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

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SUMMARY

The dimension of phase space for a rigid diatomic molecule is definitively 10, not 12. This conclusion arises because rotation along the internuclear axis is not possible, eliminating one of the three Euler angles required for orientation. Consequently, the system retains four angular degrees of freedom, in addition to three coordinates and three momenta associated with the center of mass motion.

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