The nuclear structure of $^{32}$P

The $^{32}$P nucleus was populated through two separate experiments at the FSU Fox Laboratory using $^{26}$Mg($^{11}$B, $\alpha n$) and $^{18}$O($^{16}$O,$p n$) reactions both at E$_{lab}$ = 30 MeV. Subsequent $\gamma$ decays were observed with 3 or 4 Clover spectrometers. $\gamma$-$\gamma$ coincidences were sorted into symmetric matrices and analyzed by projections. From the preliminary analysis using both data sets, several gamma ray transitions from the previous work as proposed by Chakrabarti \textit{et. al}\footnote{R. Chakrabarti \textit{et al.}, PRC \textbf{84}, 054325 (2011).} can be confirmed, however some of gamma ray transitions proposed to populate the yrast J$^{\pi}$=5$^{-}$ state cannot be confirmed, as will be discussed. Furthermore, the observed states were then compared with the FSU \textit{psdpf} shell model calculations\footnote{R. S. Lubna \textit{et al.}, PRR \textbf{2}, 043342 (2020).}. The two highest level states from the previous work which were also observed in the present work agree relatively well with the FSU 2ph configurations suggesting that cross-shell excitation might have a role not only in describing the negative parity states for the nuclei in the \textit{sd} shell, but also in describing the high spin positive parity states.