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Background: The established GADGET detection system, designed for measuring weak, low-energy $\beta$-delayed proton decays, features a gaseous Proton Detector with MICROMEGAS readout for calorimetric particle detection, surrounded by a Segmented Germanium Array for high-resolution prompt $\gamma$-ray detection. Purpose: To upgrade GADGET's Proton Detector to operate as a compact Time Projection Chamber (TPC) for the detection, 3D imaging and identification of low-energy $\beta$-delayed single- and multi-particle emissions mainly of interest to astrophysical studies. Method: A new high granularity MM board with 1024 pads has been designed, fabricated, installed and tested. A high-density data acquisition system based on Generic Electronics for TPCs has been installed and optimized to record and process the gas avalanche signals collected on the readout pads. The TPC's performance has been tested using a $^{220}$Rn $\alpha$-particle source and cosmic-ray muons. In addition, decay events in the TPC have been simulated by adapting the ATTPCROOT data analysis framework. Further, a novel application of 2D convolutional neural networks for GADGET II event classification is introduced. Results: The GADGET II TPC is capable of detecting and identifying $\alpha$-particles, as well as measuring their track direction, range, and energy. It has also been demonstrated that the GADGET II TPC is capable of tracking cosmic-ray muons. In addition to being one of the first generation of micro pattern gaseous detectors to utilize a resistive anode applied to low-energy nuclear physics, the GADGET II TPC will also be the first TPC surrounded by a high-efficiency array of high-purity germanium $\gamma$-ray detectors. \textbf{Conclusions:} The TPC of GADGET II has been designed, fabricated, tested, and is ready for operation at the FRIB for radioactive beam-line experiments.

The $^{30}$P$(p,\gamma)^{31}$S reaction plays an important role in understanding nucleosynthesis of $A\geq 30$ nuclides in oxygen-neon novae. The Gaseous Detector with Germanium Tagging was used to measure $^{31}$Cl $\beta$-delayed proton decay through the key $J^{\pi}=3/2^{+}$, 260-keV resonance. The intensity $I^{260}_{\beta p} = 8.3^{+1.2}_{-0.9} \times 10^{-6}$ represents the weakest $\beta$-delayed, charged-particle emission ever measured below 400 keV, resulting in a proton branching ratio of $\Gamma_p / \Gamma = 2.5^{+0.4}_{-0.3} \times 10^{-4}$. By combining this measurement with shell-model calculations for $\Gamma_{\gamma}$ and past work on other resonances, the total $^{30}$P$(p,\gamma)^{31}$S rate has been determined with reduced uncertainty. The new rate has been used in hydrodynamic simulations to model the composition of nova ejecta, leading to a concrete prediction of $^{30}$Si/$^{28}$Si excesses in presolar nova grains and the calibration of nuclear thermometers., Comment: 7 pages, 2 figures, accepted to Physical Review Letters on April 4, 2022

Motivated primarily by the large uncertainties in the thermonuclear rate of the $^{30}$P$(p,\gamma)^{31}$S reaction that limit our understanding of classical novae, we carried out lifetime measurements of $^{31}$S excited states using the Doppler Shift Lifetimes (DSL) facility at the TRIUMF Isotope Separator and Accelerator (ISAC-II) facility. The $^{31}$S excited states were populated by the $^{3}$He$(^{32}$S$,\alpha)^{31}$S reaction. The deexcitation $\gamma$ rays were detected by a clover-type high-purity germanium detector in coincidence with the $\alpha$ particles detected by a silicon detector telescope. We have applied modern Markov chain Monte Carlo-based Bayesian methods to perform lineshape analyses of Doppler-shift attenuation method $\gamma$-ray data for the first time. We have determined the lifetimes of the two lowest-lying $^{31}$S excited states. First experimental upper limits on the lifetimes of four higher-lying states have been obtained. The experimental results were compared to shell-model calculations using five universal $sd$-shell Hamiltonians. Evidence for $\gamma$ rays originating from the astrophysically important $J^\pi=3/2^+$, 260-keV $^{30}$P$(p,\gamma)^{31}$S resonance has also been observed, although strong constraints on the lifetime will require better statistics.

