Ion Optics for quasi-free $(p,p\alpha)$ reactions with Grand Raiden Spectrometer

Abstract

The quasi-free $(p,p\alpha)$ reaction is a powerful tool to probe preformed $\alpha$ clusters in nuclei, but it requires accurate reconstruction of both momentum and scattering angles at the reaction point. In this work, ion-optical analysis for $(p,p\alpha)$ measurements with the Grand Raiden spectrometer is presented. An under-focus optical setting was adopted to preserve sensitivity to the vertical scattering angle while maintaining high momentum resolution. The focal-plane geometry was determined independently as a purely geometrical reference. Momentum calibration was performed using elastic scattering of $^{206}$Pb$(p,p)$ at a fixed spectrometer angle. Scattering angles were reconstructed using ion-optical relations, and residual higher-order effects were corrected by a multidimensional fit. The dominant contributions to the reconstruction were found to arise from terms up to third order within the experimental acceptance. This ion-optical framework enables consistent event-by-event reconstruction of the reaction kinematics and provides a reliable basis for quasi-free $(p,p\alpha)$ analyses.