Intermediate-energy inverse-kinematics one-proton pickup reactions on neutron-deficient $fp$-shell nuclei

Background: Thick-target-induced nucleon-adding transfer reactions onto energetic rare-isotope beams are an emerging spectroscopic tool. Their sensitivity to single-particle structure complements one-nucleon removal reaction capabilities in the quest to reveal the evolution of nuclear shell structure in very exotic nuclei. Purpose: To add intermediate-energy, carbon-target-induced one-proton pickup reactions to the arsenal of $\gamma$-ray tagged direct reactions applicable in the regime of low beam intensities and to apply these for the first time to $fp$-shell nuclei. Methods: Inclusive and partial cross sections were measured for the $\nuc{12}{C}(\nuc{48}{Cr},\nuc{49}{Mn}+\gamma)$X and $\nuc{12}{C}(\nuc{50}{Fe},\nuc{51}{Co}+\gamma)$X proton pickup reactions at 56.7 and 61.2 MeV/nucleon, respectively, using coincident particle-$\gamma$ spectroscopy at the NSCL. The results are compared to reaction theory calculations using $fp$-shell-model nuclear structure input. For comparison with our previous work, the same reactions were measured on \nuc{9}{Be} targets. Results: The measured partial cross sections confirm the specific population pattern predicted by theory, with pickup into high-$\ell$ orbitals being strongly favored; driven by linear and angular momentum matching. Conclusion: Carbon target-induced pickup reactions are well-suited, in the regime of modest beam intensity, to study the evolution of nuclear structure, with specific sensitivities that are well described by theory.