It is known that an increased nuclear binging is caused by the
presence of large energy gaps in the single-particle (s.p.) nuclear
spectra. The large gaps result in a decreased average density of
s.p. levels and influence binding energies through the so-called
shell effects. These effects can be further enhanced by high
degeneracies of the s.p. levels above and/or below the energy gaps,
which results in even larger fluctuations of the average level
densities. Such degeneracies, in turn, are consequences of the
conservation of certain symmetries in the s.p. Hamiltonian. Ordinary
doubly-magic nuclei, for example, are spherically symmetric, i.e. characterized by degenarcies corresponding to the rotational group
, and indeed the most strongly bound. Apart from the group of
rotations, there exist only two other relevant symmetry groups whose
conservation leads to s.p. degeneracies higher than the two-fold
Kramers degeneracy. One of them is the point group,
, of the
regular tetrahedron, which yields two-fold and four-fold degenerate
s.p. levels. On this basis, Li and Dudek[1] suggested in
1994 that stable nuclear shapes characterized by the tetrahedral
symmetry may exist in Nature. Expected experimental signatures thereof, like shape isomers or specific rotational bands, are discussed in Refs. [2,3,4,5].
The lowest-rank multipole deformation which does not violate the
symmetry is
[3]. It represents a shape
of a regular tetrahedron with "rounded edges and corners", and is
usually called tetrahedral deformation. By using the deformed
Woods-Saxon potential, several authors[1,2,3]
examined the s.p. energies in function of
, and found
that, indeed, large energy gaps, sometimes larger than the spherical
ones, open up at neutron/proton numbers of N/Z=16, 20, 32, 40, 56-58,
70, 90-94, 100, 112, 126 or 136. They are sometimes referred to as
tetrahedral magic numbers. In the vicinity of the tetrahedrally
doubly-magic nuclei defined in this way, Strutinsky shell-correction
calculations were performed[1,2,4], and
energy minima corresponding to the tetrahedral deformation were found
in even-even
Zr,
Zr,
Yb,
Rn, and
Fm. Similarly, the Hartree-Fock+BCS (HF+BCS) calculations
[6], found tetrahedral solutions in
Zr,
and Hartree-Fock-Bogolyubov (HFB) tetrahedral solutions in
Zr and
Zr were reported in Refs.[7] and [4], respectively.
The present paper reports on the first systematic study of the tetrahedral deformation in various regions of the nuclear chart, carried out by means of self-consistent methods. We focus our study on properties of the tetrahedral minima, mainly their energies and deformations, and analyze their dependence on the Skyrme force parameterizations.