Mass-energy absorption coefficient

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. 

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. 

Mass energy absorption coefficients in air and in muscle are somewhat similar between 0.01 to 3.0 MeV. Energy loss/ unit length is obtained by multiplying absorption coefficients by density (kg/m ). This LET particle can penetrate much further into tissue. Thus, radiation dose is distributed over much greater areas, tending toward diffuse as opposed to focal distribution (Harley, 2001, 2008). 

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). 

Table D2 Mass Energy Absorption Coefficients in cm / for Gamma Rays ...

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

Mass energy absorption coefficient Mass stopping power... 

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

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). 

Another useful program is the PC code XMuDat by Nowotny (1998) which is furnished with the databases of Hubbell and Seltzer (1995) and Boone and Chavez (1996). Total mass attenuation coefficients, mass-energy absorption coefficients and half-thicknesses of some representative elements and materials have been calculated with XMuDat and plotted in O Figs. 11.8-11.13 for illustration. 

Mass-energy absorption coefficients for various human tissues (ICRU-44) and liquid water... 

HubbeD, J.H. and Seltzer, S.M. (1996) Tables of X-Ray mass attenuation coefficients and mass energy-absorption coefficients. NISTIR, 5632. Available at ... 

Each of these is characterized by a mass attenuation coefficient which are, respectively, r/p, o/p and zc/p. To each there is a corresponding total energy absorption coefficient. The mass attenuation and absorption coefficients for aluminium and water are given in Fig. 1. 

Radiation exposure is defined as the energy deposited by radiation per unit mass. For a gamma ray emitted by a point source, the radiation exposure rate i is related to the gamma-ray decay fraction /, the gamma-ray energy E (in MeV), the activity of the radionuclide a(in Bq), the linear energy absorption coefficient /u-a, the density of air p, and the distance x ... 

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

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

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 ... 

Figure 1. Calculated mass absorption coefficient vs. x-ray energy for N-allylmaleimide copolymers.

Here, L total is the depth of the etched hole per pulse and is assumed to be the sum of photochemical and photothermal contributions, Tphoto and Thermal, respectively 0Ceff is the effective photon absorption coefficient of the medium and can vary with laser emission characteristics, e g., photon density Fis the incident laser fluence Fth is the medium s threshold fluence A and F are the effective frequency factor with units of pm/pulse and the effective activation energy with units of J/cm2, respectively, for the zeroth-order thermal rate constant F0, comparable in magnitude to Fth, is important only at low fluences.64 Equation (5) is obtained after assuming that the polymer temperature T in the laser-exposed region of mass mp and the thermal rate constant k are given, respectively, as... 

X-Ray Absorption Data. The x-ray absorption data shown in Figure 2 were obtained using a computer program based on the mass absorption coefficients, y, total energy, as found in the paper of Storm and Israel (1 ) and using the fundamental absorption equation for x-rays (II). 

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