# Spin determination from the in-plane angular correlation analysis for various coordinate systems

## TL;DR

This paper compares three coordinate systems for in-plane angular correlation analysis to determine nuclear spin, demonstrating their consistency through experimental data for $^{18}$O and confirming a 4$^+$ spin-parity.

## Contribution

The study systematically evaluates and compares three coordinate systems used in angular correlation analysis for nuclear spin determination.

## Key findings

- All three coordinate systems yielded consistent spin-parity results.
- The methods effectively distinguish symmetric and non-symmetric processes.
- The analysis confirms a 4$^+$ spin-parity for the 10.29-MeV state in $^{18}$O.

## Abstract

In a reaction to excite the resonant state followed by the sequential cluster-decay, the in-plane angular correlation method is usually applied 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. Particularly the parity-symmetric and the axial-symmetric processes should be presented in a way to enhance the correlation pattern whereas the non-symmetric process should be plotted elsewhere in order to reduce the correlation background. In this article, three possible coordinate systems, which were previously adopted in the literature, are described and compared to each other. The consistency of these systems is evaluated based on the real experimental data analysis for the 10.29-MeV state in $^{18}$O. A spin-parity of 4$^+$ is obtained for all three coordinate systems.