We propose to use the semi-classical Wigner-Kirkwood (h) over bar expansion to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in (h) over bar. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a rms deviation of 630 keV.

Approximate analytical solutions of the Dirac equation with the trigonometric Pöschl-Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The case of nonrelativistic limit is studied too.

A comparative study of the S-matrix and the WKB methods for the calculation of the half widths of alpha decay of super heavy elements is presented. The extent of the reliability of the WKB methods is demonstrated through simple illustrative examples. Detailed calculations have been carried out using the microscopic alpha-daughter potentials generated in the framework of the double-folding model using densities obtained in the relativistic mean field theories. We consider alpha-nucleus systems appearing in the decay chains of super heavy parent elements having A = 277, Z = 112 and A = 269, Z = 110. For negative and small positive log T-1/2 values the results from both methods are similar even though the S-matrix results should be considered to be more accurate. However, when log inverted perpendicular(1/2) values are large and positive, the width associated with such state is infinitesimally small and hence calculation of such width by the S-matrix pole search method becomes a numerically difficult problem. We find that overall, the WKB method is reliable for the calculation of half lives of alpha decay from heavy nuclei.

The global mass dependence of the nuclear symmetry energy a(sym)(A) and its two basic ingredients due to the mean-level spacing epsilon(A) and effective strength of the isovector mean-potential K(A) is studied within the Skyrme-Hartree-Fock model. In particular, our study determines the ratio of the surface-to-volume contributions to a(sym)(A) to be r(S/V) similar to 1.6 and reveals that after removing momentum-dependent effects by rescaling epsilon and kappa with isoscalar and isovector effective masses, respectively, one obtains epsilon(star) approximate to kappa(star).

A direct fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants to the f(5/2) - f(7/2) SO splittings in Ca-40, Ni-56, and Ca-48 requires (i) a significant reduction of the standard isoscalar spin-orbit strength and (ii) strong attractive tensor coupling constants. The aim of this paper is to address the consequences of these strong attractive tensor and weak spin-orbit fields on total binding energies, two-neutron separation energies and nuclear deformability.

A systematic study of the terminating states in A similar to 50 mass region using the self-consistent Skyrme-Hartree-Fock model is presented. The objective is to use the intrinsic simplicity of the terminating states to constrain certain parameters of the local nuclear energy functional. In particular, the work focuses on the spin fields and the spin-orbit term and constrain the appropriate Landau parameters and the strength of the spin-orbit potential.