Formally, the mixing ratio can be regarded as the relative strength of the E2 component vs. the M1 component of the electroamgnetic transitions.
In other words, the mixing ratio will show the magnitude and character of the transition:
Thus, this dimensionless quantity shows that if
For the context of wobbling motion, the mixing ratio will tell:
- how much of the wobbling angular momentum is perpendicular to the rotational axis (E2 component).
- how much is along the main rotation axis (M1 component)
- Theory predicts a large E2 component in the ΔI = 1 inter-band transitions.
- The sign of δ reflects the phase relationship between M1 and E2 amplitudes.
- E2 transitions are strongest when the nucleus undergoes collective oscillation of the rotational axis — which is linked to motion perpendicular to the main angular-momentum axis.
- M1 transitions tend to reflect magnetic contributions from the odd particle, which often aligns (partially) with the main axis.
- Large |δ| → E2-dominated transition → strong collective contribution
- Small |δ| → M1-dominated transition → strong single-particle contribution
- Magnitude of δ has physical meaning (relative strength of E2 vs M1).
- Sign of δ does not indicate a unique physical property of the nucleus — it depends on phase conventions in the definition of the matrix elements.
The key points illustrated here are based on a GPT5.1 chat that is available here.
- Wobbling Motion in Nuclei
- Transverse wobbling: A collective mode in odd- A triaxial nuclei
- Guidelines for Nuclear Structure Evaluators - Read "Sign Conventions for Mixing Ratios from Angular Correlations and Angular Distributions in Electromagnetic Transitions"
- Linear polarization–direction correlations in γ -ray scattering experiments
- Timar et al Experimental Evidence for Transverse Wobbling in 105Pd
- E2/M1 mixing ratios in transitions from the gamma vibrational bands to the ground state rotational bands