Kramers’ degeneracy

Kramers degeneracy theorem states that the energy levels of systems with an odd number of electrons remain at least doubly degenerate in the presence of purely electric fields (i.e. no magnetic fields). This is a consequence of the time-reversal invariance of electric fields, and follows from an application of the antiunitary T-operator to the wavefunction of an odd number of electrons [51]. 

Here the subscript 5 stands for symplectic , a Greek word which hterally means entangled . If the system has half-integer spin and all antiunitary symmetries are broken, Kramers degeneracy is lifted and we return to the case Py. 

The JT effect is based on the following theorem If a non-linear molecule (or polyatomic ion) has a degenerate electronic level (apart from Kramers degeneracy) it is unstable with respect to displacements of the atoms. 

Equation (36) agrees with previous results, which have been derived in a more heuristic manner [30-32], The adiabatic electronic potential-energy surfaces (that is, the eigenvalues of H — TVU) are doubly degenerate (Kramers degeneracy). The adiabatic electronic wave functions carry nontrivial geometric phases which depend on the radius of the loop of integration [29-32]. 

The adiabatic potentials (58) are doubly degenerate, as it must be for a spin 1/2 system (Kramers degeneracy). For small displacements from Q = 0, (58) simplifies to... 

The 4f — 5d transitions in the case of Ce3+ and Tb3+ fall within the limit of standard spectrophotometers. The strong ultraviolet bands belonging to the terms of Ce + may split by crystal field into maximum five levels Kramers degeneracy). 

This imaginary polarizability is usually neglected in standard treatments, but in recent years it has been shown to give important new contributions to light scattering from atoms and molecules in degenerate states, particularly Kramers degeneracy associated with an odd number of electrons. 

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