Frequency dependence resonance absorption

The above discussion may lead one to think that all electrons absorb the same microwave radiation at a particular magnetic field. If this were so, then ESR spectroscopy would have limited use. However, such is not the case. The exact value of the g factor depends strongly on the local environment of the unpaired electron. This means that the exact frequency of resonant absorption depends on the specific molecule of interest. In particular, because nuclei themselves also have a spin, there is an interaction, or a coupling, between the unpaired electron s spin and the spin angular momentum of the individual nucleus, which is labeled I. 

Application of an oscillating magnetic field at the resonance frequency induces transitions in both directions between the two levels of the spin system. The rate of the induced transitions depends on the MW power which is proportional to the square of oi = (the amplitude of the oscillating magnetic field) (see equation (bl.15.7)) and also depends on the number of spins in each level. Since the probabilities of upward ( P) a)) and downward ( a) p)) transitions are equal, resonance absorption can only be detected when there is a population difference between the two spin levels. This is the case at thennal equilibrium where there is a slight excess of spins in the energetically lower p)-state. The relative population of the two-level system in thennal equilibrium is given by the Boltzmaim distribution... 

This absorber is basically a panel attached to a structural wall that is designed to absorb energy. The absorber is therefore frequency dependent and has an absorption peak at its resonant frequency. This type of absorber is not commonly used. 

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

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... 

Fig. 10.19 The microwave frequency dependence of the n changing signals at low microwave power, where n changes up or down only by 1. Resonant multiphoton transitions are observed near the expected static field Stark shifted frequencies indicated. These resonances involve the absorption of four or five microwave photons. The down n changing atom production curve was obtained with the state analyzer field EA set at 50.0 V/cm, while up n changing was studied as n = 60 atom loss with EA = 45.5 V/cm. The locations of resonances for larger direct (not stepwise) changes in n are indicated along with...

In Fig. 28a we show for T = 27°C the frequency dependence of e and s", which comprises the Debye and FIR regions. We see three maxima on the loss curve 2. The frequency dependences obtained from the empirical formulas (shown by lines) agree well the measurement data (to obtain such an agreement at the lowest frequency v = 20 cm-1 we changed a little the values of the optical constants [42] at this frequency). The evolution of the recorded quasi-resonance absorption spectra with temperature is illustrated by Fig. 28b. For the highest temperature (50°C), curve 3, there is some disagreement with the empirical... 

The line forms, described by Eqs. (371) and (373), are illustrated in Figs. 45 and 46. In the first one (Fig. 45) we compare the loss (a) and absorption (b) for the isothermal, Gross, and Lorentz lines see solid, dashed, and dashed-and-dotted curves, respectively. These curves are calculated in a vicinity of the resonance point x = 1. In Figure 45c we show the frequency dependences of a real part of the susceptibility the three curves are extended also to a low-frequency region. The collisions frequency y and the correlation factor g are fixed in Fig. 45 (y = 0.4, g = 2.5). 

In Figs. 45 and 46 we see the frequency the dependences typical for resonance-absorption. The isothermal line (at Ft) is characterized by the loss peak, whose intensity is evidently larger and bandwidth is narrower than those pertinent to two other lines. The Lorentz line (at FB) is characterized by (i) a smallest maximum loss and (ii) an absence of the loss shoulder at lower frequencies. This shoulder appears (at Ft and Fq) due to the denominator in Eqs. (370) and (372), pertinent to the self-consistent collision models. Since the plateau-like loss curve is indeed a feature characteristic for water in the... 

Optical absorption in M nanocrystals embedded in dielectric matrix depends on characteristics of matrix and interface between matrix and nanocrystals. In the classical model of Mie only macroscopical dielectric permeability of environment e 2 is taken into account [16]. In this model charges at the M nanocrystal surface are determined by s2 and so frequency coa corresponding to a peak of resonant absorption is defined from a relation [18]. 

Here, the electrons on each molecule create transient dipoles. They couple the directions of their dipoles to lower mutual energy. "Dispersion" recognizes that natural frequencies of resonance, necessary for the dipoles to dance in step, have the same physical cause as that of the absorption spectrum—the wavelength-dependent drag on light that underlies the dispersion of white light into the spectrum of a rainbow. 

Dependent on the interaction between the quadrupole moment of the nucleus and the electric-field gradients at the nucleus arising from the charge distribution in a solid. Resonant absorption of radio-frequency energy occurs when nuclei are excited to various higher-energy states related to these interactions. It is this resonant absorption that is studied... 

The Mossbauer effect is the resonant absorption of low-energy y-rays by nuclei bound in solids in such a way that there is no energy loss due to nuclear recoil. It depends upon the monoenergetic nature of the y-ray emitted from an excited nucleus. When this ray falls on an unexcited nucleus of the same isotope, it will be absorbed if the nuclei are stationary relative to each other. However, if there is relative movement, there will be a Doppler shift in the frequency of the emitted y-ray so... 

Fig. 4.8 Illustration of the appearance of a frequency dependent phase error in the spectrum. In (a) the line which is on resonance (at zero frequency) is in pure absorption, but as the offset increases the phase error increases. Such an frequency dependent phase error would result from the use of a pulse whose RF field strength was not much larger than the range of offsets. The spectrum can be returned to the absorption mode, (c), by applying a phase correction which varies with the offset in a linear manner, as shown in (b). Of course, to obtain a correctly phased spectrum we have to choose the correct slope of the graph of phase against offset.

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