Perturbed state

The X coupling parameter defines a set of intermediate hybrid states between the unperturbed and the fully perturbed states. Then, the total change in the free energy is... 

Picosecond Raman measurements have led to the proposal of a dynamic polarization model." In this model, 5i tS undergoes reversible changes in vibrational frequencies that are induced by solvent fluctuations. The mixing of a perturbing state with interconverts carbon-carbon double bonds with single bonds that leads S tS near the vertical geometry to proceed along the pathway for isomerization. 

Fig. 4. Transitions from a lower lying singlet state [S°]> to the perturbed state...

To evaluate the thermodynamic and radiation properties of a natural or perturbed state of the upper atmosphere or ionosphere, the thermal and transport properties of heated air are required. Such properties are also of particular interest in plasma physics, in gas laser systems, and in basic studies of airglow and the aurora. In the latter area the release of certain chemical species into the upper atmosphere results in luminous clouds that display the resonance electronic-vibrational-rotational spectrum of the released species. Such spectra are seen in rocket releases of chemicals for upper-atmosphere studies and on reentry into the atmosphere of artificial satellites. Of particular interest in this connection are the observed spectra of certain metallic oxides and air diatomic species. From band-intensity distribution of the spectra and knowledge of the /-values for electronic and vibrational transitions, the local conditions of the atmosphere can be determined.1... 

A situation peculiar to electronic spectra occurs when the perturbing state is dissociative, for the molecule may then undergo a radiationless transition from a stable electronic state to a dissociative one. The phenomenon, known as predissociation, may be detectable by a broadening of the rotational lines which, when the radiationless transition has high probability, become so broad that all traces of rotational structure vanish. Predissociation is observed frequently in polyatomic spectra and seriously restricts the number of band systems suitable for detailed study. 

The origin of the LR-SS difference was imputed to the incapability of the nonlinear effective solute Hamiltonian used in these solvation models to correctly describe energy expectation values of mixed solute states, i.e., states that are not stationary. Since in a perturbation approach such as the LR treatment the perturbed state can be seen as a linear combination of zeroth-order states, the inability of the effective Hamiltonian approach to treat mixed states causes an incorrect redistribution of the solvent terms among the various perturbation orders [32],... 

The important result is that, whereas the small oscillation can be influenced by very weak external fields, leading to a total collapse of the LC, the large amplitude cycle is rather stable against perturbations. This means that the system can be driven from a perturbable state to a nearly unperturbable one. Typical examples of entrained or perturbed oscillations are given in Figure 4. 

In the picture of spin-orbit perturbed Russell-Saunders states, the dipole transition moment of a spin-forbidden radiative transition is thus a sum of spin-allowed dipole transitions weighted by spin-orbit coupling coefficients (e.g., the expansion coefficients in Eq. [218]). The fact that the transition dipole moment of a spin-forbidden radiative transition is a weighted sum of spin-allowed dipole transition moments is exactly what experimentalists mean when they speak of intensity borrowing. The contribution of perturbing states to the oscillator strength can be positive or negative. In other words, per-turbers can not only lend intensity to a spin-forbidden transition, they can also take it away. 

When a hydrogen atom initially in the state 2s1/2 passes non-adiabatically into a region of atomic interferometer field strength F [1], the perturbed state vector to lowest order is... 

The a3II state is the lowest excited state of the CO molecule, see Fig. 8. The spin-forbidden transition from the o3H state to the ground A1E+ state constitutes the well-known Cameron band system [104] which has been studied in the gas phase and in the solid matrices by many different experimental techniques [105, 106, 107, 108, 109, 110, 111, 112]. Theoretical calculations of the intensity of the Cameron bands and the lifetime of the o3II state are though quite scarce [113, 112], James [113] accounted for one perturbing state AlII, i.e. the SOC perturbation between the singlet and triplet... 

The stationary states xsi are obtained using dxjdt = 0. We define a small perturbation 5x, and a positive function L 8x) called the distance. If this distance between x, and the perturbed state (xsj + 8x,) steadily decreases, in time, the stationary state is stable... 

The terms omitted are of order (77,y /7,-j - Hjj ) -, they are neglected in lowest-order perturbation theory. Thus, if a p state on a chlorine ion in KCl is coupled to an s state on its neighboring potassium ion by a matrix element /7,y (which we will relate to K,p ) and the difference in energy between the two states Hjj - H,-,- = is large compared to the coupling, the probability that an electron in the perturbed state lies on that potassium ion is... 

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