nanoparticles
Model nanoparticles in a gas scattered by ultra-cold neutrons with mathematical analysis of energy transfer probabilities. Examines differential and total cross-sections, nanoparticle size, density, and substance impact, and implications for ultra-cold neutron heating. A detailed investigation using Maxwell-Boltzmann distribution to understand the phenomenon.
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Presentation Transcript
GRANIT 2014 UCN scattering by a gas of nanoparticles V.Nesvizhevsky, A.Voronin, A.Lambrecht, S. Reynaud New Journal of Physics, 14 (2012) 093053
Model Nanoparticles form a gas, bounded to a vessel surface via Casimir-van der Waals forces Nanoparticle gas follows classical statistics (Maxwell-Boltzman distribution) UCN are elastically scattered by individual nanoparticles in c.m. system
Questions What is the probability of energy transfer from nanoparticles to ultra-cold neutrons in lab system (differential and total cross-sections)? How the size, density, substance of nanoparticle enters the problem? Can a model of nanoparticle gas explain the known facts on UCN small heating?
Energy transfer M m 5 = = (cos ' cos ) / 10 ( ' ) E V k k Vk 0 k c.m. neutron momentum 0 d dE = = ( , ', , '| 2 | cos( ') ' dE f d d cm = ( ) f q f cm
Probability of energy transfer detection 3 2 kT = V 3 R
Energy transfer integral count Diamond R=9.8, 9.4, 9.0 nm , nm2 , nm2 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 E, cm E, cm 40 60 80 100 120 140 40 60 80 100 120 140
Differential spectrum Steel R=6.6, 6.3, 6.0 nm
First comparison Steel 6.6, 6.3, 6.0 nm
Nanodroplets Fomblin nanodroplets R-10.4, 10, 9.6 nm
To be taken into account Nanoparticle one-dimensional bounding: 1 ( ) N V d dE M kT = ( , ) ( , , ) E 2 2 2 ( ) exp( ) | | E dV t k V E dk MV ' ' 0 0 N N NN 2 kT 2 mk , ' N N n ?? ?=< ? |exp( ?? ?)|? > Corrections to Born amplitude for large R (R>5nm) f f B Multiple scattering Proper? statistics
