/Multiple Scattering

Group 1

Philipp:Distorted Wave Born Approximation, is some sort of multiple scattering, because incoming beam is split into reflected and refracted beams?

Joachim: reflection from interface can be described as scattering, in Sinha paper, they discuss scattering from infinite volume and then describe reflection. Known way to deal with reflection and refraction, this gives DWBA. Scattering is not by interfaces, they are taken into account by DWBA.

Henrich: Parratt algorithm is a dynamic approach. it takes into account multiple reflections. Do not know how it can get more precise.

reflection and refraction should be excluded from multiple scattering

If we calculate all transmission and reflection coefficients, we are left with 16 reflection and transmission combination terms. Some have different momentum transfers. this is shown like reflection/refraction, reflection/reflection. should we call this multiple scattering?

Ammat: Multiple scattering: Born approximation is single scattering event. Multiple scattering comes with further scatterign events, is not included in DWBA. magnetic interactions. when they are important, we cannot reply on Born approximation, but use multiple scattering in solid state. when first scattering event happens, system responds. this process continues. is a dynamical process, not single kinematical process.

Need to decouple between "Dynamic" term bing different than dynamic (meaning energy transfer)

Boris: full solution, we have to consider changes in the sample. even i first order scattering calculations,

Philipp (question to Boris): have you ever confused the term dynamic scattering with inelastic scattering? Boris: with ToF is feasible. 100 neV (depends on wavelengths), to see this you need reasonable resolution in pulse. perfect for SNS, here at ILL we have rather broad pulse.

experiment from Sascha Frank on standing/moving waves. if it is standing waves, density gives periodic structure and same stripes. alternatively, if we have one magnon / phonon, we have one branch (stokes/antistokes). the excitations produce the harmonic.

Philipp: we consider higher orders of BA as multiple scattering? Boris: Born series valid for amplitudes and valid within the transverse coherence lengths, that all interfaces produce one plane wave in same direction if we have lateral homogeneity and interfere with each other. but, multiple scattering when events occur in sequence but are incoherent in between of them. it could be multiple specular reflection, but gap should be greater than transverse coherence length (where particles reflect multiply within 1 cm gap). It may look like a semantic difference. You take interference between events or not? multiple scattering requires than path length is much greater than mean free path (1/Sigma_total*density of the particles).

Joachim: multiple scattering (in book of Sears) is treated in terms of transport theory. need to have a distance to avoid interference

Philipp: higher order BA should not be called multiple scattering. would it make sense to call it coherence? Boris: case of neutron guide (each reflection is quantum mechanic, superrmiror, each collision is not correlated with eachother), case of waveguide (there is resonance layer in between, it is expected with microbeam waveguide where they try to get from edge of the sample and nothing comes in, because it violates the coherence). isndie, they are all coherent from top to substrate, in substrate it goes trhough the edge. if sample is smaller than coherence length,

Philipp:Henrich, do you calculate with matrix formalism reflection and transmission in each layer and you use them to calculate incoherent multiple scattering in each particle? so, this mode that calculates z-amplitude is calculated? Henrich: this is what I want to do. Boris: if you shoot through the dge and look through the other edge, is feasible. if thre is resonance layer in between, 10 microns layer and look through the edge maybe

Boris: forming microbeams using resonance layers as waveguide is OK, only when you come from the edge. only there, you will get enhancement from the other edge. Mean free path for neutrons is cm or few mm. for 1cm , I hav one particle only.

Henrich: can I have several scattering events independently? Boris: if the distance is much greater than mean free path (1/N*Sigma_total, roughly few mm)

Philipp: multiple Boris: particle, part goes in forward direction and (multiple scattering does not play a role in reflectivity)

incoherent sum of reflectivities.

Henrich: if you come with alpha_i> alpha_c, in the deptth, you can have independent events. if alpha_i< alpha_c, multiple scattering does not play a role.

Boris: In lateral direction, wave that propagates. if we have 1m, we have

Joachim: what is typical thickness of samples in conventional SANS? Henrich: 1mm to 5mm (5mm stronger intensity. mean free path length that decides. total scattering cross-section that determines

Boris: for cold neutrons, mean free path ~few mm. but, cohereence length projection 100microns, the sample should be larger than that. we have 2 constraints (one from coherence length and one from mean free path length, both compared to sample dimension).

if sample is too long, will not prevent multiple scattering happening. as long as the coherence effects are averaged out, we can have

Boris: coherence length 0.1mm, sample size 1 cm laterally. That what we usually use to fit reflectivity, we have many thousands of these coherence spots, we averaged modulus square of reflectivity. incoherent sum of all coherence length (this is why it is proportional to projected areas on the beam). with very slow neutrons, this is possible, but nothing penetrates. example is whispering gallery. when there is multiple reflection from different mirrors circled around, one can turn direction of neutron (1cm radius and coherence length is 1mm) --> in such situation, multiple off-specular scattering. but this is curved surface