Triaxial shapes of heavy deformed nuclei and a quantum many-body derivation of rotational energy

Takaharu Otsuka (University of Tokyo, Japan)

The shapes of the ground states of well-deformed nuclei are, as stressed by Aage Bohr, axially-symmetric prolate ellipsoids in the traditional view. We, however, show that triaxial shapes prevail in those nuclei, reproducing experimental data, as confirmed by state-of-the-art Configuration Interaction calculations. Two origins are suggested for the triaxial shapes: binding-energy gain by the symmetry restoration, and another gain by tensor force and hexadecupole part of central force. The first origin produces basic modest triaxiality for virtually all deformed nuclei, including ¹⁵⁴Sm, a typical showcase of axial symmetry in the past.  The second origin produces more prominent triaxiality for some nuclei, like ¹⁶⁶Er.  The prominent triaxiality is discussed from various viewpoints for some nuclei, and experimental findings, for instance, those by multiple Coulomb excitations in the past, are re-evaluated to be supportive.  Many-body structures of gamma and double-gamma bands are clarified.  Regarding the general features of rotational states of deformed many-body systems including triaxial ones, the well-known J(J+1)-K² rule of rotational excitation energies is derived, within the quantum mechanical many-body theory, without resorting to the quantization of the kinetic energy of a rotating classical rigid body. Two long-standing open problems, (i) occurrence and origins of triaxiality and (ii) quantum many-body derivation of rotational energy, are thus resolved. Possible relations to the Nambu-Goldstone mode are mentioned. Relativistic Heavy-Ion Collision is mentioned as a feasible experimental approach to the triaxiality of the 0⁺ ground state. Davydov’s claim of prevailing triaxiality is discussed. Substantial impacts on superheavy nuclei and fission are mentioned.