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THERMODYNAMIC VERSUS NEUTRON MEASUREMENTS IN He II AT LOW
TEMPERATURE
M. Sudraud, E. Varoquaux
To cite this version:
M. Sudraud, E. Varoquaux. THERMODYNAMIC VERSUS NEUTRON MEASUREMENTS IN He II AT LOW TEMPERATURE. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-213-C6-214.
�10.1051/jphyscol:1978694�. �jpa-00218374�
JOURNAL D E PHYSIQUE
Collogue C6, supplement au n" 8, Tome 39, aout 1978, page C6-213
THERMODYNAMIC VERSUS NEUTRON MEASUREMENTS IN He II AT LOW TEMPERATURE
M. Sudraud and E. Varoquaux
Inst-Ltut d'Eleatronique Fondamentale, Bdt. 220, 91405 Ovsay, France
Résumé.- Le spectre d'énergie des excitations de He II relevé par diffusion de neutrons ne repré- sente pas à la'précision requise, les valeurs de l'entropie et du fluide normal.
Abstract.- The energy spectrum of excitations in He II measured by inelastic neutron scattering does not yield to the required accuracy values for the entropy and the normal fluid density.
As postulated by L. Landau /l/, thermal ex- citations in superfluid helium are long-lived and account for the thermodynamic properties. These ele- mentary excitations have been identified to density fluctuations in the liquid and their dispersion cur- ve e(p) measured by inelastic scattering of neutrons /l/. More recent and extensive neutron studies /2,3/
have led to a rather precise knowledge to ± 0.05 K, of e in terms of p at various pressures and tempe- ratures. Even at low momentum transfer (p/H ^ 0.2 A ) where the accuracy is limited by energy resolution,
the neutron results /4,5/ are in good agreement with other probes of density fluctuations such as sound velocity and attenuation measurements /6/. From the neutron dispersion curve, the entropy S and the den- sity of the normal component p of superfluid helium can be computed, as was done first at zero pressure by Bendt et al. /!/, with the help of the following formulae :
S = 1
6tr
zrT
+ p
| £ ) ,E^I»
n 6lT2Vi3kBT
^ + P %> ^ T ) - ( I )
P_djP
(1 - exp(- j-^Mexptjpr) - 1)
o V V
(2)
which are strictly valid only when the energy le- vels e are sharply defined and temperature indepen- dent. These conditions are met in ''He below 1.1 K.
Taking these various factors into account, an accurate numerical computation of S and p can be conducted. The 50 tnK energy uncertainty of the neutron measurements yields a possible error of 2 % on the computed value of the entropy, S . The rela- tive error on p is of the same order of magnitude,
n
We compare these values S and p derived from the neutron dispersion curve to the quantities which have been measured directly S and p . We ha-
m nm ve measured the entropy at various pressures form 0.7 K to 1.3 K and discussed the agreement between the available data from various sources ll I, which is of the order of 3 %. The experimental situation is not as favourable for p . The only recent direct measurement of this quantity has teen performed by
Sobolev and Esel'son /8/ at SVP and down to 1.17 K.
It can also be derived accurately from the second sound velocity which has been measured at SVP /9/
down to 0.6 K. The only recent work at elevated pressures /10/, analysed by R. Maynard /ll/, extends down to only 1,2 K.
The outcome of the comparison between S , S and p , p is given in figures 1 and 2 where the c m
nc nm
relative difference is plotted as a function of pressure at various temperatures. The deviations for S and p exhibit the same pattern and are larger than the combined uncertainties, revealing that the neutron dispersion curves do not give an accurate description of the thermodynamic and hydrodynamic quantities, even at low temperatures.
We note that 1) above 5 bar, S and p are c 'c too large, ruling out the possible neglect of other contributions. 2) Sp /p is about twice (SS/S. This
n n
work extends to low temperatures the conclusion reached by others /12/ on the existence at high temperatures of a "sharp" thermodynamic spectrum distinct from the neutron spectrum. This extension implies that, besides interactions between real thermal excitations, the exchange of virtual exci- tations has to be taken into account differently in the liquid structure factor, measured by neutrons, and in the thermodynamic properties.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978694
P ( b a r ) P ( b a r )
Fig. I : Relative difference (S
-
S ) / S betweenthe Fig. 2 : Relative difference (S-
S )/Sm andm c m
measured entropy S and the quantity computed from ( p
-
p ) p between measured Znd Eomputed quant2- equation ( l ) , Sc ig terms of the pressure ?:it-
%tsn%r S, stars and triangles for p fromreferences 1 7 1 and 1 1 4 1
References
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36
(1973) 1135
/ 2 / Dietrich, O.W., Graf, E.H., Huang, C.H., Passell, L., Phys. Rev. (1972) 1377
/ 3 / Graf, E.H., Minkiewicz, V.J., Bjerrum, H., Mdller,
Passell, L., Phys. Rev.
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1 5 1 Stirling, W.G., Copley, J.R.D., Hilton, P.A., Int.
Symp. on Neutron Inelastic Scattering, Oct. 1977, Vienna
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