  Excited states in $^{20}$O were populated in the reaction
$^{10}$Be($^{14}$C,$\alpha$) at Florida State University. Charged particles
were detected with a particle telescope consisting of 4 annularly segmented Si
surface barrier detectors and $\gamma$ radiation was detected with the FSU
$\gamma$ detector array. Five new states were observed below 6 MeV from the
$\alpha$-$\gamma$ and $\alpha$-$\gamma$-$\gamma$ coincidence data. Shell model
calculations suggest that most of the newly observed states are core-excited
1p-1h excitations across the $N = Z = 8$ shell gap. Comparisons between
experimental data and calculations for the neutron-rich O and F isotopes imply
a steady reduction of the $p$-$sd$ shell gap as neutrons are added.
