Woods-Saxon Potential Research Articles

Three-body CsD2 calculation in Pd12 cage and E2 transition in ultra-low energy nuclear reaction

The three-body energy levels of the CsD2 quasi-molecule in a CsD2Pd12 cluster are calculated using the Cs-D, D-D, Cs-Pd and D-Pd repulsive Coulomb interactions with electronic effects, the central Woods-Saxon potential for the two-body nuclear interactions, and a nuclear three-body potential term. The calculation was performed for distances ranging from fermis to nanometers, in one pass, using 100-figure numerical precision, and for energies between the La ground state (-25.92 MeV) to the top of the Pd-barrier. The ion bases calculated results are adjusted to the electron bases chemical ones at the ground state and at the first excited state of CsD2Pd12. The possibility of Cs(2D, γ)La reaction is investigated for the E2 transition between J π = 7/2+ of CsD2 and 7/2+ of the La ground state.

Theoretical Study of Elastic Electron Scattering from 8B, 17Ne, 11Be and 11Li Halo Nuclei

The nuclear density distributions and size radii are calculated for one-proton 8B, two-proton 17Ne, one-neutron 11Be and two-neutron 11Li halo nuclei. The theoretical outlines of calculations assume that the nuclei understudy are composed of two parts: the stable core and the unstable halo. The core part is studied using the radial wave functions of harmonic-oscillator (HO) potentials, while the halo is studied through Woods-Saxon (WS) potential. The long tail behaviour which is the main characteristic of the halo nuclei are well generated in comparison with experimental data. The calculated size radii are in good agreement with experimental values. The elastic electron scattering form factors of the C0 component are also calculated for the aforementioned nuclei. The calculated form factor results give predictions for the results of future experiments on electron-radioactive ion beam colliders.

Breakup-Channel Dynamics on the Elastic Scattering Reactions for 8B+58Ni, 9Be+64Zn, and 12C+208Pb Systems

The dynamic effects of breakup Channel on for 8B+58Ni, 9Be+64Zn, and 12C+208Pb systems in elastic scattering reactions have been studied by calculating two quantities, which are the cross-section of the scattering and the distribution of the scattering barrier as functions of the angle of the center of the block and the energy of the center of the mass of some selected systems whose nuclei are Weakly Bound. The calculations are based on continuum discretized coupled-channel (CDCC) theory using code (CC) full quantum mechanics. The interpretation of the experimental findings was evaluated in the context of the optical model using the Woods-Saxon potential. both real and imaginary. In the context of the optical model of the real and imaginary parts, the interpretation of experimental results was analyzed using Woods-Saxon potential. The uncoupling and coupling channels (CC) have been calculated with the energy center Ec.m. to achieve the maximum consistency with experimental data for the systems being studied. The effect of breakup channel is giving a good description of results to be in agreement with experimental data.

Tensor force effect on pairing correlations for the Gamow–Teller transition in 42Ca, 46Ti, and 18O

Abstract We investigate the tensor force (TF) effect on the Gamow–Teller (GT) transition strength distributions in 42Ca, 46Ti, and 18O, which are known to have strong low-energy GT states, the so-called low-energy super GT (LeSGT) transition, peculiar to nuclei retaining a neutron number N = Z + 2. The TF is explicitly taken into account in the pairing channels of the residual interaction on top of the mean field described by a deformed Woods–Saxon potential. The pairing matrix elements (PMEs) comprising isoscalar and isovector parts, which consistently describe both the ground and the GT excited states, are calculated by a Brückner G-matrix based on the charge-dependent Bonn potential. By switching the TF on and off in the PMEs, we deduce meaningful correlations between the TF and the GT strength distributions. It is found that an attractive TF affects not only the ground state but also plays a crucial role in shifting the main GT peak to the low excitation-energy region leading to the LeSGT.

