Photon Energy Absorption Coefficient

If photoelectric effect or pair production takes place, all the energr of the gamma is deposited there. 

If Compton scattering occurs, only the energr of the electron is absorbed. The Ctompton-scattered gamma escapes. 

In the case of photoelectric effect, assumption (1) is valid. For pair production, however, it is questionable because only the ener r - 1.022 MeV is given to the electron-positron pair. The rest of the energy, equal to 1.022 MeV, is taken by the two annihilation gammas, and it may not be deposited in the medium. There are cases when Eq. 4.65 is modified to account for this effect. Gamma absorption coefficients, as defined by Eq. 4.65, are given in App. D. 

Example 4.18 A ICi Cs source is kept in a large water vessel. What is the energy deposited by the gammas in H2O at a distance 0.05 m from the source  

Answer Cs emits a 0.662-MeV gamma. The mass absorption coefficient for this photon in water is (App. D) 0.00327 m /kg. The total mass attenuation coefficient is 0.00862 m /kg. The energy deposited at a distance of 0.05 m from the source is (E = 

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The depth-profile of photon absorption is analogous to that for UV-visible light, i.e. I = Io exp(-Ad), where the mass energy absorption coefficient, u/g is used instead of the extinction coefficient. Particulate energy absorption can be described by relative stopping powers. 

J.H. HubbeU, Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from lOkeVto 100 GeV, NSRDS-NBS 29 (1969). 

A particularity of some of these materials, such as Qn(TCNQ)2 and TEA(TCNQ)2, is that they contain only elements H, C, or N, not heavy atoms. In consequence, their mass energy-absorption coefficients at low photon energies are about the same as those of various substances of special dosimetric interest, such as water, biological tissues, or polymers. 

Dosimeters that are sufficiently small, such as thin radiochromic films and alanine pellets, can readily be calibrated against the calorimeter, by irradiating in tandem (with a suitable radiation monitor) while encased in a phantom material that is identical in size, shape and substance to the calorimetric absorber. The main appreciable correction that is required is the ratio of mass energy-absorption coefficients of the two materials (in the case of photon irradiations) or the ratio of mass collision stopping powers of the two materials (in the case of electron beam irradiations) (McLaughlin et al., 1989). 

Since the momentum of photons, h/A, is small compared with the crystal momentum, hla (a is the lattice constant), the momentum of electrons should be conserved during the absorption of photons. The absorption coefficient a hv) for a given photon energy is proportional to the probability, P, for transition from the initial to the final state and to the density of electrons in the initial state as well as to the density of empty final states. On this basis, a relation between absorption coefficient a and photon energy ph can be derived [2, 4]. For a direct band-band transition, for which the momentum remains constant (see Fig. 1.7), it has been obtained for a parabolic energy structure (near the absorption edge) ... 

Number of photons/ MeV of particle energy - Absorption coefficient at 150 kev particle energy (cm ) Use XCT = x-ray computer tomography, PET = Positron emission tomography, Nucl = nuclear emission detection... 

Seltzer SM (1993) Calcttlation of photon mass energy-transfer and mass energy-absorption coefficients. Radiation Res 136 147-170... 

Table 2.2. Photon interaction and energy absorption coefficients for common materials"...

Pe /p) is the mass energy absorption coefficient in air for photons of energy... 

Reproduced with permission from Hubbell JH (1969) Photon cross-sections, attenuation coefficients, and energy absorption coefficients from 10keV to lOOGeV, NSRDS-NBS29. Washington, DC National Bureau of Standards. 

Here fi is they-ray linear attenuation coefficient, usually measured in cm units. It is a sum of the interaction terms described in O Chap. 6 in this Volume, hence it is also called total attenuation coefficient. Its inverse is called the mean free path, while the thickness reducing the photon beam by half is the half-thickness di/y, both are measured in cm. Frequently the mass attenuation coefficient pip is used, because it does not depend on the physical state of the material. Its dimension is cm /g if the density p is given in g/cm units. Another important quantity is the mass-energy absorption coefficient p Jp, measured in the same units, which characterizes the energy deposition by photons. AH these quantities, their units and usage have been defined by the International Commission on Radiation Units and Measurements (ICRU) in ICRU Report 33 (ICRU 1980), which has recently been superseded by two new ones (ICRU 1993c, 1998). 

Hubell, J. H. (1982). Photon mass attenuation and energy-absorption coefficients from IkeV to 20MeV, Int. J. Appl. Radiat. Isotopes, 33, 1269-1290. 

Fig. 3. Spectra showing absorption coefficient as a function of the photon energy in a direct band gap semiconductor where (—) represents absorption,...

In amorphous semiconductors, information about the width of the band tail states (or disorder) may also be extracted from the optical absorption spectra. For photon energies near bandgap energy, the optical absorption coefficient of amorphous semiconductors exhibit an exponential dependence on the photon energy, following the so-called Urbach relationship ... 

Both WDXRF and EDXRF lend themselves admirably to quantitative analysis, since there is a relationship between the wavelength or energy of a characteristic X-ray photon and the atomic number of the element from which the characteristic emission line occurs. The fluorescence intensity of a given element is proportional to the weight fraction. Emitted fluorescence radiation is partly absorbed by the matrix, depending on the total mass absorption coefficient ... 

Band-gap energies between 1.45 eV and 1.47 eV were obtained for the films. The band-gap energies were estimated using plots of (ahv)2 versus E (Fig. 6.23), where a is an absorption coefficient estimated from optical transmittance data and hv is the photon energy. Figure 6.23 shows that the band edge... 

PHOTON ENERGY (eV) Figure 18. Plots of logarithmic absorption coefficient to the incident photon energy for the low-energy tail of the J-band of [CI-MC] with [L-MS], at various temperatures, with [L-MS], at various temperatures. 

AAS measures the discrete radiation absorbed when ground state atoms are excited to higher energy levels by the absorption of a photon of energy. The radiant power of the absorbed radiation is related to the absorption coefficient of the ground state atoms using the... 

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