Exotic shape symmetries around the fourfold octupole magic number N=136: Formulation of experimental identification criteria

We employ a realistic nuclear mean-field theory using the phenomenological, Woods-Saxon Hamiltonian with newly adjusted parameters containing no parametric correlations; originally present correlations are removed employing the Monte Carlo approach. We find very large neutron shell gaps at N=136 for all the four octupole deformations α3μ=0,1,2,3. These shell gaps generate well-pronounced double potential-energy minima in the standard multipole (α20,α22,α3μ,α40) representation, often at α20=0, which in turn generate exotic symmetries C2v, D2d, Td, and D3h, discussed in detail. The main goal of the article is to formulate spectroscopic criteria for experimental identification. Calculations employing macroscopic-microscopic method are performed for nuclei with Z≥82 and N≥126 in multidimensional deformation spaces to analyze the expected exotic symmetries and octupole shape instabilities in the mass table "northeast"of the doubly magic Pb208 nucleus. Whereas the proton-unperturbed properties of neutron-generated octupole shell effects are illustrated in detail for exotic Z=82PbN>126 nuclei, our discussion is extended into even-even Z>82 nuclei approaching the less exotic Z/N ratios, to encourage experiments which could identify the predicted exotic symmetries. In addition to the tetrahedral point group symmetry, Td, of which experimental evidence has recently been published, we present D2d symmetry resulting from a superposition of axially symmetric quadrupole and tetrahedral symmetries and two new point group symmetries, D3h and C2v, associated with the octupole α33 and α31 energy minima, respectively. The multidimensional n>2 deformation spaces are treated as usual by projecting the total potential energies onto the n=2 subspace. Using the representation theory of point groups we formulate quantum mechanical criteria for experimental identification of exotic symmetries through analysis of the specific properties of the collective rotational bands generated by the symmetries. The resulting band structures happen to be markedly distinct from the structure of the bands generated by ellipsoidal symmetry quantum rotors; those various rotational properties are discussed in detail.