E.B. Ipatov – Ph.D. (Ph.-Math.), Associate Professor, Department of General Physics, Moscow Institute of Physics and Technology (State University)
S.P. Kuznetsov – Ph.D. (Ph.-Math.), Leading Researcher, Lebedev Physical Institute of the Russian Academy of Sciences
I.V. Meshkov – Ph.D. (Ph.-Math.), Senior Researcher, Lebedev Physical Institute of the Russian Academy of Sciences
A.V. Shelagin – Dr.Sc. (Ph.-Math.), Associate Professor, Department of General Physics, Moscow Institute of Physics and Technology (State University)
The given work continues working out of a technique of definition the parameters for the inhomogeneities (in particular, the parameters of carbon nanotubes) in non-uniform environments by means of very cold neutrons (VCN). This technique is based on the analysis of experimental data on scattering VCN at passage of neutrons through the sample and mathematical modeling of this process. The cross sections of elastic scattering are needed for the modeling is calculated in the first Born’s approximation. For the area of values of the neutron energy (energy range of VCN), in which the use of Born’s approximation is questionable, the cross sections of elastic scattering are calculated on the basis of the exact decision of the equation of Shredengira by a method of division of variables for samples of «correct» forms (spheres, cylinders, etc.). As an example in the work cross sections of elastic scattering VCN are given for an infinitely long solid cylinder, which are calculated in the first Born’s approximation and with the help of the method of separation variables. Values of differential cross section of the elastic scattering, which are calculated by these methods, for various values of velocity VCN of the sample – cylinder with radius of nm and nuclear optical potential eV, are compared. We compare the values of the total scattering cross-section, calculated on the basis of the exact solution and the Born’s approximation formulas for different values of the radius of the cylinder nm. Dependences the shifts of phase from the wave parameter are given also at neutrons scattering for the first members of rows, which describes the exact solution of the Schrödinger equation. Here, – is the wave number. The method of determining the parameters of inhomogeneities, which analyzed in the article, allows to expand the field of application of the obtained experimental data for definition of parameters of the scatterers.
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