The Search for $\alpha$-Clustered Toroidal Nuclei in ${}^{28}$Si

Ground state stable nuclei typically have spherical geometries, however given excitation energy and/or angular momentum, they may exhibit exotic shapes and form $\alpha$-particle clusters within their bulk. It is predicted that such clustering can promote the production of angular-momentum stabilized toroidal nuclei. By studying the 7-$\alpha$ particle disassembly of ${}^{28}$Si + ${}^{12}$C at 35 MeV/nucleon, an experiment performed on the NIMROD detector array observed evidence of high excitation energy peaks in the same range as predicted toroidal high-spin isomer states [1]. However, the peaks were not well resolved due to the angular resolution of NIMROD. The FAUST detector array uses dual-axis duo-lateral (DADL) position sensitive silicon detectors capable of sub-1mm position resolution. The mechanism of charge splitting in the DADL detector gives position-dependent characteristics in the pulse shape that lead to distortions in position reconstruction. A new waveform analysis method has been developed that reliably extracts charge values, yielding improved linearity in position reconstruction and energy resolution. A precision measurement using FAUST can provide insight to the $\alpha$-clustered structure and exotic deformation of nuclei. [1]Phys. Rev. C 99, 014606 (2019)