Small-Angle Neutron Scattering at the Pulsed Reactor IBR-2: Current Status and Prospects

Crystallography Reports - Neutron diffraction studies on the small-angle neutron spectrometer YuMO (Joint Institute for Nuclear Research, Dubna), based on the IBR-2 pulsed reactor, have been...     

Refinement of estimates for some nonhomogeneous linear forms

In this paper, estimates for nonhomogeneous linear forms in values of hypergeometric functions with irrational parameters are refined. This refinement is carried out by means of an optimal choice of the degree of the zeroth polynomial appearing in the construction of approximate functional forms.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 515–521.Original Russian Text Copyright © 2005 by P. L. Ivankov.This revised version was published online in April 2005 with a corrected issue number.     

Analysis of neutron spectra and fluxes obtained with cold and thermal moderators at IBR-2 reactor: Experimental and computer-modeling studies

The results of experimental and computer-modeling investigations of neutron spectra and fluxes obtained with cold and thermal moderators at the IBR-2 reactor (Joint Institute for Nuclear Research (JINR), Dubna) are presented. These studies are for the YuMO small-angle neutron scattering (SANS) spectrometer (IBR-2 beamline 4). The neutron spectra have been measured for two methane cold moderators for the standard configuration of the SANS instrument. The data from both moderators under different conditions of their operation are compared. The ratio of experimentally determined neutron fluxes of cold and thermal moderators is shown at different wavelengths. Monte Carlo simulations have been carried out to determine the spectra for cold-methane and thermal moderators. The results of calculations of the ratio of neutron fluxes of cold and thermal moderators at different wavelengths are demonstrated. In addition, the absorption of neutrons in the air gaps on the way from the moderator to the investigated sample is presented. SANS with the protein apoferritin was done with both cold methane and a thermal moderator and the data were compared. The prospects for the use of a cold moderator for a SANS spectrometer at IBR-2 are discussed. The advantages of using the YuMO spectrometer with a thermal moderator with respect to the tested cold moderator are shown.     

Influence of weak magnetic fields on radical-pair reactions

The time dependences of the populations of radical-pair spin states and transition amplitudes between them have been calculated for constant and pulsed magnetic fields, with allowance for hyperfine interaction. The above-mentioned characteristics have been found directly by solving the Liouville equation for the radical-pair spin density matrix. It is established that the relaxation of spin-level partial populations oscillates with a monotonic decrease in the total population. Original Russian Text ? M.N. Levin, Yu.V. Ivankov, E.Yu. Ivankova, O.A. Ivanova, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 249–252.     

On Differentiation with Respect to Parameter of a Hypergeometric Function of a Special Type

We propose an effective construction of Padé approximation for the hypergeometric function of special type and its derivative with respect to parameter and this parameter is included both in numerator and denominator of the general term of the corresponding series. The aforementioned construction has been realized by means of a modification of the method that was applied earlier in simpler situations. Thus obtained approximation is made use of afterwards to establish the lower estimates of the numerical linear forms in the values of the functions under consideration. One could obtain similar estimates by the known in the theory of transcendental numbers Siegel’s method, however the estimates obtained by this method would be of less exactness.

     

Two-step mechanisms of two-proton decays of nuclei

A formalism for describing two-step two-proton decays of nuclei is developed on the basis of the multiparticle theory of deep-subbarrier one-proton decays of nuclei that employs integral expression for the decay widths in question. This formalism relies on the idea that the interaction between the emitted protons has but a slight effect on the widths with respect to the two-proton decays being considered. It is shown that such a decay is naturally broken down into the sequential one-proton decays of an (A, Z) parent nucleus and an (A ? 1, Z ? 1) intermediate nucleus, these decays being related by the Green’s function G(A ? 1, Z ? 1) that describes the intermediate nucleus with allowance for its real and virtual states, which give rise to, respectively, the sequential and the virtual two-step two-proton decay of the parent nucleus. It is also shown that the widths with respect to sequential two-step two-proton decays coincide with the analogous widths constructed within the R-matrix theory of nuclear reactions leading to the production of unstable particles and with their counterparts obtained with the aid of solving the set of kinetic equations for the chain of nuclei undergoing radioactive decays. It is found that the widths with respect to virtual two-step two-proton decays are close in structure to the widths constructed for the simultaneous two-proton decays of nuclei by using integrated formulas within a simplified model of the method of three-particle hyperspherical polynomials.