Tensor Stark interaction

An example of the Stark effect is given in Fig.9.39. Note, that while only the tensor Stark interaction constant 03 (Sect.2.5.2) can be determined in an LC experiment (Sect.7.1.5 Fig.9.18), the scalar interaction constant ag can be obtained in this type of experiment as well as 03. In the same way, isotope shifts can be measured by direct optical high-resolution methods while resonance methods and quantum-beat spectroscopy can only be used for measurements of splittings within the same atom. 

In molecular quantum mechanics, we often find ourselves manipulating expressions so that one of a pair of interacting operators is expressed in laboratory-fixed coordinates while the other is expressed in molecule-fixed. A typical example is the Stark effect, where the molecular electric dipole moment is naturally described in the molecular framework, but the direction of an applied electric field is specified in space-fixed coordinates. We have seen already that if the molecule-fixed axes are obtained by rotation of the space-fixed axes through the Euler angles (, 6, /) = >, the spherical tensor operator in the laboratory-fixed system Tkp(A) can be expressed in terms of the molecule-fixed components by the standard transformation... 

It is well-known that the electron repulsion perturbation gives rise to LS terms or multiplets (also known as Russell-Saunders terms) which in turn are split into LSJ spin-orbital levels by spin-orbit interaction. These spin-orbital levels are further split into what are known as Stark levels by the crystalline field. The energies of the terms, the spin-orbital levels and the crystalline field levels can be calculated by one of two methods, (1) the Slater determinantal method [310-313], (2) the Racah tensor operator method [314-316]. 

Excited state properties of molecules are often important parameters in different models of interacting systems and chemical reactions. For example, excited state polarizabilities are key quantities in the description of electrochromic and solva-tochromic shifts [99-103]. In gas phase there has been a series of experiments were excited state polarizabilities have been determined from Laser Stark spectroscopy by Hese and coworkers [104-106]. However, in the experiments most often not all the tensor components can be determined uniquely without extra information from either theory or other experiments. 

The Stark effect of a rotational level is determined by the permanent electric dipole moment ju, the electric polarizability tensor a of the molecule and the applied electric field E. The Hamiltonian of these interactions can be given as ... 

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