/Multiple Scattering - Revision history

Apostolos Vagias at 07:50, 7 April 2026

2026-04-07T07:50:04Z

← Older revision		Revision as of 07:50, 7 April 2026
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	* Reflection and refraction should be excluded from multiple scattering		* Reflection and refraction should be excluded from multiple scattering
	* Need to agree on a common nomenclature		* Need to agree on a common nomenclature
			* Need to distinct between coherent multiple scattering (whether as propagation through stratified medium or scattering from different embedded particles) and incoherent multiple scattering
	* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry		* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry
	** They have to be identified before each experiment		** They have to be identified before each experiment
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	*** When you move a liquid surface and wait for it to stop, the measurement duty cycle is poor (2 min vs seconds)		*** When you move a liquid surface and wait for it to stop, the measurement duty cycle is poor (2 min vs seconds)
	If you rotate the solid sample there is much less need to wait.		If you rotate the solid sample there is much less need to wait.
	*** ID10 at the ESRF has a good setup. DCM beam tilting is used instead to avoid moving the sample.		*** ID10 at the ESRF has a good setup. The same for BM26 with a tilted beam setup for solid-liquid interfaces. DCM beam tilting is used instead to avoid moving the sample.
	*** Get inspiration from X-rays to improve the way we measure GISANS		*** Get inspiration from X-rays to improve the way we measure GISANS
	*** Most productive groups are writing their own code and have their own ways to do experiments. Leading groups spend years analysing the data from an experiment. Writing their own code. Sharing is not common.		*** Most productive groups are writing their own code and have their own ways to do experiments. Leading groups spend years analysing the data from an experiment. Writing their own code. Sharing is not common.

Apostolos Vagias at 07:44, 7 April 2026

2026-04-07T07:44:45Z

← Older revision		Revision as of 07:44, 7 April 2026
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	** X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain		** X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain

	** Sub-cases of multiple coherent scattering and distinction from incoherent multiple scattering:		* Sub-cases of multiple coherent scattering and distinction from incoherent multiple scattering:
	In the framework of the distorted-wave Born approximation (DWBA), it is essential to distinguish between two distinct processes: (i) the propagation of the incident wave through the stratified medium, which is incorporated _exactly_ in the formalism; and (ii) the scattering from embedded “particles” (additional scattering centers) which is treated perturbatively within the 1st-order Born approximation.		**In the framework of the distorted-wave Born approximation (DWBA), it is essential to distinguish between two distinct processes: (i) the propagation of the incident wave through the stratified medium, which is incorporated _exactly_ in the formalism; and (ii) the scattering from embedded “particles” (additional scattering centers) which is treated perturbatively within the 1st-order Born approximation.
	Both (i) and (ii) are within the quantum theory (‘coherent’). Only in (i), each layer is represented by an effective static potential, simplifying the description of the background medium.		Both (i) and (ii) are within the quantum theory (‘coherent’). Only in (i), each layer is represented by an effective static potential, simplifying the description of the background medium.

	The term “multiple scattering” refers to the situation in which successive scattering events are not treated independently but are combined quantum mechanically, i.e., the amplitudes from different scattering paths are added coherently.		**The term “multiple scattering” refers to the situation in which successive scattering events are not treated independently but are combined quantum mechanically, i.e., the amplitudes from different scattering paths are added coherently.

	In contrast, “incoherent multiple scattering” denotes an approximation in which scattering from each center is treated quantum mechanically, but the subsequent propagation of scattered waves is represented within a semi-classical or ray-optical picture (Gaussian optics). This approach is conceptually analogous to the semi-classical treatment of transport phenomena based on the Boltzmann equation, where phase relations between successive scattering events are neglected.		**In contrast, “incoherent multiple scattering” denotes an approximation in which scattering from each center is treated quantum mechanically, but the subsequent propagation of scattered waves is represented within a semi-classical or ray-optical picture (Gaussian optics). This approach is conceptually analogous to the semi-classical treatment of transport phenomena based on the Boltzmann equation, where phase relations between successive scattering events are neglected.

