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States in the $N=35$ and 37 isotopes $^{55,57}$Ca have been populated bydirect proton-induced nucleon removal reactions from $^{56,58}$Sc and $^{56}$Cabeams at the RIBF. In addition, the $(p,2p)$ quasi-free single-proton removalreaction from $^{56}$Ca was studied. Excited states in $^{55}$K, $^{55}$Ca, and$^{57}$Ca were established for the first time via in-beam $\gamma$-rayspectroscopy. Results for the proton and neutron removal reactions from$^{56}$Ca to states in $^{55}$K and $^{55}$Ca for the level energies, excitedstate lifetimes, and exclusive cross sections agree well with state-of-the-arttheoretical calculations using different approaches. The observation of ashort-lived state in $^{57}$Ca suggests a transition in the calcium isotopicchain from single-particle dominated states at $N=35$ to collective excitationsat $N=37$.

A First Glimpse at the Shell Structure beyond $^{54}$Ca: Spectroscopy of $^{55}$K, $^{55}$Ca, and $^{57}$Ca