On the Extinction Paradox

• Authors: W. Żakowicz
• Languages of publication: EN

Abstracts

EN

The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σ^Q=2π a^2=2σ^C for ka ≫ 1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrödinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w ≫ a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R ≫ waλ. Moderately narrow beams (1≪ w≪ a) behave as classical trajectories, and their scattering can be described in classical terms. Thus, the classical limit of quantum scattering requires not only that the de Broglie wavelength λ_B is much smaller than the size of the scatterer (a ≫ λ_B), but also that the transverse width of beams of de Broglie's waves is small, w≪ a.

Keywords

EN

32.80.Cy; 42.25.Fx; 61.10.Dp

Discipline

• 42.25.Fx: Diffraction and scattering

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2002
• Volume: 101
• Issue: 3
• Pages: 369-385

Dates

published

2002-03

received

2001-06-20

Contributors

author

W. Żakowicz

• Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, Warsaw 02-668, Poland

References

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• 9. W. Zakowicz, submitted to Phys. Rev. E
• 10. D.H. Perkins, Introduction to High Energy Physics, Polish Scientific Publishers PWN, Warsaw 1989 (in Polish)

Identifiers

DOI

10.12693/APhysPolA.101.369