Abstract
It is shown that the nuclear single-particle energy spectra obtained in the selfconsistent way obey similar particle number dependence as the spectrum of a pure 3D harmonic oscillator potential. This effect was used to improve the quality of evaluation of the shell correction energy in weakly bound nuclei. The magnitude of the traditional Strutinsky shell correction energy obtained by the smearing of the single-particle energy spectrum of light nuclei is compared with that obtained by the smoothing of the single-particle energy sums in the particle number space.
Highlights
IntroductionThe fifty years old macroscopic-microscopic model [1,2,3,4] in which one adds the shell and the pairing energy corrections to the macroscopic binding energy, evaluated e.g. using the liquid drop model, is still frequently used as an alternative to the time-consuming HFB calculations
The fifty years old macroscopic-microscopic model [1,2,3,4] in which one adds the shell and the pairing energy corrections to the macroscopic binding energy, evaluated e.g. using the liquid drop model, is still frequently used as an alternative to the time-consuming HFB calculations.The shell correction method developed in ref. [5] offers an effective tool to extract the shell and pairing effects from the microscopic energy obtained in a selfconsistent way or by using a mean-field single-particle Hamiltonian, e.g. of the Saxon-Woods or Yukawa-folded type
It was already shown in ref. [5] that the traditional Strutinsky method based on the smoothing energies of the single-particle level density and that alternative one which applies the Strutinsky smearing directly to the sum of the single-particle energies lead to different estimates of the shell correction energies of spherical nuclei while both estimates are close to each other when a nucleus is deformed
Summary
The fifty years old macroscopic-microscopic model [1,2,3,4] in which one adds the shell and the pairing energy corrections to the macroscopic binding energy, evaluated e.g. using the liquid drop model, is still frequently used as an alternative to the time-consuming HFB calculations. Contrary to the traditional Strutinsky method [2,3,4], the shell energy is evaluated in ref. A significant difference between the shell correction energy obtained with the traditional and the new method was found in particular for highly degenerated singleparticle spectra (i.e. in magic nuclei) while for deformed nuclei, where the degeneracy is lifted to a large extent, both estimates are close to each other, except the region of super or hyper-deformed shape isomers. In the present paper we compare the estimates of the shell energy obtained in both methods using the singleparticle spectra obtained within the selfconsistent HFB model with the Gogny D1S force
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