= Solution
Write $s=v+1/2$ and complete the square in the <Morse oscillator> <energy>:
$$
E(s)=hc\widetilde\omega(s-x_es^2)
=\frac{hc\widetilde\omega}{4x_e}
-hc\widetilde\omega x_e\left(s-\frac1{2x_e}\right)^2.
$$
The finite bound-level sequence approaches the dissociation limit at the vertex of this extrapolated parabola. Thus the <bond potential-well depth> is
$$
\boxed{D_e=\frac{hc\widetilde\omega}{4x_e}.}
$$
The continuous vertex is a convenient way to identify the limit; it is not an additional normalizable bound level at the threshold.
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