The Energy Spectrum

The structure of the energy spectrum is determined by the magnitude of the three terms $\frac{K(K+1)}{2\mu r_\alpha^2}$, $U_\alpha(r_\alpha)$, and $\omega_\alpha\left(v+\frac{1}{2}\right)$. These differ strongly due to their dependence on the relative nuclei mass $\mu$. In terms of the small dimensionless parameter $m/\mu$ (where $m$ is the electron mass), we have

$$U_\alpha = O(1),$$ (1.32)

$$\omega_\alpha\left(v+\frac{1}{2}\right) = O(m/\mu)^{1/2} ,$$ (1.33)

$$\frac{K(K+1)}{2\mu r_\alpha^2} = O(m/\mu), .$$ (1.34)

In spectroscopic experiments, one determined energy differences $\delta E$ which therefore are broadly determined by

$$\delta E_{\rm el}\gg \delta E_{\rm vib} \gg \delta E_{\rm rot}.$$ (1.35)