Symmetries in the Intrinsic Nuclear Frames

Abstract

Structure of symmetrization group and its influence on symmetries in the intrinsic frame for collective nuclear models is analysed.

Electric Transitions in Hypothetical Tetrahedral/Octahedral Bands

“…in Ref. [4]). Since the intrinsic state (1) by construction is defined as the product of the three components transforming according to Γ 1 , Γ 2 and Γ 3 representations respectively, the symmetrization condition requires that Γ 1 ⊗ Γ 2 ⊗ Γ 3 ⊃ A 1 .…”

“…[4]. Above, u 0 and u 1 are the one-dimensional, zero-and one-phonon oscillator eigenfunctions, respectively, where η λ = B λ ω λ , λ = {2, 3} with the mass (inertia) parameter B λ and ω λ corresponding to the angular oscillator frequency.…”

“…in Ref. [4]. In this work, for simplicity of calculations and focusing on our strategical goal, we apply the idea of the adiabatic separation of vibrational and rotational motions.…”

“…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].…”

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.…”