Anomalous scattering factors of some rare earth elements evaluated using photon interaction cross-sections

Abstract

The real and imaginary parts, f ¼´E µ and f ¼¼´E µ of the dispersion corrections to the forward Rayleigh scattering amplitude (also called anomalous scattering factors) for the elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er, have been determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoeffect cross-sections. The photoeffect cross-sections are derived from the total attenuation cross-section data set experimentally determined using high resolution high purity germanium detector in a narrow beam good geometry set-up for these elements in the photon energy range 5 to 1332 keV and reported earlier by the authors. Below 5 keV, Scofield's photoeffect cross-sections compiled in XCOM program have been interpolated and used. Simple formulae for f ¼¼ in terms of atomic number and energy have also been obtained. The data cover the energy region from 6 to 85 keV and atomic number Z from 57-68. The results obtained are found to agree fairly well with the other available data.

X-ray attenuation around K-edge of Zr, Nb, Mo and Pd: A comparative study using proton-induced X-ray emission and 241Am gamma rays

“…The intensities of X-rays available from such sources also are comparatively low for scattering studies and photoelectric measurements, though they may be sufficient for attenuation measurements. The investigations by Ramachandran et al [6], Appaji Gowda et al [7,8], Budak et al [9], Tajuddin et al [10] are typical examples of the use of this method.…”

Determination of the anomalous scattering factors of high-Zatoms using bremsstrahlung radiation

“…Similarly, several investigators have experimentally determined atomic form factors for various elements at various energies [25][26][27][28][29][30][31][32][33][34][35][36]. Normally, two methods are adopted for measuring the form factors, namely the direct method and the attenuation method.…”

“…Normally, two methods are adopted for measuring the form factors, namely the direct method and the attenuation method. The direct method is based on (a) measurement of reflection and refraction [25,26], (b) determination of the intensities of the Bragg reflected rays [27,28] and (c) x-ray interferometry [29,30], However, the measurement of atomic form factors using the attenuation method is more reliable [31][32][33][34][35][36] and does not suffer from the problems associated with the other methods. The other advantage of the attenuation method is that the atomic form factors can be determined for a laiger range of atomic numbers over a wider range of x-ray or gamma-ray energies.…”

“…In the case of silicon, they have used synchrotron radiation of energy from 5 keV to 20 keV and for silver the energy range is 15-50 keV. Appaji Gowda et al [34] have determined the anomalous scattering factors for La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er in the energy range from 6 keV to 85 keV using the gamma-ray attenuation method. Here, they have used monoenergetic gamma sources for measuring the attenuation co-efficient.…”

Dispersion corrections to the forward Rayleigh scattering amplitudes around the L‐shell of tantalum and lead

“…The attenuation coefficient method can also be used to obtain the dispersion corrections f 0 and f 00 . Sandiago et al, 14 Umesh et al 5 and Appaji Gowda et al 15 have evaluated dispersion corrections around the K-shell for the elements Cu, Ag, Zr, Sn, La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er, in the energy range 5-84 keV using the attenuation coefficient method. Drier et al 16 have reported results for Ni, Cu, Zn and Zr around the K-edge and for Ta, W, Pt and Au around the respective L-edges.…”