Woods-Saxon Potential Research Articles

The giant dipole resonance (GDR) in odd-mass 181–195Pt nuclei

Abstract This manuscript theoretically examines the Giant Dipole Resonance (GDR) in odd-mass 181-195Pt nuclei with the Translational and Galileo Invariant Qusiparticle Phonon Nuclear Model (TGI-QPNM) for the first time. TGI-QPNM includes axially symmetric Woods-Saxon potential, isovector dipole-dipole interaction and restoration forces for spontaneously broken Galilean and Translation symmetries of the nuclear Hamiltonian. Therefore, TGI-QPNM makes eliminating the spurious contributions in the E1 spectrum possible. The obtained results show that the odd-mass 181-195Pt isotopes have a two-peak structure. In 181-187Pt isotopes, while the second peak is higher than the first, in 189-195Pt isotopes, it’s the opposite. The photo-absorption result for the 195Pt is in reasonably good agreement with the experimental data.

On the low-energy electromagnetic dipole modes in 151,153,155Sm Nuclei

The recently observed low-energy magnetic dipole (M1) and electric dipole (E1) excitations in deformed 151,153,155Sm are theoretically analysed. Rotational Invariant (RI-) and Translational-Galilean Invariant (TGI-) Quasiparticle Nuclear Model (QPNM) are used in the calculation of M1 and E1 properties, respectively. Both theories consider monopole pairing between nucleons, and the deformed Woods-Saxon potential is used as the mean-field potential. Pyatov's symmetry restoration procedure is applied in these models to eliminate the spurious modes from the intrinsic nuclear excitations. Model calculations show that although E1 transitions dominate the low-energy dipole spectra of 151,153,155Sm, many low-lying M1 transitions exist in these nuclei. It is shown that the most significant contribution to E1 and M1 excitation comes from ΔK=±1 transitions. The theory satisfactorily reproduces the gross features of low-lying dipole modes determined from the Oslo Method analysis of the experimental spectra.

Influence of polarization of hot nuclear matter on the anomaly of the surface diffuseness of inter-nuclear potential

Abstract The fusion excitation functions for 12 colliding systems with 
$96\leq Z_1Z_2 \leq 608$ are analyzed using the coupled-channels
(CC) calculations based on the M3Y double-folding (DF) potential
supplemented with a repulsive potential that takes into account the
incompressibility of the nuclear matter. We also applied the
polarization effects of hot nuclear matter (PEHNM) on the
calculations of the bare nucleus-nucleus interaction potential
within the framework of the modified density-dependent
Seyler-Blanchard (SB) approach in the $T^2$ approximation. Our
results reveal that we obtain a nice description of the experimental
data of different fusion systems when we use the present theoretical
approach to calculate the energy-dependent values of the fusion
cross sections. In this paper, the influence of the PEHNM on the
surface diffuseness parameter of the Woods-Saxon (WS) potential are
also studied. In order to reach this goal, we extract the
corresponding values of this parameter based on the modified form of
the DF potential (M3Y+Repulsion+polarization). We find that the
extracted values locate in a range between $a = 0.61$ and 0.80 fm at
different incident energies. It seems that the polarization effects
of hot nuclear matter play a key role in describing the abnormally
large values of the nuclear potential diffusenesses in the heavy-ion
fusion reactions. Additionally, the regular decreasing trend for the
diffuseness parameter of the nucleus-nucleus potential with the
increase in the bombarding energies is also observed.

The electric dipole characteristics of well-deformed 171,173Yb

The electric dipole response of well-deformed 171,173Yb in the giant dipole resonance (GDR) and pygmy dipole resonance (PDR) range has been theoretically analyzed using the translation and Galileo invariant quasiparticle phonon nuclear model (TGI-QPNM). The TGI-QPNM consists of an axially symmetric Woods-Saxon Potential, monopole pairing, dipole-dipole residual interaction, and the restoration terms for broken translation and Galilean symmetries. Numerical calculations show the existence of considerable E1 excitations around the neutron separation threshold (S n ) in both isotopes. The TGI-QPNM results of the photoabsorption cross-section give a double-humped shape in both nuclei, consistent with the available experimental data. The integrated moments (σ 0, σ −1) and the centroid energies in the GDR region are also reproduced well.