Coulomb breakup reaction of loosely bound F17 with dynamic polarization potentials

We investigate the elastic scattering, inelastic scattering, breakup reaction, and total fusion reactions of the $^{17}\mathrm{F}+^{208}\mathrm{Pb}$ system using an optical model approach by including the dynamical polarization potential. In particular, we focus on the breakup reaction channels, whose effects on other reactions have been argued to be small. By exploiting two different potentials composed of a surface-type Woods-Saxon potential, which were obtained by a fitting analysis, and a Love-type optical potential, the breakup reaction cross sections are explained with other elastic and quasielastic scattering cross sections. For the breakup reaction at ${E}_{\text{lab}}=170$ MeV in the forward angle region, where only exclusive reaction data are known, inclusive breakup reaction data are deduced from available theoretical and experimental $E1$ strength values. We discuss the breakup reaction effects on the other nuclear reactions related to the $^{17}\mathrm{F}$ projectile in detail.

Antiproton-nuclei cross sections with Woods-Saxon potential at low energies

The present knowledge of the antinucleons elastic scattering and annihilation processes in matter at low energies is limited to a few nuclei data in a small phase-space. Optical potential models are useful tools for modelling nuclear strong interaction of antinucleons with matter providing predictions at very low energies where data are missing. New calculations of elastic and annihilation cross sections for antiproton with nuclei using an optical potential of Woods-Saxon (WS) shape are presented. Preliminary predictions at low energies for carbon and calcium show clearly-measurable nuclear effects for nuclear elastic cross sections at large angles and momenta greater than 50 MeV/c. Some discrepancies in annihilation cross section comparing predictions and data are present using the same fitting parameters.

Exhaustive Theoretical Investigation of~Phonon Number Alteration, Fusion Cross Sections and Barrier Distributions for \({^{30}\mathrm {Si}}+{^{90,92,94,96}\mathrm {Zr}}\) Reactions via Energy-dependent Woods–Saxon Potential and Coupled Channel Models

Exhaustive Theoretical Investigation of~Phonon Number Alteration, Fusion Cross Sections and Barrier Distributions for \({^{30}\mathrm {Si}}+{^{90,92,94,96}\mathrm {Zr}}\) Reactions via Energy-dependent Woods–Saxon Potential and Coupled Channel Models

Investigation of alpha decay half-lives within a modified Woods–Saxon potential

The predictive accuracy of the unified fission model based on a modified Woods–Saxon potential (UFMWS) is assessed by systematically calculating the decay half-lives of alpha emitters from [Formula: see text] to [Formula: see text]. The computed results are compared with recent experimental data as well as with results obtained using different semi-empirical formulas. After confirming the performance of the UFMWS, we focus on the alpha decay of even-Z superheavy nuclei with [Formula: see text]. The comparison between the experimental and the theoretical alpha-decay energies extracted from four different mass tables as well as between the experimental half-lives and those calculated by UFMWS using the theoretical values have shown that the WS4 mass model is the most accurate in the region of superheavy nuclei. The alpha decay half-lives of the nuclei of interest have then been computed with the UFMWS by inputting the WS4 decay energies. The study of the neutron number variation of decay half-lives allowed to identify regions of increased stability and to predict neutron magic numbers.

BAZI TEK ÇEKİRDEKLİ GERMANYUM İZOTOBU İÇİN DEFORME VE KÜRESEL ÇEKİRDEKLERİN LOG(FT) DEĞERLERİ

The log(ft) values of the allowed 𝛽± decay between odd-A spherical and deformed nuclei are studied for germanium isotopes in this paper. The Pyatov Method (PM) and the Schematic Model (SM)) are used to the GT strength distributions, including the schematic residual spin-isospin interaction between nucleons in the particle-hole and particle-particle channels. Particle-hole and particle-particle interaction parameters are calculated respectively with X_ph^GT= 5.2 A^(0.7 ) MeV and X_pp^GT= 0.58 A^(0.7 ) MeV. Deformed Woods-Saxon potential is used in calculations of single-particle energies and wave functions. The results are also compared with previous experiment values wherever available.

