Detailed Angular Correlation Analysis with 4π Spectrometers: Spin Determinations and Multipolarity Mixing Measurements in ¹²⁸Ba

We analyze for the first time the full γγ directional correlations from oriented states (DCO) in an experiment performed with the GASP detector array. Our analysis based on a transformation of the directional information into expansion coefficients of an orthogonal basis. With this method, which we call SpeeDCO (spectral expansion of DCO), the complete DCO information is concentrated in 12 γγ coincidence spectra. The analysis is applicable to all detector arrays which uniformly cover the solid angle. We show that the complete DCO information can be used for a reliable and unique determination of spins and multipolarity mixing ratios in weakly populated bands. We were able to establish the spins and the positive parity of the Δ I=1 ''M1 band'' in ¹²⁸Ba and multipolarity mixing ratios of M1/E2 in-band transitions were derived as well. The measured values are in good agreement with those expected for a high-K rotational band.