Tilted-axis wobbling in odd-mass nuclei

Abstract

A triaxial rotor Hamiltonian with a rigidly aligned high-$j$ quasiparticle is treated by a time-dependent variational principle, using angular momentum coherent states. The resulting classical energy function have three unique critical points in a space of generalized conjugate coordinates, which can minimize the energy for specific ordering of the inertial parameters and a fixed angular momentum state. Due to the symmetry of the problem, there are only two unique solutions, corresponding to wobbling motion around a principal axis and respectively a tilted-axis. The wobbling frequencies are obtained after a quantization procedure and then used to calculate $E2$ and $M1$ transition probabilities. The analytical results are employed in the study of the wobbling excitations of ${}^{135}$Pr nucleus, which is found to undergo a transition from low angular momentum transverse wobbling around a principal axis toward a tilted-axis wobbling at higher angular momentum.

12 pages, 7 figures, 3 tables

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Cited by in corpus (14)

• Experimental Evidence for Transverse Wobbling in ${}^{105}$Pd
• Behavior of the collective rotor in wobbling motion
• Two quasiparticle wobbling in the even-even nucleus 130Ba
• Semiclassical description of chiral geometry in triaxial nuclei
• Two-dimensional collective Hamiltonian for chiral and wobbling modes II: Electromagnetic transitions
• $g$-factor and static quadrupole moment of ${}^{135}$Pr, ${}^{105}$Pd, and ${}^{187}$Au in wobbling motion
• A new approach for the wobbling motion in the even-odd isotopes ${}^{161,163,165,167}$Lu
• Influence of moments of inertia on transverse wobbling mode in odd-mass nuclei
• Influence of triaxial deformation on wobbling motion in even-even nuclei
• Wobbling motion in ${}^{165,167}$Lu within a semi-classical framework
• A new boson approach for the wobbling motion in even-odd nuclei
• Towards a new semi-classical interpretation of the wobbling motion in ${}^{163}$Lu
• Harmonic chiral vibration in triaxial nuclei
• Parity Partner Bands in ${}^{163}$Lu: A novel approach for describing the negative parity states from a triaxial super-deformed band