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Angle dependent total cross sections and the optical theorem.

T V Levitina1, E J Brändas

  • 1Department of Quantum Chemistry, Uppsala University, Sweden. tya@levitin.mccme.ru

Computers & Chemistry
|January 12, 2001
PubMed
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The total scattering cross section of non-spherical objects can depend on the incident direction, contrary to common assumptions in low-energy scattering. This study demonstrates this angle dependence using ellipsoidal wave functions for specific potentials.

Area of Science:

  • Physics
  • Acoustics
  • Quantum Mechanics

Background:

  • Scattering cross sections are often assumed to be independent of incident angles.
  • This assumption is common in low-energy scattering and based on spherical symmetry.
  • However, this assumption may not hold for non-spherical scatterers.

Purpose of the Study:

  • To demonstrate that non-spherical scatterers can exhibit strong dependence of the total scattering cross section on the incident direction.
  • To derive the optical theorem for potentials separable in ellipsoidal coordinates, explicitly showing incident angle dependence.
  • To illustrate these findings with calculations and discuss unexpected behaviors.

Main Methods:

  • Representing scattering data using perturbed ellipsoidal (Lamé) wave functions for potentials separable in ellipsoidal coordinates.

Related Experiment Videos

  • Expanding the total scattering cross section in terms of these functions.
  • Utilizing results from classical acoustic scattering by a triaxial ellipsoid.

    • Main Results:

    • The total scattering cross section explicitly demonstrates dependence on the incident direction for potentials separable in ellipsoidal coordinates.
    • Calculations show unexpected behaviors in the total cross section versus incident direction.
    • The general character of the ellipsoidal coordinate system is highlighted.

    Conclusions:

    • The assumption of incident angle independence for total scattering cross sections is not universally valid, particularly for non-spherical scatterers.
    • Ellipsoidal wave functions provide a suitable framework for analyzing angle-dependent scattering.
    • The study emphasizes the importance of considering geometric factors in scattering phenomena.