Manifold of ensemble states

Although the emission spectra that originate from excited states of complexes have structure, the vibrational bandwidths exceed the splittings of the electronic levels. There is little sharpening at low temperature, and incorporation into a lattice does not appear to improve the resolution (15). Nonetheless, it is possible to obtain the level splittings from the decay data. If one assumes a manifold of excited states in thermal equilibrium at all temperatures, each decaying with temperature-independent decay constants, one arrives at an analytical expression for the temperature dependence of the mean decay time of the ensemble (8, 9, 10) ... 

For 5-state atoms, the momentum density is spherically symmetric and therefore n( p) = IIo(p). Nonspherical II( p) can occur in atomic states of higher angular momentum. However, these states are degenerate, and an ensemble average is required. This is equivalent to a spherical average for any one of the states in the degenerate manifold. The spherically averaged momentum density IIo(p) is also of interest for molecules because it is a quantity that can be obtained from gas-phase experiments. 

We already have a general picture suitable for considerations. As has been repeatedly emphasized, dealing with fluid polymers means dealing with an ensemble of chains which can exist in a manifold of different conformational states. Thermal equilibrium is a dynamical situation where chains change between these states activated by thermal energies. The microscopic dynamics shows up in the macroscopic experiments. Relaxation rates observed in certain mechanical or dielectrical measurements equal the rates of transitions within a certain group of conformations. 

Qualitatively, TM can be interpreted as a transition from the CE towards an electron spin ensemble, arising from manifolds of states. TM requires high radical concentrations causing a homogenously broadened spectmm arising from strong electron interactions. 

Wliatever the deteetion teehnique, the window stage of the 4WM event must eonvert these evolved vibrational wavepaekets into the third order polarization field that oseillates at an ensemble distribution of optieal frequeneies. One must be alert to the possibility that the window event after doorway ehaimel B may involve resonanees from eleetronie state manifold e to some higher manifold, say r. Thus ehaimel B followed by an e (ket) or a (bra) event might be enlianeed by an e-to-r resonanee. However, it is nonnal to eonfine the... 

Fig. 13.5 Adiabatic and diabatic selective field ionization (SFI) for -changed ensembles produced from Na 39p, 40s, 39d, and 40p states by 43 eV Na+ impact. The adiabatic peaks occur at 170-180 V/cm, and the diabatic features occur above 250 V/cm (note change of vertical scale). The diabatic SFI from -changed 50s targets most closely resembles that from 39d. In contrast, 40p and 39p targets yields SFI that indicates a different distribution of Stark sublevels lying high in the n = 39 and 38 manifolds, respectively (from ref. 10).

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