Sur les règles de sélection en spectroscopie moléculaire de vibration et de rotation. (On selection rules in vibrational and rotational molecular spectroscopy). (French) Zbl 0606.58053

The aim of this work is a rigorous proof of the selection rules in molecular spectroscopy (vibration and rotation). To get this we give mathematically rigorous definitions of the (tensor) transition operators, in this case the electric dipole moment; this is done, firstly by considering the molecule as a set of point atomic kernels performing arbitrary motions, secondly by limiting ourselves either to infinitesimal vibration motions, or to arbitrary rotation motions. Then the selection rules follow from an abstract formulation of the Wigner-Eckart theorem. In a last paragraph we discuss the problem of separating vibration and rotation motions; very simple ideas from differential geometry, linked with the ”slice theorem”, allow us to define the relative speeds, the solid motions speeds, the Coriolis energies and the moving Eckart frames.


58J90 Applications of PDEs on manifolds
58J70 Invariance and symmetry properties for PDEs on manifolds
81V55 Molecular physics
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