Measuring the $^{134}\mathrm{Te}(d,p\gamma)^{135}\mathrm{Te}$ Reaction with GODDESS to Probe the Single-Particle Structure of $^{135}\mathrm{Te}$*

The single-particle energy spectra of nuclei near shell closures provide important inputs for the nuclear shell model. $^{135}$Te ($Z=52$, $N=83$) is of particular interest due to its proximity to the $Z=50$ and $N=82$ closed shells. Additionally, neutron capture on $^{134}$Te has been identified as a key reaction in attempts to explain an overabundance of $^{134,136}$Xe observed in some pre-solar grains. The $^{134}$Te$(n,\gamma)^{135}$Te direct capture cross section can be constrained via the measurement of excitation energies, spin-parities, and spectroscopic factors of single-neutron states in $^{135}$Te using neutron transfer reactions such as $(d,p)$. The $^{135}$Te level scheme is highly fragmented, with many closely-spaced levels that are difficult to separate by charged particle measurement alone. However, enhanced resolution can be achieved by coincident measurement of gamma rays emitted by excited $^{135}$Te states. The $^{134}$Te$(d,p\gamma)^{135}$Te reaction was accordingly measured with GODDESS (GRETINA-ORRUBA: Dual Detectors for Experimental Structure Studies) at ATLAS with a 9 MeV/u $^{134}$Te beam provided by CARIBU with 60\% purity and an approximate intensity of 1200 pps incident upon a CD$_2$ target. Preliminary results will be presented.