Spacing of Nuclear Ground-State Levels in the Region $94<~N<~114$

New atomic-mass determinations are reported which establish the masses of ${}_{}{}^{174}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$ with significantly improved precision, and lead to new values for the double-neutron separation energies $S_{2n}$ of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$, and ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$. A plot of $S_{2n}$ in the region $94<~N<~114$ now shows systematic downward breaks at $N=98, 104, \mathrm{and} 108$. These features are interpreted in terms of energy gaps above the Nilsson single-particle levels ${\frac{9}{2}}^{+}\mathrm{}\left[624\right]\mathrm{}$ ($N=108\mathrm{}$), ${\frac{5}{2}}^{-}\mathrm{}\left[523\right]\mathrm{}$ ($N=98\mathrm{}$), and ${\mathrm{½}}^{-}$[512] ($N=104\mathrm{}$).