The resonator

The formal definition of this quality factor, Q, is the amount of power stored in the resonator divided by the amount of power dissipated per cycle (at 9.5 GHz a cycle time is l/(9.5 x 109) 100 picoseconds). The dissipation of power is through the resonator walls as heat, in the sample as heat, and as radiation reflected out of the resonator towards the detector. The cycle time is used in the definition because the unit time of one second would be far too long for practical purposes within one second after the microwave source has been shut off, all stored power has long been dissipated away completely. 

Good X-band resonators mounted into a spectrometer and with a sample inside have approximate quality factors of 103 or more, which means that they afford an EPR signal-to-noise ratio that is over circa three orders of magnitude better than that of a measurement on the same sample without a resonator, in free space. This is, of course, a tremendous improvement in sensitivity, and it allows us to do EPR on biomolecules in the sub-pM to mM range, but the flip side of the coin is that we are stuck with the specific resonance frequency of the resonator, and so we cannot vary the microwave frequency, and therefore we have to vary the external magnetic field strength. 

When a radiation source is placed inside a closed cavity, its radiation energy is distributed among all of the modes following Equations (2.1) and (2.2), once the system has reached equilibrium. As we have seen in Example 2.1, in spite of the large number of modes in such a closed cavity, the mean number of photons per mode corresponding to the optical region is very small. Specifically, it is very small compared to unity. This is the ultimate reason why, in thermal radiation fields, the spontaneous emission per mode by far exceeds the stimulated emission. (Remember that the stimulated emission process requires the presence of photons to induce the transition, opposite to the case of the spontaneous emission process.) 

However, it is possible to concentrate most of the radiation onto a few modes in such a way that the number of photons in those modes becomes large and the stimulated emission in those modes will dominate (although the total spontaneous emission rate into all modes may still be larger than the induced rate in these few modes). Such selection of few modes is realized in a laser by using an appropriate resonator, which should exhibit a strong feedback for those modes. The resonator will allow an intense radiation field to be built in the modes with low losses, and will prevent oscillation from being reached in the modes with high losses. 

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In an electron spin resonance spectrometer, transitions between the two states are brought about by the application of the quantum of energy hv which is equal to g H. The resonance condition is defined when hv = g H and this is achieved experimentally by varying H keeping the frequency (v) constant. Esr spectroscopy is used extensively in chemistry in the identification and elucidation of structures of radicals. 

Mosshauer effect The resonance fluorescence by y-radiation of an atomic nucleus, returning from an excited state to the ground state. The resonance energy is characteristic of the chemical environment of the nucleus and Mossbauer spectroscopy may be used to yield information about this chemical environment. Used particularly in the study of Fe. Sn and Sb compounds. 

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

The term resonance has also been applied in valency. The general idea of resonance in this sense is that if the valency electrons in a molecule are capable of several alternative arrangements which differ by only a small amount in energy and have no geometrical differences, then the actual arrangement will be a hybrid of these various alternatives. See mesomerism. The stabilization of such a system over the non-resonating forms is the resonance energy. 

Table 3.9 gives the resonance frequencies in a 9.4 tesla magnetic, field. . . 

Another oscillatory method makes use of a drop acoustically levitated in a liquid. The drop is made to oscillate in shape, and the interfacial tension can be calculated from the resonance frequency [113]. 

SERS. A phenomenon that certainly involves the adsorbent-adsorbate interaction is that of surface-enhanced resonance Raman spectroscopy, or SERS. The basic observation is that for pyridine adsorbed on surface-roughened silver, there is an amazing enhancement of the resonance Raman intensity (see Refs. 124—128). More recent work has involved other adsorbates and colloidal... 

