Narrow Results

A numerical method close to the Strutinsky procedure (but better) is proposed to calculate the deformation energy of nuclei. Quadrupole (triaxial) deformations are considered. Theoretical as well as practical aspects of the method are reviewed in this paper. A complete FORTRAN program illustrates the feasibility of the method. The numerical method employed in this paper avoids the main drawback of the Strutinsky method, that is to say the well known dependency of the results on the inherent two free parameters.

The shell and pairing correction energies are calculated for heavy and superheavy nuclei (SHN) by means of the Strutinsky's method. The single-particle (s.p.) energy levels are obtained from the diagonalization of the Woods–Saxon s.p. Hamiltonian in the deformed harmonic oscillator basis for both neutrons and protons. The residual pairing interaction is calculated by means of the usual Bardeen–Cooper–Schrieffer (BCS) approximation. A two-dimensional deformation space describing axially and reflection-symmetric shapes of nuclei has been used. Based on the shell and pairing correction energies, the signatures of the magic numbers appear at the spherical shell closures Z = 82, 114, 164 and N = 126, 184, 228 and 308. There are also signatures for some other shell closures at, e.g., Z = 108 and N = 162 which appear only when the deformation degrees of freedom is taken into account.

Based on the Woods-Saxon single-particle potential, we study the single-particle levels and the shell-corrections of super-heavy nuclei. Through comparing the results from the parameter set “universal” and “WS”, we find that the isospin dependence of symmetry potential κ had a great influence on the shell-corrections of super-heavy nuclei.

Based on a semi-empirical nuclear mass formula, the super-heavy stability island is investigated. From the calculated shell corrections of super-heavy nuclei, the region N = 172-178, Z = 116-120 with shell corrections about -6 MeV roughly gives the position of the super-heavy stability island. The probability to synthesize nuclei with Z = 126 may be much smaller than that of produced super-heavy nuclei already, according to the obtained shell corrections and the proton drip line.