Photons, energy INDEX

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

The Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL) gives the index of refraction n and the first ionization potential, a voltage I.P. corresponding to an energy e x I.P. required to rip the first electron off the material. The dielectric permittivity must equal n2 at low frequencies. (This is the constraint referred to in the "with-constraint" parameters that fit more extensive data.) The single UV absorption frequency >uv corresponds to a photon energy h o>uv = e x I.P. 

Where R is the reflectivity and d is the thickness. Very accurate values of R and T are needed when the absorptance, (id, is small. The technique of photothermal deflection spectroscopy (PDS) overcomes this problem by measuring the heat absorbed in the film, which is proportional to ad when ad 1. A laser beam passing just above the surface is deflected by the thermal change in refractive index of a liquid in which the sample is immersed. Another sensitive measurement of ad is from the speetral dependence of the photoconductivity. The constant photocurrent method (CPM) uses a background illumination to ensure that the recombination lifetime does not depend on the photon energy and intensity of the illumination. Both techniques are capable of measuring ad down to values of about 10 and provide a very sensitive measure of the absorption coefficient of thin films. 

As mentioned previously, the incident pump and Stokes laser beams must be aligned in a precise manner so that the CARS generation process is properly phased. Since gases are virtually dispersionless, i. e. the refractive index is nearly a constant over a wide frequency range, the photon energy conservation condition ujas = in-... 

The dispersion of the refractive index of alkali halides and of other materials at energies above ujq has been used to produce reasonable monochromatic radiation. In prism monochromators, a parallel beam of polychromatic radiation incident on a prism made from these materials is dispersed, with angular deviations depending on the dispersion uj2dn/duj of the refractive index with the photon energies. Before the advent of grating monochromators and Fourier transform spectrometers, the prism monochromators were widely used in optical spectroscopy and they are still used for specific experiments. 

Noble gases are intrinsically difficult to detect by spectroscopy. For example, solar photospheric spectra, which form the basis for solar abundance values of most elements, do not contain lines from noble gases (except for He, but this line cannot be used for abundance determinations). Yet, ultraviolet spectroscopy is the only or the major source of information on noble gas abundances in the atmospheres of Mercury and comets. In the Extreme Ultraviolet (EUV), photon energies exceed bond energies of molecules and the first ionization potential of all elements except F, He, and Ne, so that only these elements are visible in this part of the spectrum (Krasnopolsky et al. 1997). Other techniques can be used to determine the abundance of He where this element is a major constituent. Studies of solar oscillations (helioseismology) allow a precise determination of the He abundance in the solar interior, and the interferometer on the Galileo probe yielded a precise value for the refractive index and hence the He abundance in the upper atmosphere of Jupiter (see respective sections of this chapter). 

These tables list the index of refraction n, the extinction coefficient k, and the normal incidence reflection f (( ) = 0) as a function of photon energy E, which is expressed in electron volts (eV). To convert the energy in eV to the wavelength in pm, use X = 1.2398/ E. To compute the dielectric function e = + ie from the complex... 

For X-rays, 6 is very small (10 -10 ) and positive, i.e., the refractive index is slightly less than unity. This property of X-rays causes a near absence of reflection at interfaces and results in very clear images, even of thick specimens. X-ray microscopic samples are amplitude objects as well phase objects and X-ray microscopy can be performed in amplitude (absorption) contrast and phase contrast. Hence, at high photon energies for low-density materials it is much more favorable to image an object in phase contrast rather than in absorption contrast. In addition to natural contrast mechanisms. X-rays can provide chemical bond mapping or trace elements mapping of many elements. 

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