Intermediate fields

FIGURE 7.1 S = 3/2 rhombograms for weak-field and intermediate-field conditions. Effective g-values are plotted for v = 9.50 GHz and D = 3.0 cm"1 (weak field solid lines) or D = 0.3 cm"1 (intermediate field broken lines) as a function of the rhombicity E/D. 

For biomolecular S = 1/2 systems subject to central hyperfine interaction the intermediate-field situation (B S S I) is not likely to occur unless the micro-wave frequency is lowered to L-band values. When v = 1 GHz, the resonance field for g = 2 is at B = 357 gauss. Some Cu(II) sites in proteins have Az 200 gauss, and this would certainly define L-band EPR as a situation in which the electronic Zeeman interaction is comparable in strength to that of the copper hyperfine interaction. No relevant literature appears to be available on the subject. An early measurement of the Cun(H20)6 reference system (cf. Figure 3.4) in L-band, and its simulation using the axial form of Equation 5.18 indicated that for this system... 

In Chapter 6 we presented an expression for the transition probability (or intensity, amplitude) of field-swept spectra from randomly oriented simple 5=1/2 systems (Equation 6.4), and we could perhaps tacitly assume (as is generally done in the bioEPR literature) that the expression also holds for effective S = 1/2 systems, such as for the high-spin subspectra defined by the rhombograms discussed in Chapter 5. But what about parallel-mode spectra And how do we compute intensities in complex situations like for systems in the B S B B intermediate-field regime Clearly, we need a more generic approach towards intensity calculations. 

The label IAmsl = 2 does not mean that two quanta hv are absorbed it is simply a somewhat unfortunate but widely divulged notation to indicate a transition (A E = hv) between two levels that we happen to have labeled as 1+1) and 1-1). Strictly speaking, these labels should only apply to the strong-field situation of (S S) B S) as we discussed in Chapter 4. In the present example of Figure 11.1 we are in the weak-to-intermediate field regime (S S > B S), which means that the actual wavefunctions are linear combinations of the ones in Equation 11.5. In particular, a rhombic E-term mixes the 1+1) and 1-1) levels as can be seen from its appearance in nondiagonal positions in the zero-field energy matrix... 

A potentially interesting aspect of the X-band (in contrast to Q-band) is the ready availability of parallel-mode resonators these types of spectra (S S S B) have parallel-mode spectra of intensity comparable to the normal-mode spectra (cf. Figure 12.7), and so parallel-mode EPR is an easy way to obtain an independent data set for spectral analysis. This interesting aspect of the intermediate-field case remains to be explored and developed. 

Although simple /rSR spectra that do not depend on the nuclear terms in the spin Hamiltonian are the easiest to observe, one loses valuable information on the electronic structure. Under certain circumstances it is possible to use conventional /rSR to obtain a limited amount of information on the largest nuclear hyperfine parameters. The trick is to find an intermediate field for which the muon is selectively coupled to only the nuclei with the largest nuclear hyperfine parameters. Then a relatively simple structure is observed that gives approximate nuclear hyperfine parameters. A good example of this is shown in Fig. 3a for one of the /xSR... 

Chuntonov, L., Rybak, L., Gandman, A., and Amitay, Z. 2008. Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses. Phys. Rev. A 77 021403. 

Because the Stokes pulse precedes but overlaps the pump pulse, initially Up and all population initially in field-free state 11) coincides with flo(0)- At the final time, ilp Q5 so all of the population in flo(0) projects onto the target state 6). Note that flo(0) has no projeetion on the intermediate field-free state 5 ). The Rabi frequencies of the Stokes and pump pulses that are required for efficient STIRAP-generated population transfer satisfy the condition [66]... 

What conditions must be fulfilled for the ionization process to occur in the adiabatic fashion we have just described First, the transition from the zero field ntm states to the intermediate field Stark states must be adiabatic. Second, the traversal of the avoided crossings in the strong field regime, E > l/3n5 must be adiabatic as well. Finally, ionization only occurs at E > W2/4 if the ionization rate exceeds the inverse of the time the pulse spends with E > W2/4. 

On the other hand the high t states have quantum defect differences which are much smaller than 10-3 and they do not satisfy the adiabatic criterion of Eq. (7.5) for the same risetime. As a result, when the field is turned on they are projected diabatically onto the intermediate field states. From Eq. (7.5) it is clear that if the risetime is kept constant, the at which diabatic passage from zero field occurs becomes lower as n is increased. Since it is impossible to excite optically high t states, the statement that they pass diabatically from low field to the intermediate regime has not been tested, but it has been experimentally established that the optically accessible low ( states of n = 20 Na atoms do in fact pass adiabatically to the intermediate field regime for pulses with 1 /us risetimes. 

Fig. 7.10 Adiabatic correlation diagram for the Na nd states obtained from the known d state fine structure splitting, the intermediate field energy ordering, and applying the nocrossing rule for states of the same m (from ref. 3).

Fig. 7.12 Ratio of the signal resulting from ionization of m = 2 states (upper curve), and ionization of m = 0 states (lower curve) to the total ionization signal as a function of the slew rate from low to intermediate fields following excitation of the 34dj/2 state via the 3pifl state with o polarization (from ref. 16).

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