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TEMPERATURE DEPENDENCE OF PHONONS IN LIQUID 4He
E. Svensson, R. Scherm, A. Woods
To cite this version:
E. Svensson, R. Scherm, A. Woods. TEMPERATURE DEPENDENCE OF PHONONS IN LIQUID 4He. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-211-C6-212. �10.1051/jphyscol:1978693�.
�jpa-00218373�
JOURNAL DE PHYSIQUE Colloque C6, supplement au n° 8, Tome 39, aout 1978, page C6-211
TEMPERATURE DEPENDENCE OF PHONONS IN LIQUID 4He
E.C. Svensson, R. Scherm (*) and A.D.B. Woods
Atomic Energy of Canada Limited, Chalk River, Ontario, Canada, KOJ 1J0.
Résumé.- On a mesuré la diffusion de neutrons par ''He liquide aux vecteurs d'onde de 0.80 ; 1,13 ; 1,30 et 1,40 Â- 1 et aux températures de 1,00 ; 1,38 ; 1,77 ; 1,97 ; 2,07 ; 2,12 ; 2,15 ; 2,26 et 4,21 K. On peut voir un pic "uniphonon" dans toutes les distributions lorsque T < T\ = 2,17 K mais ce pic est absent lorsque T > T,.
Abstract.- The neutron scattering by liquid ""He for wave vectors of 0.80, 1.13, 1.30 and 1.40 A- 1
has been measured at I.00, 1.38, 1.77, 1.97, 2.07, 2.12, 2.15, 2.26 and 4.2! K. A "one-phonon" peak is evident in all distributions for T < T, = 2.17 K but is absent for T > T\.
INTRODUCTION.- As the temperature of superfluid ''He is raised towards the A-point (T. = 2.17 K) the fre- quencies and lifetimes of the "roton" modes (wave vectors Q % 1.9 A- 1) decrease in such a way that at
temperatures T ^ 2.1 K it becomes kinematically pos- sible for excitations near the first maximum of the dispersion curve (Q % 1.1 A- 1) to decay into two ro- tons. Such a process can, in principle, limit the lifetimes of these "maxons" and hence give rise to a broadening of the corresponding peaks in the spec- tra of scattered neutrons. In an earlier study /l/
of the neutron scattering from liquid ''He at T = 2.J K, carried out with a rotating-crystal time-of- flight spectrometer, peaks arising from maxon crea- tion were not observed. Although the statistical accuracy in these experiments was not sufficient to establish the absence of such peaks with confidence the possibility that the maxon modes were unobser- vable at 2.1 K because of a rapid decay into two rotons was indeed intriguing. Further interest in this question was aroused when it was discovered /2,4/ that a similar disposition of maxon and ro- ton modes induced by raising the pressure at low temperature led to only slight broadening of the maxon modes.
In order to establish more precisely the be- havior in this interesting region of wave vectors, and hopefully to achieve a better understanding of possible decay or interference /3/ mechanisms that can broaden the peaks or decrease their intensities we have carried out new neutron scattering measure- ments at nine temperatures for wave vectors, Q, of
0.80, 1.13, 1.30 and 1.40 A- 1.
EXPERIMENT.- The measurements were carried out at the NRU reactor, Chalk River, using a triple-axis crystal spectrometer operated in the constant-|Q|
mode with a fixed scattered-neutron frequency of 1.134 THz. Under these conditions the observed counting rate, after relatively simple corrections for effects such as fast-neutron back-ground, is directly proportional to the resolution-broadened dynamic structure factor S„(Q,v). Silicon (111) pla- nes and pyrolytic graphite (002) planes were used as monochromator and analyser respectively, and a beryllium filter was placed in the scattered beam.
Although a quartz filter was placed in the incident beam, the flux of higher-order neutrons was still
sufficient to distort the count rate in the inci- dentrbeam monitor. The relative numbers of the dif- ferent orders were measured and the results were corrected accordingly.
Measurements were carried out within the range -0.04 < v < 1.65 THz for four wave-vector transfers (0.80, 1.13, 1.30 and 1.40 A- 1) for each of nine temperatures (1.00, 1.38, 1.77, 1.97, 2.07, 2.12, 2.15, 2.26 and 4.^21 K ) . The scattering from the empty container at 4.21 K was also measured and after correction for the transmission by the ''He specimen, subtracted from the observed spectra. For all scans, the fast-neutron background was automa- tically measured at each point. The results were also corrected for multiple scattering which was estimated from the calculations of Sears /5/.
