THEORY OF COLD NEUTRON SCATTERING BY HOMONUCLEAR DIATOMIC LIQUIDS: I. FREE ROTATION

1966 ◽  
Vol 44 (6) ◽  
pp. 1279-1297 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Cross Section ◽  
Born Approximation ◽  
Cold Neutron ◽  
Intermolecular Forces ◽  
Inert Gases ◽  
Jones Potential ◽  
Lennard Jones ◽  
Law Of Corresponding States ◽  
Homonuclear Diatomic Molecules

The cold neutron scattering cross section for a system of homonuclear diatomic molecules with arbitrary nuclear spin and an arbitrary ortho–para ratio is calculated in first Born approximation, assuming that the molecular rotation is unhindered. The cross section is expressed in the form of an expansion in terms of the angular momentum transfer. This expansion is shown to be rapidly convergent for all the permanent homonuclear diatomic liquids. To the extent that the intermolecular forces are described by an isotropic Lennard-Jones potential, the terms in the expansion can be calculated with the help of the law of corresponding states and the observed scattering functions for the condensed inert gases. The problem of neutron diffraction by homonuclear diatomic liquids is also investigated.

scholarly journals Anharmonic Self-Consistent Theory of Crystals. II. The 2d and 3d Quartic Crystal Models

1994 ◽  
Vol 49 (6) ◽  
pp. 663-670
Author(s):  
S. Sh. Soulayman ◽  
C. Ch. Marti ◽  
Ch. Ch. Guilpin
Keyword(s):  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Three Dimensional ◽  
Inert Gases ◽  
Thermoelastic Properties ◽  
Consistent Theory ◽  
Jones Potential ◽  
Lennard Jones ◽  
2D And 3D ◽  
Strong Anharmonicity

Abstract In this paper we apply the method developed in part I for describing the crystalline state of two and three dimensional inert gases. For strong anharmonicity of fourth order, the equations of state of these gases are obtained. This way we calculate the thermoelastic properties of two and three dimensional argon, krypton and xenon using the Lennard-Jones potential. The corrections to the Helmholtz free energy and thermodynamic properties due to quantum effects are considered. The results are compared with the available experimental data.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

Variational determination of the coefficient of sound dispersion in binary gas mixtures

1988 ◽  
Vol 188 ◽  
pp. 205-221 ◽  
Author(s):  
P. Riesco-Chueca ◽  
J. Fernandez De La Mora
Keyword(s):  
Sound Speed ◽  
Inert Gases ◽  
Enskog Theory ◽  
Boltzmann Equations ◽  
Jones Potential ◽  
Lennard Jones ◽  
Exact Determination ◽  
Sound Dispersion ◽  
Zero Frequency

The propagation of plane linear acoustic wave in a mixture of inert gases is considered by means of a variational formulation of the Boltzmann equations, through which the sound speed c is expressed with errors of order ε2 in terms of trial functions determined with errors of order ε. This feature allows the exact determination of the coefficient of sound dispersion d2 ≡ [dc/dω2] at zero frequency (ω = 0), in terms of trial functions known from the Chapman—Enskog theory. Explicit results for d2 are given for all combinations of noble gases from He to Xe, assumed to interact through the Lennard—Jones potential. Comparison with previous approximate descriptions and with experiments is made.

scholarly journals Development of neutron scattering kernels for cold neutron reflector materials

2021 ◽  
pp. 1-11
Author(s):  
José Rolando Granada ◽  
José Ignacio Márquez Damián ◽  
Javier Dawidowski ◽  
José Ignacio Robledo ◽  
Christian Helman ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Cross Section ◽  
Cold Neutron ◽  
Nuclear Industry ◽  
Cross Section Data ◽  
Design And Optimization ◽  
Section Data ◽  
Diamond Nanopowder ◽  
Physics Department ◽  
Fission Reactors

The newest neutron scattering applications are highly intensity-limited techniques that demand reducing the neutron losses between source and detectors. In addition, the nuclear industry demands more accurate data and procedures for the design and optimization of advanced fission reactors, especially for the treatment of fuel and moderator materials. To meet these demands, it is necessary to improve the existing calculation tools, through the generation of better models that describe the interaction of neutrons with the systems of interest. The Neutron Physics Department at Centro Atomico Bariloche (CNEA, Argentina) has been developing over the time new models for the interaction of slow neutrons with materials, to produce scattering kernels and cross section data in the thermal and cold neutron energy region. Besides the studies carried out on neutron moderators, we have recently begun looking at materials that could serve as efficient neutron reflectors over those energy ranges. In this work we present the results of transmission and scattering experiments on diamond nanopowder and magnesium hydride, carried out simultaneously at the VESUVIO spectrometer (ISIS, UK), and compare them with newly generated cross-section libraries.

THE LAW OF CORRESPONDING STATES AND COLD NEUTRON SCATTERING BY LIQUIDS

1966 ◽  
Vol 44 (4) ◽  
pp. 867-875 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Cold Neutron ◽  
Quantum Effects ◽  
Theoretical Models ◽  
Corresponding States ◽  
Scattering Data ◽  
Velocity Spectrum ◽  
Simple Liquid ◽  
Law Of Corresponding States ◽  
The Law

Although the law of corresponding states can be used in the practical analysis of cold neutron scattering data from liquids only if quantum effects are negligible, it is of interest, nevertheless, to have a quantum mechanical derivation of this law, because it is only then that one can discuss, in a completely consistent way, the conditions under which quantum effects are negligible. Such a derivation is given in the present paper. We also present an extension of the law of corresponding states to the velocity spectrum of an atom in a simple liquid and indicate how this can be used to check the consistency and extend the range of applicability of theoretical models of the velocity spectrum.

scholarly journals Wave propagation and Landau-type damping in liquids

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Vincenzo Molinari ◽  
Domiziano Mostacci
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Intermolecular Forces ◽  
Landau Damping ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

AbstractIntermolecular forces are modeled by means of a modified Lennard-Jones potential, introducing a distance of minimum approach, and the effect of intermolecular interactions is accounted for with a self consistent field of the Vlasov type. A Vlasov equation is then written and used to investigate the propagation of perturbations in a liquid. A dispersion relation is obtained and an effect of damping, analogous to what is known in plasmas as “Landau damping”, is found to take place.

THEORY OF COLD NEUTRON SCATTERING BY HOMONUCLEAR DIATOMIC LIQUIDS: II. HINDERED ROTATION

1966 ◽  
Vol 44 (6) ◽  
pp. 1299-1311 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Distribution Function ◽  
Neutron Scattering ◽  
Partial Wave ◽  
Cross Section ◽  
Cold Neutron ◽  
Rotational Relaxation ◽  
Free Rotation ◽  
Hindered Rotation ◽  
Orientational Distribution ◽  
Orientational Distribution Function

The partial wave expansion of the cold neutron scattering cross section for a homonuclear diatomic liquid in terms of the angular momentum transfer, which was introduced in a previous article for the case of free rotation, is generalized to include hindered rotation. The cross section is expressed in terms of an orientational distribution function that is the rotational analogue of the Van Hove self-correlation function. The rotational scattering function for the lth partial wave is shown to be the Fourier transform of a rotational relaxation function, Fl(t), which is also the lth coefficient of the expansion of the orientational distribution function in terms of spherical harmonics. The functions Fl(t) are calculated for the limiting cases of free rotation and rotational diffusion. The problem of neutron diffraction by homonuclear diatomic liquids is also investigated, and it is shown that the small angle scattering is determined by the isothermal compressibility. This is a generalization of the well-known result for monatomic liquids.

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