Apostolos Vagias at 07:43, 7 April 2026

2026-04-07T07:43:28Z

← Older revision		Revision as of 07:43, 7 April 2026
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	** Diffuse scattering for X-rays at Liq-Liq interface is comparable to neutrons. The beam is below the horizon and there is an attenuated pattern seen.		** Diffuse scattering for X-rays at Liq-Liq interface is comparable to neutrons. The beam is below the horizon and there is an attenuated pattern seen.
	** X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain		** X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain

			** Sub-cases of multiple coherent scattering and distinction from incoherent multiple scattering:
			In the framework of the distorted-wave Born approximation (DWBA), it is essential to distinguish between two distinct processes: (i) the propagation of the incident wave through the stratified medium, which is incorporated _exactly_ in the formalism; and (ii) the scattering from embedded “particles” (additional scattering centers) which is treated perturbatively within the 1st-order Born approximation.
			Both (i) and (ii) are within the quantum theory (‘coherent’). Only in (i), each layer is represented by an effective static potential, simplifying the description of the background medium.

			The term “multiple scattering” refers to the situation in which successive scattering events are not treated independently but are combined quantum mechanically, i.e., the amplitudes from different scattering paths are added coherently.

			In contrast, “incoherent multiple scattering” denotes an approximation in which scattering from each center is treated quantum mechanically, but the subsequent propagation of scattered waves is represented within a semi-classical or ray-optical picture (Gaussian optics). This approach is conceptually analogous to the semi-classical treatment of transport phenomena based on the Boltzmann equation, where phase relations between successive scattering events are neglected.

Annikastellhorn at 07:31, 7 April 2026

2026-04-07T07:31:55Z

← Older revision		Revision as of 07:31, 7 April 2026
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	* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry		* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry
	** They have to be identified before each experiment		** They have to be identified before each experiment

			Detailed:
			* X-ray comparison (overlapping with topic Background):
			** MS in the end gives extra background
			** Some people use MS to enhance the signal explicitly. Or you make additional layer to enhance reflections
			** Comparing X-ray and neutron background, X-rays behave nicer in terms of MS. When absorption is strong all the scattering is from near the surface. For neutrons the absorption is weak and therefore scattering is of higher intensity.
			** Incoherent scattering cross section for hydrogen is very high and scattering attenuation of the beam penetration is limited. One has to be careful about comparing the theory for X-ray and neutrons.
			** Diffuse scattering for X-rays at Liq-Liq interface is comparable to neutrons. The beam is below the horizon and there is an attenuated pattern seen.
			** X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain


			* How to measure?
			** GIXOS grazing incidence X-ray offspecular scattering. Scattering from the object is modulated by the reflectivity, you can deduce reflectivity if you estimate the form factor.
			*** When you move a liquid surface and wait for it to stop, the measurement duty cycle is poor (2 min vs seconds)
			If you rotate the solid sample there is much less need to wait.
			*** ID10 at the ESRF has a good setup. DCM beam tilting is used instead to avoid moving the sample.
			*** Get inspiration from X-rays to improve the way we measure GISANS
			*** Most productive groups are writing their own code and have their own ways to do experiments. Leading groups spend years analysing the data from an experiment. Writing their own code. Sharing is not common.

Apostolos Vagias: Replaced content with "Short summary of discussions/breakouts: * Reflection and refraction should be excluded from multiple scattering * Need to agree on a common nomenclature * There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry ** They have to be identified before each experiment"

2026-03-19T08:02:51Z

Replaced content with "Short summary of discussions/breakouts: * Reflection and refraction should be excluded from multiple scattering * Need to agree on a common nomenclature * There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry ** They have to be identified before each experiment"

← Older revision		Revision as of 08:02, 19 March 2026
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	* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry		* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry
	** They have to be identified before each experiment		** They have to be identified before each experiment


	~~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?

	Ammar: 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:H'''enrich, 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.~~

	~~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

Annikastellhorn at 07:49, 19 March 2026

2026-03-19T07:49:55Z

← Older revision		Revision as of 07:49, 19 March 2026
Line 1:		Line 1:
			Short summary of discussions/breakouts:

			* Reflection and refraction should be excluded from multiple scattering
			* Need to agree on a common nomenclature
			* There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry
			** They have to be identified before each experiment


	Group 1		Group 1

Apostolos Vagias at 17:23, 18 March 2026

2026-03-18T17:23:30Z

← Older revision		Revision as of 17:23, 18 March 2026
Line 11:		Line 11:
	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?		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.		Ammar: 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)'''		'''Need to decouple between "Dynamic" term bing different than dynamic (meaning energy transfer)'''

Apostolos Vagias at 16:48, 18 March 2026

2026-03-18T16:48:13Z

← Older revision		Revision as of 16:48, 18 March 2026
Line 50:		Line 50:

	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.		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?		Joachim: what is typical thickness of samples in conventional SANS?

