Modified Woods-Saxon Potential Research Articles

Alpha Decay Half-Lives Calculation of Even-Even Nuclei in the62≤Z≤100Region using Woods-Saxon Potential

Alpha decay properties of even-even nuclei in the 62 ≤ Z ≤ 100 region are investigated within the Unified Fission Model based on a Modified Woods-Saxon potential. The computed alpha decay half-lives are compared to experimental data and are found to be in good agreement with it. The acquired pattern of the variation of alpha decay half-lives as a function of neutron number are explained by the nuclear shell effect. The experimental alpha decay energy Q is found to have an inverse relation with the alpha decay half-lives. This work has shown that the Unified Fission Model based on a Modified Woods-Saxon potential is sufficient to obtain the values of alpha decay half-lives.

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.

Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well

Abstract We discuss the influence of several factors on the deviations from energy spectrum of an infinite square quantum well (QW) for real microscopic systems that can be approximately modelled using particle in a box. We introduce the “blurring” potential in the form of the modified Woods-Saxon potential and solve the corresponding Schrodinger equation. It is found that the increase of the degree of blurring δ of the QW leads to the increase of number of the energy levels inside it and to increase of deviations from the quadratic dependence e (n) (e is the particle energy, n is the energy level number) typical for the infinite square QW, especially, for the energy levels close to the QW “tops”. It is most surprising that for relatively “large” values of δ the difference between the levels energies of such well and the appropriate (with the same n) levels energies of the square QW with the same depth changes sign (from positive to negative) as number n increases. We also conclude that the asymmetry of the QW and non-equality min≠mout (where min and mout are the particle effective mass inside and outside the QW) play a significant role for the relatively “shallow” well near the QW top.

Cluster decay investigation within a modified Woods–Saxon potential

The cluster decay process is studied in the WKB approximation based on the unified fission model. The cluster is considered to be emitted by tunneling through a potential barrier taken as the sum of the Coulomb potential, the centrifugal potential and the modified Woods–Saxon (MWS) nuclear potential. The results of our calculations are compared to those obtained by other theoretical models as well as experimental data. It is shown that the unified fission model with the MWS nuclear potential can be successfully used to evaluate the cluster decay half-lives of heavy nuclei.

The modified Woods-Saxon potential in the Duffin-Kemmer-Petiau equation

The scattering properties of the one-dimensional Duffin-Kemmer-Petiau (DKP) equation are studied for the modified Woods-Saxon potential. The scattering wave function, explicit formulas for the transmission and reflection coefficients are obtained in terms of hypergeometric function.

Single-Particle Levels of Spherical Nuclei in the Superheavy and Extremely Superheavy Mass Region

Single-particle levels of unknown superheavy and extremely superheavy nuclei are studied using a modified Woods–Saxon potential, which are smooth functions of the number of nucleons. This extrapolation gives that neutron shell closure remains for \(N=308\), and a proton shell has a gap at \(Z=164\), which is weaker than that of a neutron shell. Seven unknown doubly magic spherical nuclei beyond 208Pb are found: 256U164, 298Fl184, 310[126]184, 342Fl228, 366[138]228, 462[154]308, and 472[164]308. Of these, the 298Fl184 and 472[164]308 are beta-stable nuclei. The nucleus 472[164]308 seems to be the heaviest nuclei based on the analysis of neutron and proton drip lines and the fissility line.

Any l-state solutions of the Schrödinger equation for the Modified Woods–Saxon potential in arbitrary dimensions

Using the Pekeris approximation, approximate analytical solutions of the D-dimensional Schrödinger equation in the presence of Modified Woods–Saxon potential are obtained. The behavior of energy eigenvalues vs. dimension is discussed for various quantum numbers. Using the Feynman-Hellmann theorem, expectation values of some physical parameters are reported.

Analysis of fusion excitation functions of various systems using modified Woods–Saxon potential

Abstract We have analyzed the fusion excitation function data of various heavy ion systems in the near barrier energy region using the coupled channel code CCFULL and a new parameterization scheme for evaluating the depth of the Woods–Saxon nuclear potential. The potential model proposed here explains the fusion excitation function of the various heavy ion systems reasonably well. We have also discussed the role of projectile isotopic effects, target isotopic effects and the mass asymmetry in the entrance channel, by choosing the suitable projectile–target combinations, in the sub-barrier fusion enhancement.

Quasi-elastic scattering and fusion with a modified Woods-Saxon potential

The elastic and large-angle quasi-elastic scattering reactions were studied with the same nucleus-nucleus potential proposed for describing fusion reactions. The elastic scattering angle distributions of some reactions are reasonably well reproduced by the proposed Woods-Saxon potential with fixed parameters at energies much higher than the Coulomb barrier. With an empirical barrier distribution based on the modified Woods-Saxon potential and taking into account the influence of nucleon transfer, the calculated quasi-elastic scattering cross sections of a series of reactions are in good agreement with the experimental data.

Fusion-fission reactions with a modified Woods-Saxon potential

A modified Woods-Saxon potential model is proposed for a unified description of the entrance channel fusion barrier and the fission barrier of fusion-fission reactions based on the Skyrme energy-density functional approach. The fusion excitation functions of 120 reactions were systematically studied. The fusion (capture) cross sections are well described with the calculated potential and an empirical barrier distribution. Incorporating a statistical model (HIVAP code) for describing the decay of the compound nucleus, the evaporation residue (and fission) cross sections of 51 fusion-fission reactions have been systematically investigated. Optimal values of some key parameters of the HIVAP code are obtained based on the experimental data of these reactions. The experimental data are reasonably well reproduced by the calculated results. The upper and lower confidence limits of the systematic errors of the calculated results are given.

Modified Woods–Saxon Potential for Heavy-Ion Fusion Reaction

A modified Woods–Saxon (MWS) potential is proposed for describingnucleus-nucleus interaction based on the Skyrme energy-densityfunctional approach. Fusion barriers of a large number of fusionreactions from light to heavy systems can be systematically describedwell with this potential. The suitable incident energies for the fusionreactions leading to superheavy nuclei are also explored. It seems to us thatthe MWS potential can provide the suitable incidentenergies for fusion reactions for producingsuper-heavy nuclei.

Exact Polynomial Solution of $${\cal P}{\cal T}$/Non-${\cal P}{\cal T}$$- Symmetric and Non-Hermitian Modified Woods–Saxon Potential by the Nikiforov–Uvarov Method

Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the $${\cal P{\cal T}}$-/non-${\cal P}{\cal T}$$ -symmetric and non-Hermitian modified Woods–Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the $${\cal P}{\cal T}$$ -symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.

Comparisons of experimental and theoretical nucleus-nucleus potentials for heavy-ion reactions

A broad range of heavy-ion-induced fusion excitation functions are classically analyzed. The fusion-barrier parameters are compared with predictions of the proximity potential, a Yukawa-plus-exponential model, and a modified Woods-Saxon potential. The Yukawa-plus-exponential model is found to give the best overall agreement with the data. The proximity potential is too shallow, but would be in closer agreement with data if a necking contribution were added.

Inelastic electron scattering in the quark model and in the quark-diquark model

An extended version of an earlier model where the electroproduction processes were calculated using a modified Woods-Saxon potential in the quark model and in the quark-diquark model is presented in this paper. The dependence of the cross section on the quark mass is investigated and the ratio $R=\frac{{\ensuremath{\sigma}}_{L}}{{\ensuremath{\sigma}}_{T}}$ is calculated.

Use of a modified Woods-Saxon potential between a quark and a diquark

Use of a modified Woods-Saxon potential between a quark and a diquark