Is there a “universal” MAC equation?

Abstract

The search for an empirical absorption equation begins with the work of Siegbahn (1) in 1914. At that time Siegbahn showed that the value of (μ/ρ) for a given element could be expressed as a function of the wavelength (λ) of the x-ray photon by the following equationwhere C is a constant for a given material, which will have sudden jumps in value at critial absorption limits. Siegbahn found that n varied from 2.66 to 2.71 for various solids, and from 2.66 to 2.94 for various gases.Bragg and Pierce (2) , at this same time period, showed that their results on materials ranging from Al(13) to Au(79) could be represented by the followingwhere μa is the atomic absorption coefficient, Z the atomic number. Today equation (2) is known as the “Bragg-Pierce” Law. The exponent of 5/2(n) was questioned by many investigators, and that n should be closer to 3. The work of Wingardh (3) showed that the exponent of Z should be much lower, p = 2.95, however, this is much lower than that found by most investigators.