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Effective Atomic Numbers of Heterogeneous Materials


FOR a single element, the three γ-ray processes—photoelectric, Compton and pair production, can be expressed as a function of photon energy hν and the atomic number Z of the element. At a given photon energy, the interaction is proportional to Zn where n is between 4 and 5 for the photoelectric effect, 1 for the Compton effect, and 2 for pair production1,2. For the purposes of γ-ray attenuation, a heterogeneous material, consisting of a number of elements in varying proportions, can be described as a fictitious element having an effective atomic number Zeff. In the study of the X-ray energy absorption of certain biological specimens Spiers3 used the expression Z2.94eff = ɛαiZ2.94i, where Zi is the atomic number of the ith element and αi its fractional electronic content. More recent measurements4 favour a value of 3.1 instead of 2.94 for the exponent for Zeff. Glasser5, in radiological studies, used the expression Z3eff = ɛpiZ4ipiZi, where pi is the fractional part by weight of the whole mixture occupied by the element the atomic number of which is Zi. Extending this idea of the effective atomic number of a material for specific radiation, Hine4 pointed out that there is a different effective atomic number for each absorption process in a heterogeneous material, but he could obtain expressions only for the photoelectric and pair production processes as Z3.1eff = ɛpiZ3.1i, and Zeff = ɛpiZi. It can easily be shown that pi and αi are very nearly equal6. The equations of Spiers and Hine may then be expressed as Zn−1 = ɛpiZn−1i, where n has values of 4 to 5, 1 and 2, respectively for the photoelectric, Compton, and pair production processes. Hence, an expression for the effective atomic number for the Compton effect could not be obtained. In this communication the validity of these differing expressions is examined and a single effective atomic number is suggested for a heterogeneous material.

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MURTY, R. Effective Atomic Numbers of Heterogeneous Materials. Nature 207, 398–399 (1965).

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