next up previous contents index
Next: Spin Up: Radial SE Previous: Harmonic Approximation   Contents   Index

The Energy Spectrum

The structure of the energy spectrum is determined by the magnitude of the three terms \bgroup\color{col1}$ \frac{K(K+1)}{2\mu r_\alpha^2}$\egroup, \bgroup\color{col1}$ U_\alpha(r_\alpha)$\egroup, and \bgroup\color{col1}$ \omega_\alpha\left(v+\frac{1}{2}\right)$\egroup. These differ strongly due to their dependence on the relative nuclei mass \bgroup\color{col1}$ \mu$\egroup. In terms of the small dimensionless parameter \bgroup\color{col1}$ m/\mu$\egroup (where \bgroup\color{col1}$ m$\egroup is the electron mass), we have
$\displaystyle U_\alpha$ $\displaystyle =$ $\displaystyle O(1),$   electronic part (1.32)
$\displaystyle \omega_\alpha\left(v+\frac{1}{2}\right)$ $\displaystyle =$ $\displaystyle O(m/\mu)^{1/2} ,$   vibrational part (1.33)
$\displaystyle \frac{K(K+1)}{2\mu r_\alpha^2}$ $\displaystyle =$ $\displaystyle O(m/\mu),$   rotational part$\displaystyle .$ (1.34)

In spectroscopic experiments, one determined energy differences \bgroup\color{col1}$ \delta E$\egroup which therefore are broadly determined by
$\displaystyle \delta E_{\rm el}\gg \delta E_{\rm vib} \gg \delta E_{\rm rot}.$     (1.35)


next up previous contents index
Next: Spin Up: Radial SE Previous: Harmonic Approximation   Contents   Index
Tobias Brandes 2005-04-26