Skyrme Potential Research Articles

Study of the Nuclear Structure Properties in Strontium (90,92,94Sr) Isotopes Using Nuclear Shell-model Calculations

In the current research, various nuclear properties energy spectrum, reduced electromagnetic transition probabilities, nuclear moments, and the distributions of both the nuclear charge and mass density as a function of radial distance from the nucleus center (r) were computed for90,92,94Sr isotopes' using the NuShellX@MSU code. The Skyrme (SLy4) potential was utilized to compute the zirconium isotopes' wave functions with mass numbers 90, 92, and 94. By employing the Gloeckner interaction and bare G-matrix, the computed results showed good agreement with the available experimental information on the aforementioned nuclear features of all the above isotopes. Additionally, the spins and parities of energy levels were confirmed and determined in accordance with certain empirical values. Furthermore an acceptable agreement for transition strengthsB(E2;2_1^+→0_1^+ ) for 90,92,94Sr , and the dipole magnetic moment of the ground state in the90Sr isotope, was observed with the available experimental values. In these calculations, new values were predicted for the above nuclear properties, which had not been previously determined experimentally. KEYWORDS: energy spectra; gloeckner interaction; model space; nuShellX code; skyrme potential; transition strengths

Bose-Einstein condensation in finite drops of α particles

Ground-state properties of finite drops of $\ensuremath{\alpha}$ particles (Q-balls) are studied within a field-theoretical approach in the mean-field approximation. The strong interaction of $\ensuremath{\alpha}$'s is described by the scalar field with a sextic Skyrme-like potential. The radial profiles of scalar and Coulomb fields are found by solving the coupled system of Klein-Gordon and Poisson equations. The formation of shell-like nuclei, with vanishing density around the center, is predicted at high enough attractive strength of Skyrme potential. The equilibrium values of energy and baryon number of Q-balls and Q-shells are calculated for different sets of interaction parameters. Empirical binding energies of $\ensuremath{\alpha}$-conjugate nuclei are reproduced only if the gradient term in the Lagrangian is strongly enhanced. It is demonstrated that this enhancement can be explained by a finite size of $\ensuremath{\alpha}$ particles.

Large-basis calculation of 6Li nucleus with Skyrme potential

Large-basis calculation of 6Li nucleus with Skyrme potential

Preformation probability of light charged particles emitted equatorially in ternary fission of Cf252

We investigate the preformation probability of the light particle that formed in the preliminary stage of the ternary fission process of the $^{252}\mathrm{Cf}$ nucleus. Considering the equatorial cluster tripartition kinematics, the relative yields of the ternary fission channels with $^{4,6}\mathrm{He}, ^{10}\mathrm{Be}$ and $^{14}\mathrm{C}$ as light third nucleus, are calculated. We use the Wentzel-Kramers-Brillouin approximation to calculate the penetrability of the different nuclei involved in the ternary fission process, based on microscopic Skyrme potentials. The obtained results indicate the optimum total excitation energy of the heavy nuclei produced in the $\ensuremath{\alpha}$ ternary fission channels to be within the range of 3--4 MeV. The estimated $\ensuremath{\alpha}$-preformation probability corresponding to this range is comparable with that estimated for the spontaneous $\ensuremath{\alpha}$ decays of the participating heavy nuclei. While the extracted preformation probability at excitation energy less than its indicated optimum values exhibits unphysical large values, the calculations based on the higher excitation energies indicate extremely small values. In the ternary fission process, the preformation probability of the emitted light particles heavier than the $\ensuremath{\alpha}$ particle exponentially decreases with increasing its mass number. A phenomenological expression is suggested based on the obtained results to estimate the preformation probability of an emitted cluster of a given mass number.

Asymmetric nuclear matter and realistic potentials

The equation of state for asymmetric nuclear matter is presented within the Brueckner–Hartree–Fock (BHF) approach by using recent high-quality soft nucleon–nucleon potentials from next-to-leading order (NLO) up to fifth order (N4LO) of the chiral expansion for the wide range of densities and asymmetry parameter, which are very interesting these days in the heavy-ion collisions and neutron stars. For comparison purposes, the same calculations are performed for Brueckner–Hartree–Fock approach plus two-body density-dependent Skyrme potential which is equivalent to three-body forces. Also the results are compared with the other theoretical models, especially the Brueckner–Hartree–Fock plus three-body forces and the Dirac–Brueckner–Hartree–Fock approaches. Our equation-of-state models are able to reproduce the empirical symmetry energy $$\hbox {E}_\mathrm{{sym}}$$ and its slope parameter L at the empirical saturation density $$\rho _{0}$$ and are compatible with experimental data from collisions between heavy nuclei. The symmetry energy of about 30 MeV is obtained at the saturation nuclear matter density. There is very good agreement between the experimental symmetry energy value and those calculated in the Brueckner–Hartree–Fock approach.

