Experimental search for toroidal high-spin isomers in collisions of $^{28}\mathrm{Si}+^{12}\mathrm{C}$ at 35 MeV/nucleon with the Forward Array Using Silicon Technology

Experimental search for toroidal high-spin isomers in collisions of ${}^{28}{Si} + {}^{12}C$ at 35 MeV/nucleon with the Forward Array Using Silicon Technology

A. Hannaman, B. Harvey, A. B. McIntosh, K. Hagel, A. Abbott, A. Fentress, J. Gauthier, T. Hankins, Y.-W. Lui, L. McCann, L. A. McIntosh, S. Regener, R. Rider, S. Schultz, M. Q. Sorensen, J. Tobar, Z. N. Tobin, and S. J. Yennello

Phys. Rev. C 109, 054615 – Published 16 May 2024

Abstract

Ground state stable nuclei typically have near-spherical geometries but may exhibit exotic shapes and form $α$ -particle clusters within their bulk if given excitation energy and/or angular momentum. It is predicted that such clustering can promote the production of angular-momentum stabilized toroidal nuclei. Previous experiment and theory suggest that such states may be evidenced by narrow resonances at high excitation energy in peripheral intermediate energy heavy-ion collisions. There has been recent focus on potential evidence for toroidal states in the $α$ -particle disassembly of ${}^{28}{Si}$ in collisions of ${}^{28}{Si} + {}^{12}C$ at 35 MeV/nucleon; however, prior evidence is limited by the angular resolution and statistical uncertainties that exist in the measurement. The present work aims to measure the excitation energy distribution for these disassembly events with improved angular resolution and reduced statistical uncertainty using the Forward Array Using Silicon Technology (FAUST). FAUST is equipped with resistive dual-axis duolateral (DADL) position-sensitive silicon detectors capable of submillimeter position resolution. The performance and response of the array was previously characterized in detail to accurately predict the expected resolution of measuring narrow resonances. The measured excitation energy distributions for 7- and 8- $α$ disassembly events showed no strong evidence for highly excited states at the cross section and widths suggested by previous experiment. Further investigation of collision properties that lead to these exit channels revealed challenges in isolating clean projectile-mass decays, where many 7- $α$ events do not originate from a single ${}^{28}{Si}$ source. A statistical likelihood analysis was performed to determine the sensitivity of the present measurement for confidently determining resonant yield, providing an upper limit to toroidal high-spin isomer cross section as a function of the excitation energy and width of potential states.