The Theory of Neutron Diffraction by Gases. I

Abstract

An expression for the total, elastic and inelastic, differential cross section for scattering of thermal neutrons by a rigid polyatomic molecule is derived. In summing over the final rotational states of the molecule the change in energy of the neutron is assumed negligibly small compared to the neutron's initial energy. The validity of this approximation is discussed. The rigidity of the molecule is then relaxed and the expression obtained for the cross section amended to take account of the vibrational motion of the nuclei. It is shown that the elastic scattering from a vibrating molecule is equivalent to that from a set of uncoupled anisotropic oscillators placed at the mean nuclear sites. Detailed results are given for spherical top molecules of the type YX4. Good agreement is found with the experimental pattern of carbon tetrafluoride but not with that of methane.

A neutron inelastic scattering study of the chloroethanes

“…The intensities of these transitions in the neutron crosssection can be deduced from the general expression obtained by Pope [8] (7) is the cross-section for a scattering event in which the neutron gains a quantum of energy h~ol from the j= 1 normal mode, and Zl=exp (-hcol/kBT).…”

“…The matrices in [8] have their usual significance [9,10], and the matrix C of the vectors r is given by T= M-1/2C. Figures 1 (a)-I (f) show the time-of-flight spectra for the different chloroethanes at various angles of scatter.…”

The aqueous-polyelectrolyte dye solution as an active laser medium

“…More than 50 years of research have been devoted to the development of calculation methods and models able to describe the scattering of slow and thermal neutrons from simple molecular systems, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] representing only part of the huge work on the subject. Most studies on the dynamical response to neutrons of light molecular gases and liquids-mainly hydrogen and methane-were stimulated, beyond their fundamental physical significance, by important applications in the field of neutron science and technology (e.g.…”

“…moderators in neutron sources, cold neutron sources, neutron shielding, etc). As a matter of fact, the general interest in the refinement of models for the computation of the neutron differential cross-sections (either self or distinct, or both, as explained in the following sections) of simple molecules such as hydrogen, methane, their heavy counterparts (D 2 , CD 4 ) and, to some approximation, of other di-and polyatomic fluids, has never faded through the years. This is partly due to the experimental work devoted, in the last decade and at present, to the accurate determination of the microscopic static structure of quantum and classical molecular fluids by neutron diffraction techniques [19][20][21][22][23][24][25], which requires both a reasonable evaluation of the inelastic contributions to the scattered intensity and a good modelling of the intra-and intermolecular neutron cross-sections, necessary to allow for the extraction of the centre-of-mass (CM) structure factor of the measured samples.…”

“…Of course, several original contributions are reported also. The case of the hydrogens (H 2 and D 2 ) will be discussed, as well as that of methane (CH 4 and CD 4 ). For the latter, a smooth quantum-mechanical calculation, also allowing for the treatment of the lowest vibrational transitions, is proposed here and tested against experimental data.…”