# Constraining the Neutron Star Compactness: Extraction of the $^{23}$Al($p,\gamma$) Reaction Rate for the $rp$-Process

## TL;DR

This paper introduces a novel experimental technique combining advanced detectors to precisely measure the $^{23}$Al($p,$) reaction rate, crucial for understanding neutron star properties and X-ray burst energetics.

## Contribution

The study presents a new method for constraining the $^{23}$Al($p,$) reaction rate by combining GRETINA, LENDA, and the S800 spectrograph, resolving previous ambiguities.

## Key findings

- Disentangled a predicted doublet in $^{24}$Si states.
- First simultaneous extraction of spectroscopic factors with GRETINA and LENDA.
- Provided a more accurate reaction rate for astrophysical models.

## Abstract

The $^{23}$Al($p,\gamma$)$^{24}$Si reaction is among the most important reactions driving the energy generation in Type-I X-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. Here, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The $^{23}$Al($d,n$) reaction was used to populate the astrophysically important states in $^{24}$Si. This enables a measurement in complete kinematics for extracting all relevant inputs necessary to calculate the reaction rate. For the first time, a predicted close-lying doublet of a 2$_2^+$ and (4$_1^+$,0$_2^+$) state in $^{24}$Si was disentangled, finally resolving conflicting results from two previous measurements. Moreover, it was possible to extract spectroscopic factors using GRETINA and LENDA simultaneously. This new technique may be used to constrain other important reaction rates for various astrophysical scenarios.