The Tetrahedral–octahedral Bases for the Generalized Rotor

Abstract

The rotational basis for irreducible representations of the point groups T d , O and O h for nuclear angular momenta J = 0, 1 . . . , 5 is constructed.

Generalized projection operators for intrinsic rotation groups and nuclear collective models

“…Notice that the rotation matrix in ( 13) is identical as in the overall rotation rule for the coordinates of a Cartesian vector ⃗ A (see, e.g., [6]). As can also be seen, in equation ( 13) the matrix R is transposed with respect to the corresponding rotation matrix entering equation (10), used to transform a function of Cartesian variables.…”

“…of equation ( 6) depending on the Euler angles Ω and for angular momenta limited to the values = { } J 0, 1, 2, 3, 4, 5 . Each Γ R JM 3 solution belongs to an allowed Γ 3 irreducible representation of the symmetrization group (compare with rotational basis constructed in [10] for the octahedral symmetrization group). Acting with the generalized projection operator (8) on linear combinations of the Wigner functions…”

Electric Transitions in Hypothetical Tetrahedral/Octahedral Bands

“…The details of the procedures leading to such states and the way of constructing the rotational states R Γ 3 JM (Ω) are presented in Refs. [1,4,5].…”