Resonance condition microwave frequency

Figure 17-5 EPR spectra of bovine calcineurin under different redox conditions. Calcineurin was isolated from bovine brain as described [94] and concentrated to 20mgml for the sample shown in (A). The broad features from 100-150mT represent high spin Fe + bound to calcineurin while the sharp feature at g = 4.3 is contributed by a small amount of adventitious Fe " in the sample. Anaerobic treatment of the enzyme with SOmM ascorbic acid (B) had no effect on the EPR signal of the Fe + ion of calcineurin but led to a slight decrease of the resonance of adventitious iron at g = 4.3. Anaerobic addition of 2.0mM Na2S204 and 50/xM methylviologen (C) completely abolished the EPR signals of all Fe + species. The buffer in all samples was 20 mM Tris-HCl, 0.1 niM EDTA, l.OmM magnesium acetate, l.OmM dithiothreitol, 0.15m KCl, pH 7.5. EPR conditions microwave frequency, 9.233 GHz modulation, 1.0 mT at 100 kHz temperature, 4.0 K microwave power, 0.2 mW.

ESR experiments in commercial spectrometers consist in exposing a sample containing paramagnetic species to the combined action of a flux of microwaves at constant frequency and a magnetic field of about 3300 G which is varied in order to satisfy the resonance condition. Operating frequencies of the microwave generator (klystron) are in the range of 1-100 GHz (X band 9.5 GHz, X 3.2 cm K band 24 GHz, 1 1.25 cm Q band 35 GHz, X 0.85 cm). 

Figure A2.1 Microwave frequency dependent HF-EPR spectra of aqueous Cr2+ (0.1-0.2 m), sulfate counterion. Experimental conditions temperature 10 K microwave frequency as indicated. In the spectrum taken at 329 GHz a sharp signal from aqueous Cr3+ impurity at g = 2 is indicated and the resonances due to Cr2+ are labeled (Figure A2.2).

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 ... 

Intercollisional interference. We note that at the lowest frequencies the simple proportionality between absorption coefficient and product of gas densities breaks down. Under such conditions, certain many-body interactions affect the observations and modify the shape or intensities of the binary spectra, often quite strikingly. An example is shown in Fig. 3.3, a measurement of the absorption in a neon-xenon mixture in the microwave region, at the fixed frequency of 4.4 cm-1. Because of the frequency-dependent factor of g(v) that falls off to zero frequency as v2, absorption is extremely small at such frequencies, Eq. 3.2. As a consequence, it has generally been necessary to use sensitive resonator techniques for a measurement of the absorption at microwave frequencies... 

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. 

We discuss now an analytical procedure for the calculation of critical ionization fields that is based on Chirikov s overlap criterion. For a given microwave frequency u we first compute the locations I m of all 1/M type resonances. We then determine a list of fields, m i defined as the critical fields of overlap between the 1/M type resonance and the 1/(M — 1) type resonance, i.e. m is determined from the 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]. 

The radiatively assisted collisional resonances shown in Fig. 8 are taken under the condition that the microwave frequency far exceeds the linewidth of the collisions. If the frequency is far less than the linewidth, or equivalently the duration of the collision is short compared to the rf period, then the rf field simply adds to the static field. If in a static field the collisional resonance occurs at the field Er, then if the collision occurs at time i - 0 in the combined field... 

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). 

Electron spin resonance spectrometers are available commercially, and typical operating conditions are a frequency/of 10 ° cps (x band), and a magnetic field H of 3600 gauss. Sometimes the measurements are made at other frequencies such as 2.4 X 10 cps (k band). The samples may be examined as a function of the microwave power, the microwave frequency, the modulation conditions, and the temperature. 

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