The primary interaction of low-energy x rays within matter, viz. photoabsorption and coherent scattering, have been described for photon energies outside the absorption threshold regions by using atomic scattering factors, f = f1 + i f2 The atomic photoabsorption cross section, µa may be readily obtained from the values of f2 using the relation,

μ<SUB>a</SUB> = 2 × r<SUB>0</SUB> × λ × f<SUB>2</SUB>

where r0 is the classical electron radius, and λ is the wavelength. The transmission of x rays through a slab of thickness d is then given by,

T = exp (- N µa d),

where N is the number of atoms per unit volume in the slab. The index of refraction n for a material is calculated by,

n<SUB>r</SUB> = 1 - <em>n</em> r<SUB>0</SUB> λ <SUP>2</SUP>
(f<SUB>1</SUB> + <em>i</em> f<SUB>2</SUB>)/(2π)

These (semi-empirical) atomic scattering factors are based upon photoabsorption measurements of elements in their elemental state. The basic assumption is that condensed matter may be modeled as a collection of non-interacting atoms. This assumption is in general a good one for energies sufficiently far from absorption thresholds. In the threshold regions, the specific chemical state is important and direct experimental measurements must be made. Note also that the inelastic Compton scattering cross section (from ref. 2) has been included in the transmission calculations of a solid and of a gas but not in the others. The Compton cross section is significant for the light elements (Z < 10) at the higher energies considered here (10 keV to 30 keV).

These tables are based on a compilation of the available experimental measurements and theoretical calculations. For many elements there is little or no published data and in such cases it was necessary to rely on theoretical calculations and interpolations across Z. In order to improve the accuracy in the future considerably more experimental measurements are needed.


  1. B.L. Henke, E.M. Gullikson, and J.C. Davis, X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92, Atomic Data and Nuclear Data Tables 54 no.2, 181-342 (July 1993).
  2. J.H. Hubbell, W.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer, and R.J. Howerton, Atomic Form Factors, Incoherent Scattering Functions, and Photon Scattering Cross Sections, J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in 6, 615-616 (1977).

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© 1995