Hartree-Bogoliubov calculations with spherical restriction

Abstract

The structure of the Hartree-Bogoliubov theory with spherical restrictions (SHB theory) is investigated. The SHB equations exhibit a strong instability if solutions are determined by iterations but this can be overcome by using the splitting of the SHB transformations according to Bloch and Messiah. Results of SHB calculations are presented for such nuclei where comparisons to deformed HB solutions are possible. It is shown that for light nuclei (18 < A < 40) the SHB solutions are energetically rather high (coexistence of spherical and deformed structures), whereas for ¹⁸O and the Ca isotopes the SHB solutions have about the same binding compared to the deformed ones, indicating that these nuclei can be treated equivalently as spherical or (weakly) deformed structures.