Limits of validity of trajectory simulation: correlation of the error with density of scatterers and particle wavelength
2009 (English)In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, ISSN 0168-583X, Vol. 267, 3409-3419 p.Article in journal (Refereed) Published
To a first approximation, the elastic scattering of long wavelength particles in amorphous matter may be modelled as scattering in a volume filled with a density n of N point scatterers in random positions. For not too large N (up to about 2×103), the error in trajectory simulation (classical transport theory) due to the neglect of interference effects can then be determined in detail by means of a comparison with an exact quantum calculation of the plural or multiple scattering process. A relative error RE is defined and calculated for the scattering in different directions as well as for the distribution of scattering events inside the volume. A very strong correlation is found between the relative error and the ratio λ/dnn, where λ is the wavelength of the incident particle and dnn=n-1/3 is an average distance between nearest neighbour scatterers. For scattering in a volume of dimensions large compared to the particle wavelength, present calculations suggest that the correlation can be described as RE≈a·(λ/dnn)b, where the parameters a<0.05 and b∼2 depend on the s-wave phaseshift δ0 in the scattering process. The condition for validity of trajectory simulation, defined in terms of a limit of validity L (maximum acceptable relative error), may thus be written λ/dnn<ξ, where ξ=(L/a)1/b∼1. For λ/dnn<1, the relative error is generally less than 5%, and trajectory simulation may be regarded as valid with at least 95% accuracy. In the exact quantum calculation, two features of pronounced quantum character are observed in the distribution of scattering events: oscillations due to quantum interference in finite volumes, and, for small negative δ0, randomly localized peaks due to proximity resonance.
Place, publisher, year, edition, pages
Elsevier , 2009. Vol. 267, 3409-3419 p.
Transport theory, Multiple scattering, Point scatterer
Other Physics Topics
Research subject Physics
IdentifiersURN: urn:nbn:se:su:diva-30106DOI: 10.1016/j.nimb.2009.08.013ISI: 000271252300004OAI: oai:DiVA.org:su-30106DiVA: diva2:241454