Pseudospin symmetry in resonant states and its dependence on the shape of potential

The complex momentum representation method is used to explore the single particle resonances in nuclei. The energies, widths, and wavefunctions are obtained by solving the Dirac equation with a Woods-Saxon potential, in which the parameters are determined from the RMF calculations for 132Sn. The pseudospin symmetry is investigated for the resonant states in comparison with bound states. Approximate degeneracy is shown in the energies, widths, and wavefunctions between the pseudospin doublets including the resonant and bound states. The influence of the potential shape on the pseudospin symmetry is checked. The quality of pseudospin symmetry is shown to be dependent of the parameters, which is explained in terms of the change of potential with these parameters. The energy and width splittings between the pseudospin doublets are sensitive to the potential parameters, which is clarified by the change of the derivative of potential with r. Moreover, the pseudospin splitting in the wavefunctions and its dependence on potential shape are analyzed. The wave function splitting between the pseudospin doublets is quantitatively obtained in the momentum space for the resonant states because they are local and square integrable. Considering that a real nuclear field is similar to a Woods-Saxon potential, the change of the parameters in Woods-Saxon potential can reflect the change of nuclear field from stable nuclei to drop-line nuclei. Therefore, the present researches are helpful to understand the level structure of the weakly bound nuclei and their exotic properties.

First observation of high-K isomeric states in $$^{249}$$Md and $$^{251}$$Md

Decay spectroscopy of the odd-proton nuclei $^{249}$Md and $^{251}$Md has been performed. High-$K$ isomeric states were identified for the first time in these two nuclei through the measurement of their electromagnetic decay. An isomeric state with a half-life of $2.8(5)$ ms and an excitation energy $\geq 910$ keV was found in $^{249}$Md. In $^{251}$Md, an isomeric state with a half-life of $1.4(3)$ s and an excitation energy $\geq 844$ keV was found. Similarly to the neighbouring $^{255}$Lr, these two isomeric states are interpreted as 3 quasi-particle high-$K$ states and compared to new theoretical calculations. Excited nuclear configurations were calculated within two scenarios: via blocking nuclear states located in proximity to the Fermi surface or/and using the quasiparticle Bardeen-Cooper-Schrieffer method. Relevant states were selected on the basis of the microscopic-macroscopic model with a deformed Woods-Saxon potential. The most probable candidates for the configurations of $K$-isomeric states in Md nuclei are proposed.

Shell evolution in neutron-rich nuclei: the single particle perspective * *Supported by the National Natural Science Foundation of China (12075121, 11605089), and the Natural Science Foundation of Jiangsu Province (BK20190067, BK20150762)

The isospin dependence of spin-orbit (SO) splitting becomes increasingly important as N/Z increases in neutron-rich nuclei. Following the initial independent-particle strategy toward explaining the occurrence of magic numbers, we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term. It is found that new magic numbers N = 14 and N =16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling, whereas the traditional magic number, N = 20, may disappear. The magic number N = 28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting, corresponding to the strength of the SO coupling term. Meanwhile, the N = 50 and 82 shells may persist within the single particle scheme, although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei. Besides, an appreciable energy gap appears at N = 32 and 34 in neutron-rich Ca isotopes. All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model. The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrè chart.

Analysis of elastic and inelastic scattering of Ne20 on Ge76 at 306 MeV

Angular distributions of the differential cross section for $^{20}\mathrm{Ne}+^{76}\mathrm{Ge}$ elastic and inelastic scattering at energy 306 MeV are analyzed in the framework of the optical model. The analysis is performed using the coupled-channels mechanism by taking into account the effect of the low-lying states, ${0}^{+}$ and ${2}^{+}$ for the projectile $^{20}\mathrm{Ne}$ $({E}_{\mathrm{ex}.}=1.634 \mathrm{MeV})$, target $^{76}\mathrm{Ge}$ $({E}_{\mathrm{ex}.}=0.563 \mathrm{MeV})$ nuclei, and their mutual excitation $({2}^{+},{2}^{+})$. Results are obtained with the conventional phenomenological Woods-Saxon potential and three different semimicroscopic potentials using the double folding model. Two real cluster potential models are calculated based upon the cluster structure of $^{20}\mathrm{Ne}$ nucleus as 5\ensuremath{\alpha} and $\ensuremath{\alpha}+^{16}\mathrm{O}$. For the sake of comparison, the real of the density-energy-dependent CDM3Y6 potential is considered. The imaginary part for the three real potentials is treated in a standard Woods-Saxon form. The calculations show that the experimental data can be reproduced successfully with a scale factor close to 1. The coupled channels have a weak effect on the elastic scattering with significant differences in calculations of the volume integrals and the total reaction cross sections compared to the available previous study for this reaction. Other future studies are, therefore, required.

