Volume 13: Pages 344-349, 2000

SPECIAL ISSUE IN HONOR OF PROF. UGO FANO — PART 2

Electron Scattering from Polar Molecules: Frame Transformation and the Born Closure Approximation

Yukikazu Itikawa ¹

¹Institute of Space and Astronautical Science, Yoshinodai, Sagamihara 229‐8510 Japan

In 1972, E.S. Chang and U. Fano published a monumental paper [Phys. Rev. A 6, 173 (1972)] in which they clearly showed the connection between the laboratory‐frame and the body‐frame treatments of electron collisions with molecules. They further proposed a mixed use of the two treatments to simplify the calculation. For an electron scattering from a polar molecule, the fixed‐nuclei approximation, which is widely employed, results in a cross section divergent at the forward‐scattering angle. This is caused by the slow convergence of the partial wave expansion due to the very long range interaction between the incident electron and the dipole moment of the target molecule. To avoid this difficulty, the Born closure formula is applied to the distant collision, together with the fixed‐nuclei approximation for the close collision. This is essentially the same philosophy as the approach proposed by Chang and Fano. Recently the present author proposed another way of treating the electron‐polar‐molecule collision, in which the Born closure formula is applied to the scattering amplitude. With this new method, it is much easier to confirm the convergence of the partial wave expansion and hence to obtain a reliable cross section. The present paper reviews the theoretical treatments of the electron scattering from polar molecules and thereby clarifies the role played by Prof. Fano in electron‐polar‐molecule collisions.

Keywords: electron collision, polar molecule, frame transformation, fixed‐nuclei approximation, Born closure

Received: April 25, 2000; Final version received: December 15, 2008