$^{72}$As is a promising positron emitter for diagnostic imaging that can be employed locally using a $^{72}$Se generator. However, current reaction pathways to $^{72}$Se have insufficient nuclear data for efficient production using regional 100-200 MeV high-intensity proton accelerators. In order to address this deficiency, stacked-target irradiations were performed at LBNL, LANL, and BNL to measure the production of the $^{72}$Se/$^{72}$As PET generator system via $^{75}$As(p,x) between 35 and 200 MeV. This work provides the most well-characterized excitation function for $^{75}$As(p,4n)$^{72}$Se starting from threshold. Additional focus was given to report the first measurements of $^{75}$As(p,x)$^{68}$Ge and bolster an already robust production capability for the highly valuable $^{68}$Ge/$^{68}$Ga PET generator. Thick target yield comparisons with prior established formation routes to both generators are made. In total, high-energy proton-induced cross sections are reported for 55 measured residual products from $^{75}$As, Cu, and Ti targets, where the latter two materials were present as monitor foils. These results were compared with literature data as well as the default theoretical calculations of the nuclear model codes TALYS, CoH, EMPIRE, and ALICE. Reaction modeling at these energies is typically unsatisfactory due to few prior published data and many interacting physics models. Therefore, a detailed assessment of the TALYS code was performed with simultaneous parameter adjustments applied according to a standardized procedure. Particular attention was paid to the formulation of the two-component exciton model in the transition between the compound and pre-equilibrium regions, with a linked investigation of level density models for nuclei off of stability and their impact on modeling predictive power.
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