  This experimental study of high-spin structure near N = Z = 20 nuclei was
focused on $^{41}$K, but will also mention three newly observed $\gamma$
transitions in $^{41}$Ca observed in the same reaction. High-spin states were
populated using the $^{26}$Mg($^{18}$O, $p2n\gamma$)$^{41}$K and
$^{26}$Mg($^{18}$O, $3n\gamma$)$^{41}$Ca reactions. The experiment was carried
out at an incident beam energy of 50 MeV at the Florida State University (FSU)
John D. Fox Superconducting Linear Accelerator Laboratory and used the FSU
high-purity germanium detector array. The $^{41}$K level scheme was extended to
12325 keV, possibly with J$^{\pi}$ = 25/2$^-$ or 27/2$^+$, by means of 25 new
transitions and that of $^{41}$Ca to 9916 keV. Linear polarization and a
measure of angular distribution results are also reported and used to provide
information on the spins and parities of several states in the $^{41}$K decay
scheme. The results have been compared to the $spsdpf$ cross-shell FSU shell
model interaction calculations. The theoretical results from configurations
involving no or one additional nucleon promoted from the $sd$ to the $fp$ shell
agree relatively well with the energies of known states, while those that
involve multi-particle excitations paint an interesting and complex picture of
interplay between single-particle excitations, collective pairing, and
deformation. This presents an interesting challenge for future theory.
