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

Abstract

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 ${\ensuremath{\alpha}}_{3\ensuremath{\mu}=0,1,2,3}$. These shell gaps generate well-pronounced double potential-energy minima in the standard multipole $({\ensuremath{\alpha}}_{20},{\ensuremath{\alpha}}_{22},{\ensuremath{\alpha}}_{3\ensuremath{\mu}},{\ensuremath{\alpha}}_{40})$ representation, often at ${\ensuremath{\alpha}}_{20}=0$, which in turn generate exotic symmetries ${C}_{2v}$, ${D}_{2d}$, ${T}_{d}$, and ${D}_{3h}$, 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 $Z\ensuremath{\ge}82$ and $N\ensuremath{\ge}126$ in multidimensional deformation spaces to analyze the expected exotic symmetries and octupole shape instabilities in the mass table ``northeast'' of the doubly magic $^{208}\mathrm{Pb}$ nucleus. Whereas the proton-unperturbed properties of neutron-generated octupole shell effects are illustrated in detail for exotic ${}_{Z=82}{\mathrm{Pb}}_{N>126}$ 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, ${T}_{d}$, of which experimental evidence has recently been published, we present ${D}_{2d}$ symmetry resulting from a superposition of axially symmetric quadrupole and tetrahedral symmetries and two new point group symmetries, ${D}_{3h}$ and ${C}_{2v}$, associated with the octupole ${\ensuremath{\alpha}}_{33}$ and ${\ensuremath{\alpha}}_{31}$ 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.