Study of Klein Gordon Equation with Minimum Length Effect for Woods-Saxon Potetial using Nikiforov-Uvarov Functional Analysis

The equation of Klein-Gordon for Woods-Saxon potential was discussed in the minimal length effect. We have found the completion of this equation using an approximation by suggesting a new wave function. The Klein-Gordon equation in minimal length formalism for the Woods-Sadon potential is reduced to the form of the Schrodinger-like equation. Then the equation was accomplished by Nikiforov-Uvarov Functional Analysis (NUFA) with Pekeris approximation. This method is applied to gain the radial eigensolutions with chosen exponential-type potential models. The method of NUFA is more compatible by eliminating vanishing the strict mathematical manipulations found in other methods. The energy calculation results showed that angular momentum, radial quantum number, minimal length parameter, and atomic mass influenced it. The higher the radial quantum number and angular momentum, the lower the energg. In contrast to the the minimal length, the energy will increase in value when the minimal length parameter is enlarged. An increase in atomic mass also causes energy to increase as the radial quantum number and angular momentum are held constant.

Determination of Energy Spectra By Using Proper Quantization Rule of Woods-Saxon Potential

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) is calculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimized potential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of the nuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution of energy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlab calculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the result with the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four light nuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of these nuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearson correlation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, we plot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a good agreement between the results of this work and experimental values.

Solving the Deformed Woods–Saxon Potential with $$\eta $$-Pseudo-hermetic Generator

Solving the Deformed Woods–Saxon Potential with $$\eta $$-Pseudo-hermetic Generator

Role of triaxiality in deformed halo nuclei

It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $\Omega$ quantum number is admixed in a single-particle wave function, where $\Omega$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deformation. In this way, the area of halo nuclei may be extended when triaxial deformation is considered. We demonstrate this idea using a deformed Woods-Saxon potential for nuclei with neutron number N=13 and 43.

β-decay of N = 126 isotones for the r-process nucleosynthesis

The β-decay properties of nuclei with neutron number N = 126 is investigated in this paper. Two different versions of the proton-neutron quasi particle random phase (pn-QRPA) model were employed to compute β-decay rates and half-lives for the N = 126 isotones. The first set of calculation solves the pn-QRPA equations using the schematic model (SM) approach. The Woods-Saxon potential was employed as a mean-field basis. A spherical shape assigned for each waiting point nuclei throughout all simulations. Both allowed Gamow-Teller (GT) and first-forbidden (FF) transitions were considered in the particle-hole (ph) channel. The second set uses the pn-QRPA model in deformed Nilsson basis to calculate β-decay rates for allowed GT and unique first-forbidden (U1F) transitions under terrestrial and stellar conditions. Our results are in agreement with shell model findings that first-forbidden transitions lead to a considerable decrement in the calculated half-lives of the isotones. Inclusion of the first-forbidden contribution led to a decent agreement of our computed terrestrial β-decay half-lives with measured ones, much better than the previous calculations. The possible implication of the waiting point nuclei on r-process nucleosynthesis is discussed briefly.

Cluster folding optical potential analysis for 6Li+28Si elastic scattering

Available experimental angular distribution data for 6Li+28Si elastic scattering in the energy range 16 – 318 MeV are re-analyzed phenomenologically on the basis of optical model using Woods-Saxon (WS) potentials for both real and imaginary parts, while the semi microscopic analysis was performed on the basis of cluster folding potential. Cluster folding potential was generated based on the appreciable cluster structure and breakup of 6Li into a deuteron orbiting a core of α-particle. Although several data sets in a wide range of energies are subjected to investigation, the theoretical calculations using the different concerned potentials are fairly reproduced the experimental data in the whole energy range. The extracted real and imaginary volume integrals and reaction cross sections values are compared to the previously reported ones and they found to be in a good agreement

An investigation of alpha-transfer reaction 28Si(20Ne,16O)32S

The alpha-transfer reaction 28Si(20Ne,16O)32S at 52.3 and 70 MeV is examined by using the double-folding (DF) based on the optical model. The real part is obtained for ten different density distributions of 20Ne projectile. For the imaginary part, the Woods-Saxon potential is used. The obtained results are compared with the experimental data of alpha-transfer reaction as well as the literature results. It is seen that the results are in good agreement with the data, and are better than the literature results.