Monochromatization

After integrating Eq. 2.7, the transmitted intensity (/,) is easily calculated in terms of a fraction of the initial intensity of the beam (/q)  

The continuous change of the liner absorption along each of the two branches is approximately defined as p = kZ, where Z is the atomic number of the chemical element and A is a constant, specific for each of the two continuous parts of the absorption function. The continuous branches correspond to the absorption occurring due to random scattering of photons by electrons, which is observed in all directions, thus reducing the number of photons in the transmitted beam in the direction of the propagation vector. 

The appearance of the discontinuity (i.e. the presence of the K absorption edge) is known as the true absorption and it can be understood by considering Eq. 2.3. As the wavelength decreases, the energy of the x-ray photons increases and at a certain X it becomes sufficient to excite K electrons. This not only causes a rapid increase in the number of the absorbed photons but also results in the transitions of upper level electrons to 

The general rule for choosing the P-filter is to use a material, which is rich in a chemical element, one atomic number less than the anode material in the periodic table. This assures proper location of the K absorption edge, i.e. between the Kai and Kp lines. For heavy anode materials (e.g. Mo), this rule can be extended to two atomic numbers below the element of the anode. A list of p-filter elements, suitable for the most commonly used anode materials, is found in Table 2.1. Thus, for a Cu anode, a foil made from Ni will work best as the P-filter, while for Mo radiation both Nb and Zr are good P-filters. The former material (Zr) is more often used in practice because its K absorption edge is closer to the wavelength of the Kai line. 

Considering Eq. 2.8 and the as-produced ratio of intensities between Kai and Kp lines (5 1), the filtered /ku/ kp intensity ratio can be expressed as follows  

---

Bragg scattering Coherent elastic scattering of monochromatic neutrons by a set of crystal planes. 

X-ray spectrometer An apparatus used in the X-ray study of crystals in which a fine beam of monochromatic X-rays impinges at a measured angle on the face of a crystal mounted in its path, and in which the intensity of the X-rays diffracted in various directions by the crystal is measured with an ionization chamber mounted on an arm of the spectrometer table, or is recorded photographically. 

A much better way would be to use phase contrast, rather than attenuation contrast, since the phase change, due to changes in index of refraction, can be up to 1000 times larger than the change in amplitude. However, phase contrast techniques require the disposal of monochromatic X-ray sources, such as synchrotrons, combined with special optics, such as double crystal monochromatics and interferometers [2]. Recently [3] it has been shown that one can also obtain phase contrast by using a polychromatic X-ray source provided the source size and detector resolution are small enough to maintain sufficient spatial coherence. 

Let us consider the scheme showed in Fig. I to calculate the field scattered by a rough cylindrical surface (i.e. a wire). The wire is illuminated by a monochromatic, linearly polarized plane wave at an angle of incidence a with its axis of symmetry. The surface is described, in a system fixed to the wire, by p = h (cylindrical coordinates. We shall denote the incident wave vector lying on the x-z plane as kj and the emergent wave vector simply as k. 

In ellipsometry monochromatic light such as from a He-Ne laser, is passed through a polarizer, rotated by passing through a compensator before it impinges on the interface to be studied [142]. The reflected beam will be elliptically polarized and is measured by a polarization analyzer. In null ellipsometry, the polarizer, compensator, and analyzer are rotated to produce maximum extinction. The phase shift between the parallel and perpendicular components A and the ratio of the amplitudes of these components, tan are related to the polarizer and analyzer angles p and a, respectively. The changes in A and when a film is present can be related in an implicit form to the complex index of refraction and thickness of the film. 

RS Raman spectroscopy [210, 211] Scattered monochromatic visible light shows frequency shifts corresponding to vibrational states of surface material Can observe IR-forbidden absorptions low sensitivity... 

We now add die field back into the Hamiltonian, and examine the simplest case of a two-level system coupled to coherent, monochromatic radiation. This material is included in many textbooks (e.g. [6, 7, 8, 9, 10 and 11]). The system is described by a Hamiltonian having only two eigenstates, i and with energies = and Define coq = - co. The most general wavefunction for this system may be written as... 

Ozenne J-B, Pham D and Durup J 1972 Photodissociation ofH by monochromatic light with energy analysis of the e]ected H" ions Chem. Phys. Lett. 17 422-4... 

Such electronic excitation processes can be made very fast with sufficiently intense laser fields. For example, if one considers monochromatic excitation with a wavenumber in the UV region (60 000 cm ) and a coupling strength / he 4000 (e.g. 1 Debye in equation (A3.13.59), / 50 TW cm ),... 

Steinfeld J I and Klemperer W 1965 Energy-transfer processes in monochromatically excited iodine molecules. I. Experimental resulted. Chem. Phys. 42 3475-97... 

Quack M 1978 Theory of unimolecular reactions induced by monochromatic infrared radiation J. Chem. Phys. 69 1282-307... 

Quack M and Sutcliffe E 1986 Program 515. URIMIR unimolecular reactions induced by monochromatic infrared radiation QCPE Bull. 6 98... 

Continuous wave (CW) lasers such as Ar and He-Ne are employed in conmionplace Raman spectrometers. However laser sources for Raman spectroscopy now extend from the edge of the vacuum UV to the near infrared. Lasers serve as an energetic source which at the same hme can be highly monochromatic, thus effectively supplying the single excitation frequency, v. The beams have a small diameter which may be... 

Here we consider the response of the system to a monochromatic pump beam at a frequency oi. 

A strong point of EELS is that it detects losses in a very broad energy range, which comprises the entire infrared regime and extends even to electronic transitions at several electron volts. EELS spectrometers have to satisfy a number of stringent requirements. First, the primary electrons should be monochromatic. Second,... 

He Y, Pochert J, Quack M, Ranz R and Seyfang G 1995 Dynamics of unimolecular reactions induced by monochromatic infrared radiation experiment and theory for C F XI—> C F X + I probed with hyperfine-, Doppler- and uncertainty limited time resolution of iodine atom infrared absorption J. Chem. Soc. Faraday Discuss. 102 275-300... 

Evans D G, Coalson R D, Kim H J and Dakhnovskii Y 1995 Inducing coherent oscillations in an electron transfer dynamics of a strongly dissipative system with pulsed monochromatic light Phys. Rev. Lett. 75 3649... 

Luminous intensity candela cd Luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 X 10 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. 

Radiation exits the monochromator and passes to the detector. As shown in Figure 10.12, a polychromatic source of radiation at the entrance slit is converted at the exit slit to a monochromatic source of finite effective bandwidth. The choice of... 

One instrumental limitation to Beer s law is the use of polychromatic radiation instead of monochromatic radiation. Consider a radiation source that emits two wavelengths of... 

---