Neutron Star Matter and Baryonic Interactions

The properties of neutron-star matter up to the appearance of hyperons are calculated with the aid of Skyrme potentials. The conditions for the appearance of Λ hyperons in matter and values of the density at the point of their appearance are analyzed for various parametrizations of nucleon-nucleon and hyperon-nucleon interactions. The dependence of the results on the magnitude of density-dependent forces, the degree of nonlocality, the behavior of the symmetry energy, and incompressibility of nuclear matter is examined.

Large-scale shell model calculations of the <SUP align="right">25,26</SUP>Mg, <SUP align="right">27</SUP>Al and <SUP align="right">19</SUP>F nucleus

Shell model calculations were performed to study the energy levels for the 25,26Mg and 27Al nuclei by employing the sdpfnow effective interaction with the large-scale sdpf model space by using the shell model code [email protected] for Windows. The electron scattering form factors for 19F nucleus also have been studied with and without effective charge on the sdpf-model space and Tassie model. The Harmonic Oscillator and Skyrme potentials have been used to calculate the wave functions of radial single-particle matrix elements. The level schemes are compared with the experimental data. Coulomb and magnetic form factors in the present work include the transitions from ground state (1/2+ 1/2) to the (7/2+ 1/2), (9/2+ 1/2), (3/2− 1/2), and (11/2− 1/2) states in 19F. Good agreements were obtained for all nuclei under study for energy levels and form factors comparing with the available experimental data.

Inelastic electric and magnetic electron scattering form factors of 24Mg nucleus: Role of g factors

The electric and magnetic transitions in the [Formula: see text]Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective [Formula: see text] factors are made as adjustable parameters in order to describe the experimental data.

Nuclear spectroscopy of 40–48Ca isotopes

The nature of the excited states of the 40–48Ca isotopes is analyzed in the region of energies below the nucleon separation threshold. A peculiar feature of the 40–48Ca isotopes is the predominant filling of the 1f 7/2 neutron shell. Interaction between the neutrons of the 1f 7/2 shell and the nucleons of the 1d2s core results in formation of multiparticle excited states with a few vacancies in the 1d2s shell. The energies of single-particle proton states in the 40–48Ca isotopes are calculated using the Hartree-Fock potential with the Skyrme potential. The manner in which the energy of single-particle states varies, the magic numbers N = 20, 28 are formed, and the charge and nucleon density vary in the 40–48Ca isotopes as the neutron number increases from 20 to 28 is shown. Coherent interactions of the 1f 7/2 shell and 1d2s core nucleons also manifest themselves in the region above the nucleon separation threshold, leading to the configuration and isospin splitting of the GDR.

Mean-field analysis of ground-state and low-lying electric dipole strength inC22

Properties of neutron-rich $^{22}$C are studied using the mean-field approach with Skyrme energy density functionals. Its weak binding and large total reaction cross section, which are suggested by recent experiments, are simulated by modifying the central part of Skyrme potential. Calculating $E1$ strength distribution by using the random-phase approximation, we investigate developments of low-lying electric dipole ($E1$) strength and a contribution of core excitations of $^{20}$C. As the neutron Fermi level approaches the zero energy threshold ($\varepsilon_F >\sim -1$ MeV), we find that the low-lying $E1$ strength exceeds the energy-weighted cluster sum rule, which indicates an importance of the core excitations with the $1d_{5/2}$ orbit.

The properties of nuclear matter at zero and finite temperatures

The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T2-approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.

Vector BPS Skyrme model

We analyze the vector meson formulation of the Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model in ($3+1$) dimensions, where the term of sixth power in first derivatives characteristic for the original, integrable BPS Skyrme model (the topological or baryon current squared) is replaced by a coupling between the vector meson ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ and the baryon current. We find that the model remains integrable in the sense of generalized integrability and almost solvable (reducible to a set of two first-order ordinary differential equations) for any value of the baryon charge. Further, we analyze the appearance of topological solitons for two one-parameter families of one-vacuum potentials: the old Skyrme potentials and the so-called BPS potentials. Depending on the value of the parameters, we find several qualitatively different possibilities. In the massless case, we have a parameter region with no Skyrmions, a unique compact Skyrmion with a discontinuous first derivative at the boundary (equivalently, with a source term located at the boundary, which screens the topological charge), and Coulomb-like localized solitons. For the massive vector meson, besides the no-Skyrmion region and a unique $C$-compact soliton, we find exponentially as well as power-like localized Skyrmions. Further, we find (for a specific potential) BPS solutions, i.e., Skyrmions saturating a Bogomolny bound (both for the massless and massive vector mesons), which are unstable for higher values of the baryon charge. The properties of the model are finally compared with its baby version in ($2+1$) dimensions and with the original BPS Skyrme model, contributing to a better understanding of the latter.

