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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, Box 518, S-751 20, Uppsala, Sweden

Computational Biology and Chemistry
|August 21, 2003
PubMed
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The total scattering cross section of non-spherical objects can depend on the incident direction, challenging common assumptions. This study uses ellipsoidal wave functions to demonstrate this angle dependence for specific potentials.

Area of Science:

  • Quantum mechanics
  • Scattering theory
  • Mathematical physics

Context:

  • Typically, total scattering cross sections are assumed to be independent of incident angles.
  • This assumption holds for spherical scatterers but may fail for non-spherical objects.

Purpose:

  • To investigate the incident angle dependence of the total scattering cross section for non-spherical scatterers.
  • To demonstrate this dependence using a theoretical framework based on ellipsoidal coordinates and Lamé wave functions.

Summary:

  • This paper introduces a method to calculate scattering cross sections for potentials separable in ellipsoidal coordinates.
  • Using perturbed ellipsoidal (Lamé) wave functions, the study derives the optical theorem and explicitly shows the incident angle dependence of the total cross section.

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  • The findings challenge the conventional view by revealing that non-spherical scatterers can exhibit significant directional dependence.

    • Impact:

    • Provides a theoretical framework and computational method for analyzing scattering from non-spherical potentials.
    • Highlights the limitations of assuming angle independence in scattering cross sections, particularly for complex geometries.
    • Offers insights into phenomena where incident directionality is crucial, with potential applications in acoustics and other wave-scattering fields.