Complex partition function of 1-dimensional Dirac particle confined in Woods-Saxon interaction

We present the bound state solutions of one-dimensional Schrödinger and Dirac equations for a particle confined in Woods-Saxon potential. In each case the wavefunctions and the energy eigenvalues have been obtained in terms of the Jacobi polynomials by using the Nikiforov-Uvarov method. The complex eigenenergy obtained from the Dirac equation is explicitly shown to contain the nonrelativistic energies plus complex relativistic correction terms The quantum partition functions obtained using the relativistic and the nonrelativistic energies have been used to generate important thermodynamic properties of the system in the high temperature limit. In particular, the complex partition function obtained in the relativistic regime is taken to indicate some important physical effects in the system.

The Optical Model Absorption Term in the Frame of Fractional Derivatives

The complex optical model has been widely used to describe the elastic scattering of the nucleon–nucleus. The imaginary term of the optical potential takes into account the non-elastic scattering processes. This term was taken to be a Woods–Saxon form factor or its derivative to simulate the volume absorption or the absorption localized at the surface of the target, respectively. In this study, a fractional derivative of the Woods–Saxon potential with 0<α<1 was used, where α=0 and α=1 give the volume and the surface absorption form factor, respectively.

Observational analysis on warm tachyon scalar field inflation via Woods–Saxon, valley hybrid, exponential, quartic, quasi exponential potentials

In this paper, we study the tachyon scalar field inflationary scenario considering FRW universe in context of modified Chaplygin gas model. For this purpose, we consider some well-known potential models such as Woods–Saxon potential , Valley hybrid potential, exponential potential, quartic potential, and Quasi exponential potential. We develop the relations for the number of e-folds N, slow roll parameters ϵ,η, scalar spectral index ns, scalar to tensor ratio r, and running scalar spectral index αs. To understand how the inflationary parameters behave, the planes of ns−r and ns−αs are plotted. Through these plotted planes, we check the consistency of these inflationary parameters for assumed potentials in light of the Planck 2018 observational data and compare our outcomes with these observation by incorporating observational contours. We found that the obtained results are compatible and consistent with the recent observational data.

Investigation of two proton decay using modified wood saxon potential

Investigation of two proton decay using modified wood saxon potential

Uniform descriptions of pseudospin symmetries in bound and resonant states

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states.

Comparative study of alpha scattering from various nuclei at 130 MeV: Microscopic potentials and coupled channel calculations

The angular distributions of the elastic and inelastic scattering cross sections of alpha projectiles on different heavy ion target nuclei including 12C, 16O, 24Mg, 28Si and 40Ca at energy of 130 MeV have been studied using two different microscopic real potentials generated by the energy density functional (EDF) theory, and single folding cluster model as well as phenomenological Woods-Saxon potentials. A new parameterization was considered for the first time by EDF and to make the normalization coefficient tend to unity, it is necessary to consider correction to the calculated real potential. Coupled channel calculations for various low-lying states were performed, and the best fit values for the deformation length with the above models were extracted by fitting the inelastic scattering cross section and compared to previous work values. The total reaction cross section, as well as the real and imaginary volume integrals, have been studied.

Further investigation for the 18O + 40Ca, 76Se and 116Sn elastic scattering angular distributions

At 275MeV energy, the efficiency of analysing the newly measured angular distributions for 18O ions elastically scattered from 40Ca, 76Se and 116Sn targets is examined using double and cluster folding models. Two choices for the imaginary potential part, phenomenological squared Woods Saxon (WS) and (double or cluster) folded forms, were implemented in the calculations. Different 18O density distributions, including its cluster structure (14C + α), were put forward for preparing the folding potentials of the considered systems. Furthermore, we investigated the impact of other channels coupling using two distinct methods: incorporating a dynamic polarization surface potential into non-renormalized cluster folded potentials, and employing the continuum discrete coupled channels (CDCC) approach. To facilitate comparison, we also utilized the phenomenological optical model with real WS and imaginary squared WS potentials. The theoretical results demonstrated significant agreement with the experimental data, providing strong evidence for the efficacy of the methodologies under investigation.

Constraining the Woods-Saxon potential in fusion reactions based on the neural network

Constraining the Woods-Saxon potential in fusion reactions based on the neural network

State dependence of tunneling processes and thermonuclear fusion

We discuss the sensitivity of tunneling processes to the initial preparation of the quantum state. We compare the case of Gaussian wave packets of different positional variances using a generalized Woods-Saxon potential for which analytical expressions of the tunneling coefficients are available. Using realistic parameters for barrier potentials we find that the usual plane wave approximation underestimates fusion reactivities by an order of magnitude in a range of temperatures of practical relevance for controlled energy production.

