pairing interaction between the valence neutrons discussed e.g., in $^{11}$Li and $^6$He. A possible experimental implication of the repulsive correlation is also discussed.

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126* *Supported by the National Natural Science Foundation of China (11575120, 11822504), and Science Specialty Program of Sichuan University (2020SCUNL210)

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β − decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.

Calculation of the Magnetic Dipole and Electric Quadrupole Moments of some Sodium Isotopes using Shell Model with Skyrme Interaction

In the present work, the magnetic dipole and electric quadrupole moments for some sodium isotopes have been calculated using the shell model, considering the effect of the two-body effective interactions and the single-particle potentials. These isotopes are; 21Na (3/2+), 23Na (3/2+), 25Na (5/2+), 26Na (3+), 27Na (5/2+), 28Na (1+) and, 29Na (3/2+). The one-body transition density matrix elements (OBDM) have been calculated using the (USDA, USDB, HBUMSD and W) two-body effective interactions carried out in the sd-shell model space. The sd shell model space consists of the active 2s1/2, 1d5/2, and1d1/2 valence orbits above the inert 16O nucleus core, which remains closed. Skyrme interaction was implemented to generate the single-particle matrix elements with Hartree-Fock approximation and compared with those of harmonic oscillator and Wood-Saxon potentials. From the outcome of our investigation, it is possible to conclude that the shell model calculations with Skyrme-type interaction give a reasonable description for most of the selected Na isotopes. No significant difference was noticed for the magnetic dipole moments and electric quadrupole moments with experimental data, where all signs for the experimental data are reproduced correctly.

Investigation of electrical and magnetical multipoles contributions to the total longitudinal and transverse form factors in some positive and negative 27Al states using different interactions

The shell model and Skyrme interaction calculations were used to study the nuclear structure of the 27Al nucleus. In particular, inelastic electron scattering form factors, energy levels, and transition probabilities for positive and some negative parity low energy states have been calculated. The sd shell model was used with SKX parameters for positive parity cases. The calculations were performed on sd space interactions and the best results were obtained from HBUMSD, HBUSD, CWH, PW, and W interactions. For negative parity cases, the zbm model space with SKXcsb parameters has been used with zwm interactions. The excitation energies and transitions probabilities to the ground state 5/2+ for positive parity states have been also calculated. The calculated form factors, energy level diagrams, and transition probabilities were compared with the available experimental data. It was confirmed that the Skyrme interaction is suitable with the shell model to study the nuclear structure.

Investigation Of Electrical And Magnatical Multiples Contributions To The Total Longitudinal And Transvers Firm Factors In Some Positive 25mg States Using Different Interactions

The nuclear structure of the 25Mg nucleus was studied using the shell model and Skyrme computations. For positive parity low (energy states, inelastic electron scattering form factors, energy levels, charge density distribution, and transition probabilities) have all been determined. The SKX parameters were used with the sd shell model. The best results were obtained from HBUMSD, HBUSD, CWH, PW, and W interactions, which were calculated on sd space interactions. For positive parity states, the excitation energies and transition probabilities to the ground state 5/2+ have also been determined. The experimental data was compared to the estimated form factors, energy level diagrams, and transition probabilities. The Skyrme interaction was shown to be compatible with a shell model is used to explore nuclear structure.