Abstract
A radioactive beam of $^{24}\mathrm{Na}$ with $90%$ of its content in its ${1}^{+}$ isomeric state (${\mathrm{E}}_{ex}$ = 0.472 MeV, ${t}_{1/2}$ = 20.18 ms) has been developed and used to perform a measurement of the $^{24}\mathrm{Na}^{m}(d,\phantom{\rule{0.16em}{0ex}}p)^{25}\mathrm{Na}$ reaction at the John D. Fox Accelerator Laboratory at Florida State University. This reaction selectively populated $\ensuremath{\ell}$ = 0 transfers, allowing the study of low-spin states in $^{25}\mathrm{Na}$. Mirror symmetry arguments were then used to investigate the effects of the isomeric state of $^{24}\mathrm{Al}$ (${\mathrm{E}}_{ex}$ = 0.426 MeV, ${t}_{1/2}$ = 130 ms) on the astrophysical rate of the $^{24}\mathrm{Al}^{m}(p,\ensuremath{\gamma})^{25}\mathrm{Si}$ reaction. Experimental parameters were extracted to provide, for the first time, an experimental reaction rate for the destruction of $^{24}\mathrm{Al}$ via proton captures in its isomeric state relevant to $rp$-process nucleosynthesis.
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