Ebook An introduction to x- ray physics, optics, and applications: Part 2
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Ebook An introduction to x- ray physics, optics, and applications: Part 2
PART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2 of light or X rays is incident on a material, photons can he absorbed, causing electrons to be emitted. From the point of view of the electron, this process is called photoelectric emission. From the point of view of the photon, it is termed photoelectric absorption. T is knock-out of an electron i Ebook An introduction to x- ray physics, optics, and applications: Part 2s the same process discussed in section 4.7 on x-ray fuorescence. although in that case the emphasis was on what happened next if the emitted electronEbook An introduction to x- ray physics, optics, and applications: Part 2
came from a core level. Absorption can be regarded as causing a fuctuation of the electron energy up to a virtual level, as shown in Figure 9-1. For PART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2n can be regarded as the fluctuation of the electron energy up to a "virtual" electron level.iron, but it is not necessary that the incoming photon energy match a dilierence in electron energy levels, as is the case for the emitted photon in x-ray fuoresccnce. illustrated in Figure 4-3.1 c rate al w Ebook An introduction to x- ray physics, optics, and applications: Part 2hich photons will be absorbed by a single atom is given in terms of a cross section ơlb for absorption.^ãb. 1 _Ebook An introduction to x- ray physics, optics, and applications: Part 2
n rate for a single atom, and ‘/'is the photon intensity, the number of photons per area per second in the beam, lor comparison, the rale Pal which phPART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2ibed in units of barns, where 1 barn= 10 24 cm2. ( T e unit is a reference to an old saying referring to someone with poor aim as not being able to hit “the broad side of a barn." A barn is a large cross section in nuclear physics.)140 a Chapter 9.A sense of the dependence of the cross section on ph Ebook An introduction to x- ray physics, optics, and applications: Part 2oton energy and atomic number can be found from a rough estimate based on a quantum mechanical calculation similar to that of equation 4-6 from sectioEbook An introduction to x- ray physics, optics, and applications: Part 2
n 4.3 on characteristic spectra. According to Fermi’s golden rule, the transition probability is proportional to the Hamiltonian matrix element H,f. wPART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2d the fnal state has the free electron and no photon. T e matrix element Hit-depends on the integral over the initial bound state of the electron (for X rays generally a K or L shell electron), and so depends on the coulomb energy, which, according to equation 4-2 is proportional to z2. so that °C z Ebook An introduction to x- ray physics, optics, and applications: Part 22. T e Hamiltonian for photon absorption includes the photon annihilation operator, which has a normalization factor of-l^oc—L^. T e condition 4Õ) VutEbook An introduction to x- ray physics, optics, and applications: Part 2
hat the kinetic energy of the ejected electron be equal to the difference between the photon energy and the electron binding energy introduces a factoPART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2tric absorption depends on the photon energy Ư and the atomic number z of the material asu9z4’(9-5)where u, = 1 keV (so that U.’UC is a unitless energy), and Ơ. is a constant. For the ejection of K shell electrons. Ơ «38.8 barns.oT e energy and atomic number dependences in equation 9-5 mean that hig Ebook An introduction to x- ray physics, optics, and applications: Part 2h-energy photons have a lower cross section and hence are more penetrating, and that high-Z materials stop photons more effectively, as was asserted iEbook An introduction to x- ray physics, optics, and applications: Part 2
n chapter 1.EXAMPLE 9-1: CROSS SECTIONNickel has atomic number 28. Silicon has atomic number 14. For photon energies of 10 and 20 keV. estimate the atPART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beam Ebook An introduction to x- ray physics, optics, and applications: Part 2 for the rest of the development in this chapter, but the results ate again useful. More discussion of quantum calculations can be found in the texts listed in the further reading for chapter 4.Photoelectric Absorption, Absorption Spectroscopy, Imaging, and Detection141 Ebook An introduction to x- ray physics, optics, and applications: Part 2PART IIIX-RAY INTERACTIONS WITH MATTER9PHOTOELECTRIC ABSORPTION, ABSORPTIONSPECTROSCOPY, IMAGING, AND DETECTION9.1 Absorption coefficientsWhen a beamGọi ngay
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