$\beta$-Delayed Proton Pandemonium: A first look at the $^{31}$Cl($\beta p \gamma$)$^{30}$P decay scheme

Positron decays of proton-rich nuclides exhibit large $Q$ values, producing complex cascades which often involve various radiations, including protons and $\gamma$ rays. Often, only one of the two are measured in a single experiment, limiting the accuracy and completeness of the decay scheme. An example is $^{31}$Cl, for which protons and $\gamma$ rays have been measured in detail individually but never with substantial sensitivity to proton-$\gamma$ coincidences. The purpose of this work is to provide detailed measurements of $^{31}$Cl $\beta$-delayed proton decay including $\beta$-$p$-$\gamma$ sequences, extract spectroscopic information on $^{31}$S excited states as well as their $\beta$ feeding, and compare to shell-model calculations. A fast, fragmented beam of $^{31}$Cl provided was deposited in the Gaseous Detector with Germanium Tagging (GADGET) system. GADGET's gas-filled Proton Detector was used to detect $\beta$-delayed protons, and the Segmented Germanium Array (SeGA) was used to detect $\beta$-delayed $\gamma$ rays. Up to 20 previously unobserved $\beta$-delayed proton transitions have been discovered, most of which populate excited states of $^{30}$P. Here present the first detailed $^{31}$Cl($\beta p \gamma$)$^{30}$P decay scheme and find improved agreement with theoretical calculations of the Gamow-Teller strength distribution for $^{31}$S excitation energies $7.5 < E_x < 9.5$ MeV. The present work demonstrates that the capability to detect $\beta$-delayed protons and $\gamma$ rays in coincidence is essential to construct accurate positron decay schemes for comparison to theoretical nuclear structure calculations. In some respects, this phenomenon for $\beta$-delayed protons resembles the pandemonium effect originally introduced for $\beta$-delayed $\gamma$ rays.