The resonance vector analysis has been used to explore all of the questions raised above on the fate of the polyad numbers in larger molecules, the most thoroughly investigated case so far probably being C2FI2- This molecule has been very extensively probed by absorption as well as stimulated emission pumping and dispersed fluorescence teclmiques [, 53, 70 and 71], the experimental spectra have been analysed in... 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

The energy spectrum of the resonance states will be quasi-discrete it consists of a series of broadened levels with Lorentzian lineshapes whose full-width at half-maximum T is related to the lifetime by F = Fn. The resonances are said to be isolated if the widths of their levels are small compared with the distances (spacings) between them, that is... 

Time-dependent quantum mechanical calcnlations have also been perfomied to study the HCO resonance states [90,91]. The resonance energies, linewidths and quantum number assigmnents detemiined from these calcnlations are in excellent agreement with the experimental results. 

If all the resonance states which fomi a microcanonical ensemble have random i, and are thus intrinsically unassignable, a situation arises which is caWtA. statistical state-specific behaviour [95]. Since the wavefunction coefficients of the i / are Gaussian random variables when projected onto (]). basis fiinctions for any zero-order representation [96], the distribution of the state-specific rate constants will be as statistical as possible. If these within the energy interval E E+ AE fomi a conthuious distribution, Levine [97] has argued that the probability of a particular k is given by the Porter-Thomas [98] distribution... 

Skokov S and Bowman J M 1999 Variation of the resonance width of HOCI (6uq ) with total angular momentum comparison between ab /M/o theory and experiment J. Chem. Phys. 110 9789-92... 

The siim-over-states method for calculating the resonant enlrancement begins with an expression for the resonance Raman intensity, /.y, for the transition from initial state to final state /in the ground electronic state, and is given by [14]... 

It is also possible to detennine the resonant Raman intensities via a time-dependent method [16]. It has the... 

First, it is possible to excite a chromophore corresponding to the active site, and detennine which modes interact with it. Second, by using UV excitation, the amino acids with phenyl rings (tryptophan and tyrosine, and a small contribution from phenylalanine) can be selectively excited [4], The frequency shifts in the resonance Raman spectrum associated with them provide infomiation on their enviromnent. 

Infonuation about the haeme macrocycle modes is obtained by comparing the resonance Raman spectra of deoxyHb with HbCO. The d-d transitions of the metal are too weak to produce large enliancement, so the... 

The unique feature in spontaneous Raman spectroscopy (SR) is that field 2 is not an incident field but (at room temperature and at optical frequencies) it is resonantly drawn into action from the zero-point field of the ubiquitous blackbody (bb) radiation. Its active frequency is spontaneously selected (from the infinite colours available in the blackbody) by the resonance with the Raman transition at co - 0I2 r material. The effective bb field mtensity may be obtained from its energy density per unit circular frequency, the... 

RRS has also introduced the concept of a Raman excitation profile (REPy for thefth mode) [46, 4lZ, 48, 49, 50 and M]. An REP. is obtained by measuring the resonance Raman scattering strength of thefth mode as a fiinction of the excitation frequency [, 53]. Flow does the scattering intensity for a given (thefth) Raman active vibration vary with excitation frequency within an electronic absorption band In turn, this has led to transfomi theories that try to predict... 

One group has successfiilly obtained infonnation about potential energy surfaces without measuring REPs. Instead, easily measured second derivative absorption profiles are obtained and linked to the fiill RRS spectrum taken at a single incident frequency. In this way, the painstaking task of measuring a REP is replaced by carefiilly recording the second derivative of the electronic absorption spectrum of the resonant transition [, 59],... 

Tripathi G N R and Schuler R H 1984 The resonance Raman spectrum of phenoxyl radical J. Chem. Phys. 81 113-21... 

Here E(t) denotes the applied optical field, and-e andm represent, respectively, the electronic charge and mass. The (angular) frequency oIq defines the resonance of the hamionic component of the response, and y represents a phenomenological damping rate for the oscillator. The nonlinear restoring force has been written in a Taylor expansion the temis + ) correspond to tlie corrections to the hamionic... 

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