  Inelastic neutron scattering for Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ near
optimal doping ($x \approx 0.155$, $T_{c} = 25 \mathrm{K}$) reveals that the
dynamic magnetic susceptibility at the antiferromagnetic zone center exhibits
two characteristic energies in the superconducting state: $\omega_1 \approx 6.4
\mathrm{meV}$ and $\omega_2 \approx 4.5 \mathrm{meV}$. These two magnetic
energies agree $quantitatively$ with the $B_{1g}$ / $B_{2g}$ and $A_{1g}$
features previously observed in electronic Raman scattering, where the former
is believed to indicate the maximum electronic gap and the origin of the
smaller $A_{1g}$ feature has remained unexplained. The susceptibility change
upon cooling into the superconducting state is inconsistent with previous
claims of the existence of a magnetic resonance mode near 10 meV, but
consistent with a resonance at $\omega_2$.
