Evolution of shell gaps in the neutron-poor calcium region from invariant-mass spectroscopy of Sc37,38, Ca35, and K34

A fast secondary beam of ${}^{37}\mathrm{Ca}$ impinged on a ${}^9\mathrm{Be}$ target resulting in a set of reactions populating proton-rich nuclei including ${}^{35}\mathrm{Ca}$ and the first observations of ${}^{37,38}\mathrm{Sc}$ and ${}^{34}\mathrm{K}$. Invariant-mass spectroscopy, used to reconstruct proton decays for these nuclei, yielded three new ground-state masses and information on their low-lying structures. The newly measured mass excesses are: $\mathrm{\Delta }\mathrm{M}\left({}^{37}\mathrm{Sc}\right)=3500\left(410\right)\mathrm{keV}, \mathrm{\Delta }\mathrm{M}\left({}^{38}\mathrm{Sc}\right)=-4656\left(14\right)\mathrm{keV}$, and $\mathrm{\Delta }\mathrm{M}\left({}^{34}\mathrm{K}\right)=-1487\left(17\right)\mathrm{keV}$. These nuclei straddle the well-known $Z=20$ shell closure as well as the $N=16$ subshell closure. Trends in separation energies help elucidate how nuclear structure evolves showing a fading of the $Z=20$ shell gap for $N\le 18$ and indications of a $N=16$ subshell gap.