Stark scalar

We could now choose explicit vector and scalar potential functions as we did in section 3.7. However, when we come to perform the various coordinate transformations outlined in the previous section, it is more convenient to treat the Zeeman and Stark Hamiltonians for the molecule as a whole. Accordingly we combine the expressions from section 3.7 with equations (3.272) and (3.273) to give... 

The Stark Hamiltonian is more straightforward. We use the scalar potentials... 

Rydberg states of Ba and Sr in an external magnetic field have been considered by Halley, Delande, and Taylor (35), by means of the R-matrix complex rotation method. Seipp and Taylor (36) used the same method for the Stark and Stark-Zeeman problem of Rydberg states of Na. Themelis and Nicolaides (96) investigated the ls 2s 2p 3s 5, 3p 4s 5, and 3d bound states of Na. They used the CESE method to compute tunneling rates and scalar and tensor polarizabilities and hyperpolarizabilities. Medikeri, Nair, and Mishra (145,146) considered shape resonances in Be", Mg" and Ca" in two-particle-one-hole-Tamm-Dancoff approximation. Photodetachment rate for Cl" described by one-electron model was computed by Yao and Chu (73)... 

Three different techniques have been presented that all measure different flavors of photoinitiated CT distances. Indeed, a comparison of the techniques in Table 1 indicates many differences between them. Notably, the difference between vector and scalar dipole moment differences must be considered with respect to the geometry of the analyte, since scalar measurements do not necessarily yield the actual CT distances. Also, the analyte spectrum components must be clearly resolved. For example. Stark absorption on (bpy)Re(CO)3Cl would be very difficult due to overlapping ligand TTjTT and MLCT bands. Alternatively, its emission spectrum exhibits only the MLCT band, allowing Stark emission to easily measure the CT distance. The need for Stark spectroscopy samples... 

Oq and 02 being the scalar and tensor polarizability constants, respectively, can be determined experimentally and calculated theoretically. For J = 0 or 1/2, for which the formula breaks down, there is only a scalar effect. The Stark effect can be seen as an admixture of other states into the state under study. Perturbing states are those for which there are allowed electric dipole transitions (Sect.4.2) to the state under study. Energetically close-lying states have the greatest influence. A theoretical calculation of the constants Oq and 02 involves an evaluation of the matrix elements of the electric dipole operator (Chap.4). Investigations of the Stark effect are therefore, from a theoretical point of view, closely related to studies of transition probabilities and lifetimes of excited states. (Sects. 4.1 and 9.4.5). In Fig. 2.13 an example of the Stark effect is given different aspects of this phenomenon have been treated in [2.31]. 

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. 

T. C. Lubensky, H. Stark, Phys. Rev. 1996, E53, 714. These authors introduce a pseudo-scalar order parameter for this critical point. 

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