Spin determination by in-plane angular correlation analysis in various coordinate systems

In the excitation of the resonant state followed by the sequential cluster-decay, the in-plane angular correlation method is usually employed to determine the spin of the mother nucleus. However, the correlation pattern exhibited in a two-dimensional angular-correlation spectrum depends on the selected coordinate system. In particular, the parity-symmetric and axial-symmetric processes should be presented in a way to enhance the correlation pattern, whereas the non-symmetric process should be plotted separately to reduce the background. In this study, three coordinate systems previously adopted for correlation patterns in the literature are described and compared to each other. The consistency among these systems is evaluated based on the experimental data analysis for the 10.29-MeV state in O-18. A spin-parity of 4(+) is obtained for all three coordinate systems.