Currently, the explosion mechanism of core-collapse supernovae is yet to be fully understood. New insight may come through observations of ⁴⁴Ti cosmic γ rays, enabling the mass cut point of the star to be found. However, a roadblock in this procedure comes from the uncertain ⁴⁵V(p,γ)⁴⁶Cr reaction that destroys ⁴⁴Ti. This thesis, therefore, unveils a better understanding of the ⁴⁵V(p,γ)⁴⁶Cr reaction by performing γ-ray spectroscopy of ⁴⁶Cr, to identify proton-unbound resonant states. The experiment was conducted at Argonne National Laboratory, using the ¹²C(³⁶Ar,2n)⁴⁶Cr fusion-evaporation reaction and GRETINA+FMA setup. Identified γ rays in ⁴⁶Cr include decays from nine previously unidentified states above the proton-emission threshold, corresponding to resonances in the ⁴⁵V+p system. This new information on the resonant states is applied to the calculation of the reaction rate, resulting in a rate uncertainty that is reduced by over 2 orders of magnitude compared to the previous estimation.

The deformation of nuclei located in the f_7/2 shell is driven by the mixing of the f_7/2 and p_3/2 levels. The analysis of data following Coulomb-excitation experiments has been invaluable in determining nuclear deformation, however the codes used are being adapted to enable alternative analysis of data. Therefore, present in this thesis is a study into the deformation of the lowest-lying states in ⁵⁰Cr and ⁵⁰Ti, examined using a modified GOSIA χ² minimisation wrapper for a first time simultaneous analysis of two beam species. Experimental data was collected at Argonne National Laboratory using the CHICO2+GRETINA setup. A ¹⁵⁰Nd cocktail beam, with contaminants of ⁵⁰Cr and ⁵⁰Ti, was impinged onto a ²⁰⁸Pb target up to the “safe” Coulomb-excitation limit. Since this is the first instance the modified minimiser has been employed, the performance was rigorously tested. Results emphasise the necessity to know the beam species ratio for future use of this analysis technique.