Volume 3, Number 1 (2018)
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Home > Journals > SCIREA Journal of Physics > Archive > Paper Information

Scattering of scalar waves on a single crystalline plane

Volume 3, Issue 1, February 2018    |    PP. 35-51    |PDF (677 K)|    Pub. Date: January 7, 2018
130 Downloads     794 Views  

Author(s)
Ignatovich V.K., Doctor of phys.-math. Sc. leading scientist Of Laboratory of Neutron Physics of the Joint Institute for Nuclear Research, Dubna RF

Abstract
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.

Keywords
neutron optics, diffraction, multiple waves scattering, spherical waves.

Cite this paper
Ignatovich V.K., Scattering of scalar waves on a single crystalline plane, SCIREA Journal of Physics. Vol. 3 , No. 1 , 2018 , pp. 35 - 51 .

References

[ 1 ] Paul Peter Ewald ``Kristalle und Röntgenstrahlen'' (Springer, 1923)
[ 2 ] G.E. Bacon ``Neutron Diffraction'' Oxford University Press 1955.
[ 3 ] R.T. Bush ''The Ewald Construction and the Bragg Law of Diffraction in a First Course in Solid-State Physics.'' Am. J. Phys. 37, 669 (1969)
[ 4 ] B. D. Hall ``Introductory crystallography for solid-state physics: Computer simulations in two dimensions.'' Am. J. Phys. 66, 19 (1998).
[ 5 ] M. Utsuro, V. K. Ignatovich, “Handbook of Neutron Optics” (Wiley-VCH, Weinheim, 2010).
[ 6 ] Ignatovich VK. Contradictions in scattering theory. Concepts of
[ 7 ] Phys. 1 51-104 (2004).
[ 8 ] It is common to write sign + before scattered spherical wave, but it is more appropriate to write there minus, which means redefinition of the sign of the scattering amplitude b. With such a choice positive b corresponds to positive optical potential of a medium u=4πN0b, where N0 is atomic density of the medium [5].
[ 9 ] Foldy L.L. ``The multiple scatteling of waves.'' Phys.Rev. 67 (3) 107-19 (1945)
[ 10 ] Lax M. ``Multiple scattering of waves''. Rev.Mod.Phys. 23 287-310 (1951).
[ 11 ] Lax M. ``Multiple scattering of waves II. The Effective Field in Dense Systems''. Phys.Rev. 85 (4) 621-629 (1952).
[ 12 ] Glasser M.L. ``The evaluation of lattice sums. I. Analytic procedures.'' J.Math. Phys. 14 (3) 409-413 (1973).

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