= Solution
Write the upper <Morse oscillator> term values in <wavenumber> units as
$$
G(v)=\widetilde\omega_e(v+\tfrac12)-a(v+\tfrac12)^2,\qquad a=\widetilde\omega_ex_e.
$$
The spacing is $G(v+1)-G(v)=\widetilde\omega_e-2a(v+1)$. A <Birge-Sponer plot> therefore falls linearly in this model and can be extrapolated to zero spacing. If its horizontal coordinate is $x=v+1/2$, the plotted line is $y=(\widetilde\omega_e-a)-2ax$. Its area from $x=0$ to its zero gives
$$
\boxed{\widetilde D_0=\frac{(\widetilde\omega_e-a)^2}{4a}.}
$$
Equivalently a plot against $v+1$ has intercept $\widetilde\omega_e$ and triangle area $\widetilde D_e=\widetilde\omega_e^2/(4a)$; subtracting $G(0)=\widetilde\omega_e/2-a/4$ recovers $\widetilde D_0$. These conventions distinguish dissociation from the potential minimum and from the lowest vibrational level.
Measured consecutive members fix a local slope and intercept, so unobserved members can be supplied by extrapolation under an explicit spacing law. The upper-state limit on the <absorption> scale is $\widetilde\nu_{\rm lim}=\widetilde\nu_{00}+\widetilde D_0$. A local high-v fit can likewise estimate the remaining energy above an observed member without knowing its absolute v index. Near dissociation a real potential need not remain Morse-like, so an extrapolated triangle has model uncertainty; missing lines must not be silently assumed consecutive.
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