$^{26}$Al,$^{30}$P(d,n) transfer reaction studies of key hydrogen burning resonances relevant for cosmic $\gamma$-ray emission and heavy element production in novae

$^{26}$Al(d,n)$^{27}$Si and $^{30}$P(d,n)$^{31}$S transfer reactions have been studied in inverse kinematics to study key astrophysical resonances in $^{27}$Si and $^{31}$S. These are relevant for abundance calculations of the cosmic $\gamma$-ray emitter $^{26}$Al, and for the abundances of heavy elements (e.g. silicon), highly dependent on the $^{30}$P(p,$\gamma$)$^{31}$S reaction, observed in novae ejecta. A primary beam of $^{36}$Ar (150 MeV/A) impinging on a Be target produced around 30 MeV/u beams of $^{26}$Al and $^{30}$P which bombarded a 10~mg~cm$^{-2}$-thick CD$_2$ target (CH$_2$ for background). The $^{27}$Si/$^{31}$S ions were analyzed by the S800 spectrometer and identified by energy loss and time-of-flight measurements. $\gamma$ rays from the decays of excited states in $^{27}$Si/$^{31}$S were detected in coincidence with the recoiling $^{27}$Si/$^{31}$S ions using GRETINA. By measuring the number of coincident events, and correcting for the angular distributions of the $\gamma$ rays, this provides an angle integrated measurement of the $(d,n)$ cross-sections, and a measure of the proton partial widths for the key astrophysical resonances in $^{27}$Si and $^{31}$S.