RESULTS AND DISCUSSION.- In this paper, we will con- centrate on the region of the one-phonon peak and (*) Summer visitor from Institut Laue-Langevin,
156X Centre de Tri, 38042 Grenoble Cedex, France.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978693
FREQUENCY ( TH z
1
Fig. 1 : The c o r r e c t e d s c a t t e r i n g by l i q u i d ' ~ e f o r Q = 1.13 and 0.1 <
v
< 0 . 6 THz. These r e s u l t s a r e d i r e c t l y p r o p o r t i o n a l t o t h e resolution-broadened dynamic s t r u c t u r e f a c t o r , SR(Q,v), w i t h t h e same cons- t a n t of p r o p o r t i o n a l i t y f o r each temperature. Note t h e l o g a r i t h m i c i n t e n s i t y s c a l e .on Q = 1.13 ;-l. The c o r r e c t e d s i g n a l c o u n t s , which reasonably w e l l d e f i n e d e x c i t a t i o n s , i n t h e s e n s e a r e p r o p o r t i o n a l t o SR(Q,v), f o r Q = 1.13 A-' and t h a t t h e i r widths a r e l e s s t h a n t h e i r mean frequen- 0.1 < v <0.6 THz a r e shown i n f i g u r e I . The s p e c t r a c i e s , e x i s t f o r a l l t e m p e r a t u r e s c 2 . 1 5 K b u t not f o r T = 1.00 and 1.38 K a r e v e r y s i m i l a r and show f o r temperatures above t h e h-point. There i s no e v i - t h e f a m i l i a r / l
l
s h a r p peak a t V = 0.288 THz c o r r e s - .dence f o r any sudden changes w i t h temperature i n ponding t o t h e e x c i t a t i o n of a s i n g l e phonon. The t h e r e g i o n T<TX ; t h e broadening and t h e d e c r e a s e width of t h i s peak (= 0.05 THz) is e s s e n t i a l l y the i n h e i g h t of t h e "one-phonon" peaks appears t o pro- e x p e r i m e n t a l r e s o l u t i o n . A second r i s e i n t h e spec- ceed smoothly a s t h e temperature is r a i s e d .t r a begins a t approximately twice t h e r o t o n energy
(=: 0.36 THz) corresponding t o t h e t h r e s h o l d f o r two- .ACKNOWLEDGMENTS.- We wish t o thank H.F. Nieman and r o t o n s c a t t e r i n g . A s t h e temperature i s i n c r e a s e d D.C. Tennant f o r v a l u a b l e t e c h n i c a l a s s i s t a n c e . t h e h e i g h t of t h e s h a r p peak d e c r e a s e s w h i l e i t s
width i n c r e a s e s b u t t h e r e i s s t i l l a r e c o g n i z a b l e
Re£ e r e n c e s
peak at = ' ' I 5 K * Only Oao2 K the '-point' / l / Cowley, R.A. and Woods, A.D.B., Can J. Phys.
2
A l l of t h e s p e c t r a f o r T
2
2.15 K a r e c h a r a c t e r i z e d (1971) 177.by a n a b r u p t change i n s l o p e between 0.34 and 0.38 121 Graf, E-H., Minkiewicz, V-J.9 Bjerrum-Mbller, H.
and P a s s e l l , L., Phys. Rev.
A 1 0
(1974) 1748.THz. Above t h e X-point, however, t h e s p e c t r a con-
/3/ Svensson, E.C., Martel, P . , S e a r s , V.F. and sist of a s i n g l e broad peak w i t h no evidence of t h i s Woods, A.D.B., Can. J ; Phys.
54
(1976) 2178.change i n s l o p e - The the
Q
va-/i/
Smith, A. S . , Cowley, R.A., Woods, A.D.B., S t i r - l u e s s t u d i e d is q u a l i t a t i v e l y very s i m i l a r . l i n g , W.G. and M a r t e l , P., J. Phys. C . 1 0 (1977)543.
From t h i s s t u d y we may t h e r e f o r e conclude t h a t
1 5 / S e a r s , V.F., Nucl. Instrum. Methods
