Microwave resonance condition

ESR spectroscopy can be transformed into an imaging method, ESRI, for samples containing unpaired electron spins, if the spectra are measured in the presence of magnetic field gradients. In an ESRI experiment the microwave power is absorbed by the unpaired electrons located at point x when the resonance condition, Equation (10), is fulfilled. 

The term d(umn — co) is a function which requires that the resonance condition be satisfied that is, the microwave frequency must equal the resonance frequency. 

The y-facior. The 0-factor takes into account the fact that the local magnetic field experienced by a particular atom in a molecule may not be the same as the applied field owing to the existence of local field effects. In the absence of such effects, g for any particular radical would simply have the same value as that of the free electron, 2.0023, and all radicals would come into resonance at the same applied field for a given microwave frequency. We can thus express the resonance condition (equation 2.173) as ... 

ENDOR spectroscopy has proven to be a valuable technique to provide information on both free and protein bound flavin radicals. Since flavin radical ESR spectra can be partially saturated at moderate microwave power, ENDOR spectra may be observed as nuclear spin transitions by detection of changes in the partially saturated ESR signal as a function of nuclear radio frequency. The resonance condition for nuclei (when I = Vz) is described by the following equation ... 

A microwave cavity placed between SI and S2 can induce spin-flip transitions (F,Mp) = (1,1) —i (1,-1) if tuned to zvhf(H). In order to produce a positive signal, i.e. an increase in counting rate after S2 under resonance condition, S2 will be rotated by 180 degrees with respect to SI. Therefore, the (1, —1) state where Mp = —1 is defined with respect to the magnetic field direction in SI will be a (1,1) state in S2, while the (1,1) state of SI without spin flip would correspond to a (1, —1) state in S2. As a result, if the microwave frequency is off resonance, no H atoms will reach behind S2, while on resonance an increase in the number of atoms should be detected after S2. 

There is another way to separate the overlapping signals, i.e., to work at higher magnetic fields. This follows from the resonance condition hu = gpeBo and implies, at the same time, the use of a higher microwave fre-... 

In order for optical detection of microwave resonances to be feasible for a given molecular system, four important conditions must be satisfied (a) the triplet state in question must display luminescence (b) some mechanism must exist for creating the triplet state in a state of spin alignment (c) this population imbalance, once created, must persist for a time sufficient to allow... 

From Eq. (2-8), the Zeeman splitting is equal to the energy of an applied microwave (/id) in the resonance condition of ESR. Thus, the ration can be given as... 

Absorption of microwave radiation occurs when the following resonance condition,... 

Having examined the n - - 2)s — (n, 3) transitions as resonances we are now able to explain the apparently random fields required to drive the (n -b 3)s — (n, 3) transitions by a microwave field alone. Observation of the transition has two requirements, the levels must be resonant and the Rabi frequency must be adequate. Analyzing the data of Fig. 7 show that the Rabi frequency is adequate if = 0.7 (Ec - s, ) for all the states. In the absence of a static field the resonance condition is met when the AC Stark shift of the (n -b 3)s state brings it into resonance, which is random. Typically, the two conditions are only met simultaneously for a random microwave field amplitude larger than the anticrossing field, but for the 19s state in a 9.2789 GHz field the resonance condition is met for the 27 photon transition at E = 515 V/cm, 0.9 c> leading to the small resonant peak in the signal [18]. 

CW experiments (sometimes called stationary or steady state ) are ones in which either no modulations are used, or they are so low in frequency that no spectral complications ensue. (This is only approximately the case if 100 kHz field modulation is employed. This frequency gives rise to modulation sidebands and, under saturating conditions, rapid passage effects.) Time-domain ESR involves monitoring the spin system response as a function of time. Pulse ESR can be divided into two broad categories the response of spin systems to sequences of microwave pulses (spin echo) and the response of spin systems to step changes in resonance conditions (saturation recovery). 

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