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Frequency Spectrum of Liquids and Cold Neutron Scattering; Spectre de frequences des liquides et diffusion de neutrons froids; Chastotnyj spektr zhidkostej i rasseyanie kholodnykh nejtronov; Espectro de frecuencias de los liquidos y dispersion de neutrones frios

Abstract

An important question which arises in connection with slow neutron scattering by liquids is: does there exist a frequency spectrum tor liquids analogous to that in solids? The answer to this question is given by showing that the width function {gamma}(t) of the Gaussian space-time self-correlation function G{sub s}(r,t) can be expressed, by using the frequency spectrum of the velocity auto-correlation function, in a form which is formally identical with that of a harmonic solid. Thus a knowledge of the frequency spectrum of the velocity auto-correlation function should enable one to calculate slow neutron scattering by liquids as has been emphasized by Egelstaff and co-workers. Using a stochastic model of a liquid, the frequency spectrum f({omega}) of the velocity auto-correlation function is calculated for water at 300{sup o}K and for liquid lead at 620{sup o}K. In the case of water a maximum in f({omega}) corresponding to {Dirac_h} 75{sup o}K is predicted. For lead the maximum also occurs at nearly the same {omega}-value. There also occurs a minimum in f({omega})in both cases. Larsson and Dahlborg have observed a maximum in f({omega}) at the above predicted {omega}-value. A recent observation in liquid lead of Cotter et al. probably confirms our prediction too.  More>>
Authors:
Singwi, K S; Sjolander, A; Rahman, A [1] 
  1. Argonne National Laboratory, Argonne, IL (United States)
Publication Date:
Jan 15, 1963
Product Type:
Conference
Resource Relation:
Conference: Symposium on Inelastic Scattering of Neutrons in Solids and Liquids, Chalk River (Canada), 10-14 Sep 1962; Other Information: Abstract also available in Russian; 11 refs.; Related Information: In: Inelastic Scattering of Neutrons in Solids and Liquids. V. I. Proceedings of the Symposium on Inelastic Scattering of Neurons in Solids and Liquids| 486 p.
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COLD NEUTRONS; CORRELATION FUNCTIONS; LEAD; LIQUIDS; NEUTRON DIFFRACTION; SLOW NEUTRONS; SPECTRA; STOCHASTIC PROCESSES; TEMPERATURE DEPENDENCE
OSTI ID:
22086599
Research Organizations:
International Atomic Energy Agency, Vienna (Austria); United Nations Educational, Scientific and Cultural Organization (France)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13R0085045037
Submitting Site:
INIS
Size:
page(s) 215-226
Announcement Date:
Apr 18, 2013