Nuclear and Neutron Matter Properties Using BHF Approximation

Results of cold and hot symmetric nuclear matter and pure neutron matter calculations are presented. The Brueckner-Hartree-Fock (BHF) approximation + two body density dependent Skyrme potential which is equivalent to three body interaction are used. Various modern nucleon-nucleon (NN) potentials are used in the framework of BHF approxima- tion, e.g.: CD-Bonn potential, Nijm1 potential, Reid 93 potential and Argonne V18 potential. The bulk properties of asym- metric nuclear matter are computed such as the equation of state (EOS) at (T = 0), pressure at (T = 0, 5 and 10 MeV), single particle potential, free energy at (T = 5 and 10 MeV), nuclear matter incompressibility and the symmetry energy. Also the bulk properties of pure neutron matter are computed such as the EOS at (T = 0), pressure at (T = 0, 3 and 6 MeV), single particle potential, free energy at (T = 3 and 6MeV). Good agreement is obtained in comparison with previous theoretical estimates and experimental data.

Vector BPS baby Skyrme model

We investigate the relation between the BPS baby Skyrme model and its vector meson formulation, where the baby Skyrme term is replaced by a coupling between the topological current $B_\mu$ and the vector meson field $\omega_\mu$. The vector model still possesses infinitely many symmetries leading to infinitely many conserved currents which stand behind its solvability. It turns out that the similarities and differences of the two models depend strongly on the specific form of the potential. We find, for instance, that compactons (which exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of the vector counterpart. Specifically, for the vector model with the old baby Skyrme potential we find that it has compacton solutions only provided that a delta function source term effectively screening the topological charge is inserted at the compacton boundary. For the old baby Skyrme potential squared we find that the vector model supports exponentially localized solitons, like the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which is a nonlinear function of the topological charge and, as a consequence, higher solitons are unstable w.r.t. decay into smaller ones, which is at variance with the more conventional situation (a linear BPS bound and stable solitons) in the BPS baby Skyrme model.

Influence of incidence channel condition on isospin fractionation ratio based on the revised isospin-dependent quantum molecular dynamics

Isospin degree of freedom is introduced in Skyrme potential and momentum dependent interaction to obtain the revised isospin dependent quantum molecular dynamics. The isospin effect of isospin fractionation ratio is studied for different beam energies and different colliding systems based on the revised isospin dependent quantum molecular dynamics. It is found that the isospin effect of isospin fractionation ratios is important for different incident channel conditions，for example，the isospin fractionation ratios for different incident channel conditions are reduced after the isospin degree of freedom in Skyrme potential and momentum dependent interaction are included. However, the isospin fractionation ratio is also sensitive to symmetry potential. In this case it is also a good probe for extracting information on the symmetry potential in heavy ion collisions.

Asymmetric nuclear matter and Skyrme potential

The binding energy, symmetry energy, pressure, incompressibility, and the velocity of sound are calculated for asymmetric nuclear matter using Skyrme interaction SkO’. The behavior of these physical quantities is studied for different values of the asymmetry parameter α τ , the density ρ, and the temperature T. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions**Supported by National Natural Science Foundation of China (10435080, 10447006, 10575075), CAS Knowledge Innovation Project (KJCX2-SW-N02) and Major State Basic Research Development Program in China (G2000077400), the Scientific ResearchFunds for the Doctor,University of Shanghai for Science and Technology. the Science and Technological Fund of

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.

Tensor interaction contributions to single-particle energies

We calculate the contribution of the nucleon-nucleon tensor interaction to single-particle energies with finite-range G-matrix potentials and with zero-range Skyrme potentials. The Skx Skyrme parameters including the zero-range tensor terms with strengths calibrated to the finite-range results are refitted to nuclear properties. The fit allows the zero-range proton-neutron tensor interaction as calibrated to the finite-range potential results which gives the observed change in the single-particle gap {epsilon}(h{sub 11/2})-{epsilon}(g{sub 7/2}) going from {sup 114}Sn to {sup 132}Sn. However, the experimental l dependence of the spin-orbit splittings in {sup 132}Sn and {sup 208}Pb is not well described when the tensor is added, owing to a change in the radial dependence of the total spin-orbit potential. The gap shift and a good fit to the l dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the G matrix.

Incompressibility and single-particle potential for asymmetric nuclear matter with Skyrme potential

The incompressibility and the single-particle potential of asymmetric nuclear matter have been investigated in the framework of the Skyrme interaction. These parameters have been studied as functions of the nuclear density, the neutron excess parameter, and the temperature. The ratio of the isothermal incompressibility of hot nuclear matter to the incompressibility of cold nuclear matter for different values of neutron excess as a function of temperature is calculated. It is observed that this ratio decreases with temperature increasing apart from pure neutron matter when the growth of temperature leads to the growth of incompressibility. The symmetry incompressibility has been calculated as a function of density for different values of temperature.

Hopf solitons and Hopf Q-balls on S3

Field theories with a S2-valued unit vector field living on S3×ℝ space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on S3 with arbitrary values of the Hopf index. Using these results, we then find a set of hopfions with topological charge QH=m2, m∈Z, in the integrable subsector of the pure CP1 model. In addition, we show that the CP1 model with a potential term provides time-dependent solitons. In the case of the so-called “new baby Skyrme” potential we find, e.g., exact stationary hopfions, i.e., topological Q-balls. Our results further enable us to construct exact static and stationary Hopf solitons in the Faddeev–Niemi model with or without the new baby Skyrme potential. Generalizations for a large class of models are also discussed.