Apostolos Vagias at 14:28, 18 March 2026

2026-03-18T14:28:47Z

Apostolos Vagias at 14:07, 18 March 2026

2026-03-18T14:07:28Z

← Older revision		Revision as of 14:07, 18 March 2026
Line 31:		Line 31:
	Joachim: multiple scattering (in book of Sears) is treated in terms of transport theory.		Joachim: multiple scattering (in book of Sears) is treated in terms of transport theory.
	need to have a distance to avoid interference		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: neutron guide (each reflection is quantum mechanic, superrmiror, each collision is not correlated with eachother), waveguide (there is resonance layer in between, it is expected with microbam waveguide whre thy ry 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:Hnrich, 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 particl 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 akpha_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 neutrins, mean free path ~few mm. but, cohereence length projection 100microns, the sample should be larger than that. we have 2 constraints.

			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

← Older revision		Revision as of 14:28, 18 March 2026
Line 1:		Line 1:
	Group 1		Group 1

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

	~~Concerning slide where we define "nomenclature"~~		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.

	~~Distorted Wave Born Approximation, is some sort of multiple scattering, because incoming bam is split into reflected and refracted beams~~

	Joachim: reflection from interface can be described as scattering, in Sinha paper,~~m thye~~ discuss scattering from ~~inginite~~ volume and then describe reflection. Known way ~~tod eal~~ 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.		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		'''reflection and refraction should be excluded from multiple scattering'''

	if we calculate all transmission and reflection coefficients, we are left with 16 ~~rflection~~ and transmission combination terms. ~~some~~ have different momentum transfers. this is shown like reflection/refraction, reflection/reflection. should we call this 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. ~~Multile~~ 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.		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.

	"Dynamic" term different than dynamic (meaning energy transfer)		'''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 ~~scattring~~ calculations,		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?		Philipp (question to Boris): have you ever confused the term dynamic scattering with inelastic scattering?
Line 25:		Line 23:

	Philipp: we consider higher orders of BA as multiple scattering?		Philipp: we consider higher orders of BA as multiple scattering?
	Boris: ~~object, because~~ 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 in sequence but incoherent in between of them. it could be multiple specular reflection, but gap should be greater than transverse coherence length (where particles ~~reflct~~ multiply within 1 cm gap). may look like a semantic ~~differenc~~.~~e you~~ take interference between ~~ecvents~~ or not? multiple scattering requires than path length is much greater than mean free path (1/Sigma_total*density of the particles).		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).

	~~when BA is valid, or,~~

	Joachim: multiple scattering (in book of Sears) is treated in terms of transport theory.		'''Joachim: multiple scattering (in book of Sears) is treated in terms of transport theory.'''
	need to have a distance to avoid interference		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?		Philipp: higher order BA should not be called multiple scattering. would it make sense to call it coherence?
	Boris: neutron guide (each reflection is quantum mechanic, superrmiror, each collision is not correlated with eachother), waveguide (there is resonance layer in between, it is expected with ~~microbam~~ waveguide ~~whre thy ry~~ 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.		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,		if sample is smaller than coherence length,


	Philipp:~~Hnrich~~, 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?		Philipp:H'''enrich, 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.		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: 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 ~~particl~~ only.		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?		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)		Boris: '''if the distance is much greater than mean free path (1/N*Sigma_total, roughly few mm)'''

	Philipp: multiple		Philipp: multiple
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	incoherent sum of reflectivities.		incoherent sum of reflectivities.

	Henrich: if you come with ~~akpha_i~~> alpha_c, in the deptth, you can have independent events. if alpha_i< alpha_c, multiple scattering does not play a role.		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		Boris: In lateral direction, wave that propagates. if we have 1m, we have
Line 59:		Line 56:
	Henrich: 1mm to 5mm (5mm stronger intensity. mean free path length that decides. total scattering cross-section that determines		Henrich: 1mm to 5mm (5mm stronger intensity. mean free path length that decides. total scattering cross-section that determines

	Boris: for cold ~~neutrins~~, mean free path ~few mm. but, cohereence length projection 100microns, the sample should be larger than that. we have 2 constraints.		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		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		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