Single Folding Potential Calculations in 141Pr

In this study, Skyrme and Gogny forces have been used to describe interactions for Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) calculations, considering all nucleons to evaluate nucleon densities. The nucleon densities of the 141Pr were calculated by using the Skyrme-HF (SHF) method with Woods-Saxon Potential (SHF-WS) and with Harmonic Oscillator Potential (SHF-HO), HFB method with Skyrme (HFB-S) and with Gogny (HFB-G) interactions. In these calculations, the effects of the three-body force have been accounted for in both Skyrme and Gogny forces through a density-dependent term necessary to describe various properties of nuclei and nuclear matter. The root-mean-square (rms) radii of proton, neutron, and charge densities of the nucleus were calculated using the density-dependent Skyrme-type effective nucleon-nucleon (NN) interaction in the HF approach. The Folding potential, developed to describe nucleon-nucleus (n-Pr) elastic scattering data, was obtained by single folding potential to calculate reaction cross-section calculations for 141Pr target. The calculated cross-sections, obtained using density data from four different models, were compared with each other and with experimental data from the literature for analysis and interpretation of the results.

Solitary Wave Effects of Woods-Saxon Potential in Schrödinger Equation with 3d Cubic Nonlinearity

Solitary Wave Effects of Woods-Saxon Potential in Schrödinger Equation with 3d Cubic Nonlinearity

Jost function formalism with complex potential

The Jost function formalism is extended with use of the complex potential in this paper. We derive the Jost function by taking into account the dual state which is defined by the complex conjugate the complex Hamiltonian. By using the unitarity of the S-matrix which is defined by the Jost function, the optical theorem with the complex potential is also derived. The role of the imaginary part of the complex potential for both the bound states and the scattering states is figured out. The numerical calculation is performed by using the complex Woods-Saxon potential, and some numerical results are demonstrated to confirmed the properties of extended Jost function formalism.

Fusion dynamics of 12C + 46,48,50Ti reactions

Fusion dynamics of 12C + 46,48,50Ti reactions are examined by considering EDWSP and coupled channel (CC) formalism. The coupled channel outputs point out that there are significant contributions of the vibrational states of the Ti-isotopes and without taking into account of these states one cannot explain the behavior of the fusion outcomes of given reactions. The EDWSP based outputs govern barrier modifications and subsequently decreases effective fusion barrier between the participants. Because of it, EDWSP based computations consistently retrieve the fusion data of studied systems. Aforementioned models decently explored fusion behavior of given systems, which clearly reflects that barrier changing effects are appeared due to energy dependency in Woods-Saxon potential are quite similar to that of dominant channel couplings in CC approach.

Neutron rearrangement of the magic number 90Zr-core determined by the matter density difference between 90Zr and 92Zr

Matter density distributions and root-mean-square matter radii for 90Zr and 92Zr were determined through fitting the small-angle differential cross sections of proton elastic scattering at 0.8 GeV with the Glauber model. With the obtained neutron densities, a neutron rearrangement beyond the expectation for the magic number 90Zr-core was found from 90Zr to 92Zr by adding two valence neutrons. By considering the surface-peaked term, the rearrangement was reproduced by the shell model calculations with the realistic Woods-Saxon potentials. It indicates that the surface-peaked term related to surface nucleon interactions plays an important role in describing the nucleon rearrangement, since the surface-peaked term would improve the description of the radial wave functions.

GaAs Quantum Dot Confined with a Woods–Saxon Potential: Role of Structural Parameters on Binding Energy and Optical Absorption

We present the first detailed study of optical absorption coefficients (OACs) in a GaAs quantum dot confined with a Woods–Saxon potential containing a hydrogenic impurity at its center. We use a finite difference method to solve the Schrödinger equation within the framework of the effective mass approximation. First, we compute energy levels and probability densities for different parameters governing the confining potential. We then calculate dipole matrix elements and energy differences, E1p−E1s, and discuss their role with respect to the OACs. Our findings demonstrate the important role of these parameters in tuning the OAC to enable blue or red shifts and alter its amplitude. Our simulations provide a guided path to fabricating new optoelectronic devices by adjusting the confining potential shape.

Estimation of the S34(0) S-factor for 3He(α, γ)7Be reaction by using distorted wave born approximation and artificial neural network

The astrophysical S-factor and total cross-section of radiative capture reaction are analyzed using the first-order distorted wave born approximation and artificial neural network. To make estimations of S34(0) at energies going to zero, we have used an artificial neural network model as a new approximation in this area. First, we obtain distorted wave born approximation results using the Gaussian and Woods-Saxon potentials. After, we evaluate artificial neural network approximation to analyze reaction observables of the system. Our results show that artificial neural network model is a powerful candidate as an extrapolation model for astrophysical energies for estimating of the S-factor observable.