Citation Formats

Singwi, K S, Sjolander, A, and Rahman, A. Frequency Spectrum of Liquids and Cold Neutron Scattering; Spectre de frequences des liquides et diffusion de neutrons froids; Chastotnyj spektr zhidkostej i rasseyanie kholodnykh nejtronov; Espectro de frecuencias de los liquidos y dispersion de neutrones frios. IAEA: N. p., 1963. Web.
Singwi, K S, Sjolander, A, & Rahman, A. Frequency Spectrum of Liquids and Cold Neutron Scattering; Spectre de frequences des liquides et diffusion de neutrons froids; Chastotnyj spektr zhidkostej i rasseyanie kholodnykh nejtronov; Espectro de frecuencias de los liquidos y dispersion de neutrones frios. IAEA.
Singwi, K S, Sjolander, A, and Rahman, A. 1963. "Frequency Spectrum of Liquids and Cold Neutron Scattering; Spectre de frequences des liquides et diffusion de neutrons froids; Chastotnyj spektr zhidkostej i rasseyanie kholodnykh nejtronov; Espectro de frecuencias de los liquidos y dispersion de neutrones frios." IAEA.
@misc{etde_22086599,
title = {Frequency Spectrum of Liquids and Cold Neutron Scattering; Spectre de frequences des liquides et diffusion de neutrons froids; Chastotnyj spektr zhidkostej i rasseyanie kholodnykh nejtronov; Espectro de frecuencias de los liquidos y dispersion de neutrones frios}
author = {Singwi, K S, Sjolander, A, and Rahman, A}
abstractNote = {An important question which arises in connection with slow neutron scattering by liquids is: does there exist a frequency spectrum tor liquids analogous to that in solids? The answer to this question is given by showing that the width function {gamma}(t) of the Gaussian space-time self-correlation function G{sub s}(r,t) can be expressed, by using the frequency spectrum of the velocity auto-correlation function, in a form which is formally identical with that of a harmonic solid. Thus a knowledge of the frequency spectrum of the velocity auto-correlation function should enable one to calculate slow neutron scattering by liquids as has been emphasized by Egelstaff and co-workers. Using a stochastic model of a liquid, the frequency spectrum f({omega}) of the velocity auto-correlation function is calculated for water at 300{sup o}K and for liquid lead at 620{sup o}K. In the case of water a maximum in f({omega}) corresponding to {Dirac_h} 75{sup o}K is predicted. For lead the maximum also occurs at nearly the same {omega}-value. There also occurs a minimum in f({omega})in both cases. Larsson and Dahlborg have observed a maximum in f({omega}) at the above predicted {omega}-value. A recent observation in liquid lead of Cotter et al. probably confirms our prediction too. (author) [French] Dans le domaine de la diffusion des neutrons lents par des liquides une question importante se pose: existe-t-il un spectre de frequences pour les liquides analogue au spectre pour les solides? On peut repondre d cette quesnon en montrant que la fonction de largeur {gamma}(t) de la fonction gaussienne spatio-temporelle d'auto-correlation G{sub s}(r,t) peut etre exprimee, en employant le spectre de frequences de la fonction d'auto-correlation des vitesses, sous uune forme qui presente le membe aspect formel que celle d'un solide harmonique. par consequent, la connaissance du spectre de frequences de la fonction d'auto-correlation des vitesses devrait permettre de calculer la diffusion des neutrons lents par les liquides comme l'ont souligne Egelstaff et ses colllaborateurs. Les auteurs calculent, a l'aide d'un modele stochastique, le spectre des frequences f({omega}) de la fonction d'auto-correlation des vitesses dans l'eau a 300{sup o}K et dans le plomb liquide a 620{sup o}K. Dans le cas de l'eau ils prevoient un maximum de la fonction f({omega}) correspondant a {Dirac_h} {omega}75{sup o}K. Dans le plomb, le maximum se manifeste a une valeur a peu pres analogue. II existe aussi un minimum de la fonction f({omega}) dans les deux cas. Larsson et Dahlborg ont observe un maximum de la fonction f({omega}) a la valeur d'{omega} prevue ci-dessus. Des observations faites recemment dans du plomb liquide par Cotter et al. confirment vraisemblablement les previsions des auteurs. (author) [Spanish] Una cuestion importante que se plantea respecto de la dispersion de neeutrones lentos por los liquidos es la siguiente: Existe un espectro de frecuencia de los liquidos analogo al de los solidos? para contestar a esta pregunta, basta demostrar que la funcion de amplitud {gamma}(t) de la funcion gaussiana de autocorrelacion espacio G{sup s}(r,t) puede expresarse, utilizando el espectro de frecuencias de la funcion de autocorreclation de velocidad, en form identica a la correspondiente a un solido armonico. Es decir, si se conoce el especro de frecuencias de la funcion de autocorrelacion de velocidad, se debe poder calcular la dispersion de neutrones lentos por los liquidos, como han senalado Egelstaff y colaboradores. Los autores calculan, utilizando un modelo estocastico de liquido, el espectro de frecuencia f({omega}) de la funcion de autocorrelacion de velocidad, en el caso del agua a 300{sup o}K y del plomo liquido a 620{sup o}K. Predicen para la primera un maximo de f({omega}) correspondiente a {Dirac_h}{omega} 75{sup o}K. Enel caso del plomo, el maximo se presenta tambien para el mismo valor de oj, aproximadamente. Ademas, en ambos casos f({omega})pasa por un minimo. Larsson y Dahlborg han observado un maximo de f({omega}) para el valor de {omega} previsto por los autores. Al parecer una comprobacion recientemente efectuada por Cotter y colaboradores en el caso del plomo liquido tambien confirma la prevision de los autores acerca de este metal. (author)}
place = {IAEA}
year = {1963}
month = {Jan}
}