Abstract Taking into consideration the changes of the geometric shielding effect in a molecule as the energy of incident electrons varies, this paper presents an empirical fraction, which depends on the energy of incident electrons, the target's molecular dimension and the atomic and electronic numbers in the molecule. Using this empirical fraction, it proposes a new formulation of the additivity rule. Employing the new additivity rule, it calculates the total cross sections of electron scattering by C$_{2}$H$_{4}$, C$_{6}$H$_{6}$, C$_{6}$H$_{14}$ and C$_{8}$H$_{18}$ over the energy range from 50 to 5000 eV. In order to exclude the calculation deviations caused by solving the radial Schrödinger equation of electron scattering by atoms, here the atomic cross sections are derived from the experimental total cross section results of simple molecules (H$_{2}$, O$_{2}$, CO) via the inversion algorithm. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, even at energy of several tens of eV.
Received: 10 October 2007
Revised: 09 November 2007
Accepted manuscript online:
(Calculations and mathematical techniques in atomic and molecular physics)
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10574039) and the
Program for Science and Technology Innovation Talents in
Universities of Henan
Province in China (Grant No 2008HASTIT008).
Cite this article:
Shi De-Heng(施德恒), Sun Jin-Feng(孙金锋), Zhu Zun-Lüe(朱遵略), and Liu Yu-Fang(刘玉芳) Additivity rule for electron--molecule total cross section calculations at 50--5000eV: a new geometrical approach 2008 Chin. Phys. B 17 2103
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