Is the Dimension of Phase Space for a Rigid Diatomic Molecule Actually 12?

[tyogav]

Dimension of Phase Space of a rigid diatomic molecule is 10. Shouldn't it be 12?

 

[DrClaude]

There is no rotation possible along the internuclear axis. That removes one angle from the 3 Euler angles needed to describe the orientation of the molecule, and hence also removes an angular momentum component. That leaves 4 angular degrees of freedom, plus 3 coordinates and 3 momenta for the center of mass motion.