Electric Transitions in Hypothetical Tetrahedral/Octahedral Bands

Abstract

A collective approach combining zero-and one-phonon excitations in nuclear quadrupole and octupole modes together with the rotational motion up to spin J = 5 is used to verify the possibility of reproducing the experimental electric B(Eλ) probabilities in 156 Gd nucleus in presence of the high-rank tetrahedral/octahedral symmetries in collective quadrupole, octupole and rotational states.

Generalized projection operators for intrinsic rotation groups and nuclear collective models

“…where ′ ( ) R g kk is the rotation matrix corresponding to the laboratory group element g and ĝ is the corresponding rotation operator acting in the laboratory frame, . Performing the action (12) on the right-hand sides of equations (11) one obtains the coordinates of the rotated vector ′ ⃗ r :…”

“…Let us recall that the symmetrization group depends directly on the choice of the deformation space α λμ . Since only real parts of the complex spaces α λμ for λ = { } or the quadrupole-octupole motion discussed in [11,12], but is now its subgroup D4 . We want to strongly emphasize that, in general, one should clearly distinguish the intrinsic symmetry group, which is usually associated with the shape of the nuclear body, from the symmetrization group, whose sense has been recalled in section 2.…”

Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions

“…Previously this problem was solved only for a pair of coupled particles [11,12]. The developed approach will be also applicable to the microscopic study of tetrahedral-and octahedral-symmetric nuclei [13] that can be considered in the basis of seven-dimensional harmonic oscillator eigenfunctions [14]. The aim of this paper is to present a convenient formulation of the problem stated above and the calculation methods, algorithms, and programs for solving it.…”