3 Body Nuclear Kinematic Modeling

When observing the reactions induced by a $^{10}$Be beam incident on a helium gas target using the Prototype Active-Target Time-Projection Chamber (PAT-TPC), three-body decays were observed, consisting of two $\alpha$ particles and a $^{6}$He nucleus. This three-body decay provides insight into $\alpha$ clustering of light atomic nuclei and increases understanding of astrophysical nuclear synthesis. The experiment consisted of a $\sim38$MeV $^{10}$Be beam targeted on the PAT-TPC containing a 90:10 He:CO$_2$ gas, backed by a Micromegas gaseous amplifier. Detector efficiency will be normalized via a Monte Carlo simulation. Such a simulation requires a robust code base including kinematic modelling of the the 3-body reaction which computes all allowable decay tracks given user-defined input settings. Analysis is ongoing and preliminary results will be presented.