Hidden symmetries in the intrinsic frame

Symmetry properties of eigenproblems in intrinsic frames

“…This property can lead to more complicated forms of collective Hamiltonians, but on the other hand, it simplifies the structure of the collective space. An important feature of the Euler angles Ω defined by (10) and the quadrupole part (11) of the nuclear surface which parameterizes rotations of the nucleus as a whole is that the transformation of local rotation (10) to the intrinsic frame is determined by the same set of angles for all required multipolarities λ. This implies that we deal with a body-fixed frame.…”

“…The set of these operators forms an algebraic structure of the group G S ; in this case one obtains the octahedral point group O. We call the symmetry group of transformations (10) and (11) the symmetrization group because the space of physical states has to consist of states belonging to the scalar irreducible representation of this group. This is required to have one-to-one correspondence between states obtained in the intrinsic frame and the states constructed in the laboratory frame; see the following.…”

“…In a sense the first example concerning the collective space and this definition of the body-fixed frame coincide. More-general descriptions of intrinsic frames and interesting applications that make it possible to adapt the required intrinsic frame to a given physical situation can be found, e.g., in [9][10][11].…”

“…In this paper we follow a general definition of intrinsic frame which is based on the group theory formalism [10,13]. In this description the transformations among the laboratory and intrinsic variables are identified with some group operators parameterized by a set of appropriate parameters which, in turn, are considered part of the intrinsic coordinates.…”

Finite Element Method for Solving the Collective Nuclear Model with Tetrahedral Symmetry

“…The algorithms for construction the symmetrized basis was considered in [4,5] w.r.t. symmetrization group [6,7,8]. In paper [9] the BVP in 2D domain describing the above quadrupole vibration collective nuclear model of 156 Dy nucleus with tetrahedral symmetry [10] has been solved by a finite difference method (FDM) that was a part of the BVP in 6D domain.…”