$\beta$-decay spectroscopy provides valuable information on exotic nuclei and a stringent test for nuclear theories beyond the stability line. To search for new $\beta$-delayed protons and $\gamma$ rays of $^{25}$Si to investigate the properties of $^{25}$Al excited states. $^{25}$Si $\beta$ decays were measured by using the Gaseous Detector with Germanium Tagging system at the National Superconducting Cyclotron Laboratory. The protons and $\gamma$ rays emitted in the decay were detected simultaneously. A Monte Carlo method was used to model the Doppler broadening of $^{24}$Mg $\gamma$-ray lines caused by nuclear recoil from proton emission. Shell-model calculations using two newly developed universal \textit{sd}-shell Hamiltonians, USDC and USDI, were performed. The most precise $^{25}$Si half-life to date has been determined. A new proton branch at 724(4)~keV and new proton-$\gamma$-ray coincidences have been identified. Three $^{24}$Mg $\gamma$-ray lines and eight $^{25}$Al $\gamma$-ray lines are observed for the first time in $^{25}$Si decay. The first measurement of the $^{25}$Si $\beta$-delayed $\gamma$ ray intensities through the $^{25}$Al unbound states is reported. All the bound states of $^{25}$Al are observed to be populated in the $\beta$ decay of $^{25}$Si. Several inconsistencies between the previous measurements have been resolved, and new information on the $^{25}$Al level scheme is provided. An enhanced decay scheme has been constructed and compared to the mirror decay of $^{25}$Na and the shell-model calculations. The measured excitation energies, $\gamma$-ray and proton branchings, log~$ft$ values, and Gamow-Teller transition strengths for the states of $^{25}$Al populated in the $\beta$ decay of $^{25}$Si are in good agreement with the shell-model calculations, offering gratifyingly consistent insights into the fine nuclear structure of $^{25}$Al.

The radionuclide $^{22}$Na is a target of $\gamma$-ray astronomy searches, predicted to be produced during thermonuclear runaways driving classical novae. The $^{22}$Na(p,$\gamma$)$^{23}$Mg reaction is the main destruction channel of $^{22}$Na during a nova, hence, its rate is needed to accurately predict the $^{22}$Na yield. However, experimental determinations of the resonance strengths have led to inconsistent results. In this work, we report a measurement of the branching ratios of the $^{23}$Al $\beta$-delayed protons, as a probe of the key 204--keV (center-of-mass) $^{22}$Na(p,$\gamma$)$^{23}$Mg resonance strength. We report a factor of 5 lower branching ratio compared to the most recent literature value. The variation in $^{22}$Na yield due to nuclear data inconsistencies was assessed using a series of hydrodynamic nova outburst simulations and has increased to a factor of 3.8, corresponding to a factor of $\sim$2 uncertainty in the maximum detectability distance. This is the first reported scientific measurement using the Gaseous Detector with Germanium Tagging (GADGET) system.

The mass of $^{27}$P was predicted to impact the X-ray burst (XRB) model predictions of burst light curves and the composition of the burst ashes. To address the uncertainties and inconsistencies in the reported $^{27}$P masses in literature, a wealth of information has been extracted from the $\beta$-decay spectroscopy of the drip-line nucleus $^{27}$S. We determine the most precise mass excess of $^{27}$P to date to be $-659(9)$~keV, which is 63~keV (2.3$\sigma$) higher than the AME2016 recommended value of $-722(26)$~keV. The experimentally unknown mass excess of $^{27}$S was estimated to be 17030(400)~keV in AME2016, and we constrain this mass to be 17678(77)~keV based on the measured $\beta$-delayed two-proton energy. In the temperature region of $(0.06-0.3)$~GK, the $^{26}$Si$(p,\gamma)^{27}$P reaction rate determined in this work is significantly lower than the rate recommended in the reaction rate libraries, up to two orders of magnitude around 0.1~GK. The impact of these newly determined masses and well-constrained rate on the modeling of the explosive astrophysical scenarios has been explored by hydrodynamic nova and post-processing XRB models. No substantial change was found in the nova contribution to the synthesis of galactic $^{26}$Al or in the XRB energy generation rate, but we found that the calculated abundances of $^{26}$Al and $^{26}$Si at the last stage of XRB are increased by a factor of 2.4. We also conclude that $^{27}$S is not a significant waiting point in the rapid proton capture process.