Molecular Form Factors and Photon Coherent Scattering Cross Sections of Water

Abstract

Tabulations are presented of molecular form factors F (x), tor values of.t = sin(tJ /2)1 A from 0 to 1.25 A -1, for liquid ,,:ate~ at eight temperatures b~t~een 4 °C andl200 °C and for the free water molecule. For bqUld water, x = 0 to 1.25 A 1, the tabulated values are interpolated from exper!menta1 values of Narten and Levy (1971). For~he free water molecule, x = 0 to 1.25 A -1, the tabulated values are interpolated from calculated values of . For x = 1.25to 10 9 A-I, the independent atomic scatterin~ hypothesis is assumed and the water molecular form factor F (x) is calculated from thel hydrogen and oxygen atomic form factors given by Hubbell and Overbo (1979). Tabl~s of coherent scattering cross sections, obtained by numerical integration of the ThoJnson formula, weighted by F2(X), are presented for liquid water at eight temperatures be~ween 4 °C and 200 °C and for the free water molecule, for photon energies 5 ke V to 1 MeiV.

X-ray scattering intensities of water at extreme pressure and temperature

“…[29]), but similarly are not applicable to the extreme thermodynamic conditions of this work. As a result, we have chosen to normalize to the form factor calculated by the independent atomic scattering method (IAM) [29]. Ultimately, the choice of parameters for normalization are unimportant for the scope of this work., since we have focused our efforts on comparing I(Q)calculated by different methods, and on the determination of improved atomic scattering factors.…”

“…Molecular form factors for water at lower temperature and pressure are available (e. g., Ref. [29]), but similarly are not applicable to the extreme thermodynamic conditions of this work. As a result, we have chosen to normalize to the form factor calculated by the independent atomic scattering method (IAM) [29].…”

CTmod—A toolkit for Monte Carlo simulation of projections including scatter in computed tomography

“…Cross sections and incoherent scattering functions were obtained from the EPDL97 data library. Molecular form factors for water were obtained from Morin [39]. Figure 12 shows the the estimate of mean energy imparted per unit area to a detector element i by primary, I p (i), and scattered, I s (i), photons.…”

Integral-transport-based deterministic brachytherapy dose calculations

“…Rayleigh scattering cross section is described in terms of atomic form factor as shown in equation (4.5) and the data for water is from Morin, 1982. [114] where /V is number of atoms in unit volume,…”