THE ROTON LIFETIME IN 3He - 4He MIXTURES

(1)

HAL Id: jpa-00218368

https://hal.archives-ouvertes.fr/jpa-00218368

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE ROTON LIFETIME IN 3He - 4He MIXTURES

R. Scherm, W. Stirling, P. Hilton

To cite this version:

R. Scherm, W. Stirling, P. Hilton. THE ROTON LIFETIME IN 3He - 4He MIXTURES. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-198-C6-200. �10.1051/jphyscol:1978688�. �jpa-00218368�

(2)

JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aoGt 1978, page C6-198

T H E ROTON

LIFETIME

IN 3 ~ e

-

^{4 ~ e}^MIXTURES

R. Scherm, W.G. Stirling and P.A. Hilton t

I n s t i t u t Laue-Langevin, 256X, 38042 Grenoble Cedes, France t University o f Edinburgh, U.K.

Rdsumd.- Nous avons observd des "rotons" dans un mdlange de 6 % 3 ~ e dans 4 ~ e , par diffusion inblas- tique des neutrons, 1 des tempgratures entre 1,27 K et 2,15 K. La durde de vie ddrivde de ces mesu- res est en trSs bon accord avec des rdsultats antdrieurs par diffusion des neutrons et diffusion Raman.

Abstract.- Rotons have been observed by neutron inelastic scattering in a 6 % mixture of 'He in 4 ~ e , at temperatures between 1.27 K and 2.15 K. Estimates of the roton lifetime derived from these measurements are in very good agreement with previous Raman and neutron results.

Many of the low temperature properties of a dilute solution of 3 ~ e in superfluid 4 ~ e can be un- derstood by treating the 3 ~ e as a weakly interacting Fermi gas in a background of neutral %e. We may expect the general features of the 4 ~ e phonon roton spectrum to persist, and the 3 ~ e impurity may be regarded as a modified free particle excitation.

Thete concepts were invoked by Landau and Pomeran- chuk /I/ who originally proposed a quadratic form for the 3 ~ e excitation spectrum. Part of this spectrum has been directly observed by inelastic neutron scattering /2/, Recent speculation, whether and' how the 3 ~ e spectrum deviates from this simple quadratic form still remains a subject of controver- sy (See reference /2/ and references therein).

The Landau Pomeranchuk model neglects quasi- particle interactions ; however the coupling of the various excitations may have a significant influen- ce on the physical properties of the mixture. Trans- port properties like spin diffusion and thermal con- ductivity depend on the scattering of 3 ~ e impurities by phonons, rotons and the 3 ~ e . In the limit of very low temperatures the 3 ~ e - 3 ~ e scattering is dominant but at temperatures near the I K the 3~e-roton and 3~e-phonon interactions must be taken into ac- count. Furthermore if the roton energy becomes de- generate with the 3 ~ e particle hole continuum, roton decay processes are also possible 131.

Neutron inelastic scattering provides the ideal probe for examination of the excitation spec- tra and their interactions, in dilute 3 ~ e - 4 ~ e mixtures, particularly in the region of the roton mi-

nimum. In a previous publication 121, experiments on neutron scattering in the temperature range between 0.6 and 1.5 K have been reported. We now pre-

sent further results, obtained from a 6 % 3 ~ e - 4 ~ e mixture at 1.27, 1.65, 1.80 and 2.15 K.

The experiments were performed on the time of flight spectrometer IN5 at the Institut Laue- Langevin, Grenoble, the experimental technique be- ing as described in reference 121. The incident

4

neutron wavelength was 4.9 A and time of flight scans were made at wavevector transfers between 1.23 and 2.17

i-'.

Measurements on pure 4 ~ e were made at T = 1.27 K, where the roton linewidth is practicallv negligible.

Effectively, this measurement defines the instrumental resolution,which could be described by a Gaussian of full width, (2rres) = 1.91 K at Q = 1.93 ;-I. The data for the mixtures were then fitted to Voigt functions, the convolution of the above Gaussian and a Lorentzian, from which the Lorentzian halfwidths (T) can be extracted. The latter is corrected for the fact that our time of flight scans are not made at constant wavevector transfer

.

The observed linewidths in the mixture, T, are fairly constant within the wavevector range of the experiment. In figure 1 we present the linewidth at the roton minimum,

r

as a function of temperature (full circles), together with our previous measurements /2/ (open circles).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978688

(3)

TEMPERATURE (K)

Fig. 1 : The roton linewidth in a 6 % 3 ~ e - 4 ~ e mixture. T and TLK are as defined in the text. a in- dicates the roton width in pure 4 ~ e . Circles and squares refer to neutron scattering measurements, and triangles to Raman scattering measurements.

The latter set of data were analysed as described above, but the Gaussian defining the resolution was measured at 0.6 K. We expect the linewidth of pure 4 ~ e measured at 0.6 K to be practi- cally identical to that measured at 1.27 K. The so- lid curve shown in the upper half of figure 1 is a fit to the Landau-Khalatnikov formula /4/

of the Raman data of Greytak and Yan /5/ for pure +He, in the temperature range from 1.35

-

^{1.83 K.}

The L.K. theory for roton lifetimes assumes roton- roton scattering to be the dominant process. Our measurements for pure 4 ~ e at temperatures of 1.55 and 1.92 K agree reasonably well with this curve.

The lower half of the figure shows the difference T

-

TLK, plus earlier neutron /6/ and Raman results 17, 81. In these earlier results the linewidths were derived using 4 ~ e measured at the same temperature as the mixture. Also, for presentation on this figure, the data of references/6, 7 and 8 / have all been scaled to a 3 ~ e concentration of 6 %, assuming the linewidth to be linear with 3 ~ e concentration /2/. It should be noted however that the Raman scattering in fact meastires the increase in half width

volving two rotons and two phonons. At T = 0.6 K for example, two roton, two phonon processes are expected to dominate the roton lifetime. It is not obvious that 1/2rpair can be identified with the linewidth T , although the agreement between the four sets of measurements presented in figure 1 is encouraging.

In the roton region, the interactions between the 3 ~ e quasiparticles and the 4 ~ e are of two types : Firstly scattering of rotons and 3 ~ e quasiparticles and secondly the:hybridisation of rotons and 3 ~ e quasiparticles

.

These two mechanisms have been discussed in detail b~Ruvaldset al. 1 3 , lo/.

Reference /lo/ calculates an upper bound of 2.4 x erg.cm3 for the slope of the linewidth as a function of 3 ~ e particle density, from processes involving scattering of rotons and 3 ~ e . This limit agrees quite well with the value of 2.9 t 0 . 3 ~ 1 0 ~ ~ erg.cm3, extracted from our data for the 6 % mixture at T = 0.6 K.

However, for reasonable values of m*, and assuming a parabolic 3 ~ e continuum, in a 6 % mixture one would expect the 3 ~ e continuum to envelop the 4 ~ e roton minimum and thus the decay channel for rotons into the 3 ~ e continuum would be open.

The experimental slope quoted above therefore should include contributions from 3~e-roton scattering and roton decay. Unfortunately as Ruvald's calculations indicate only an upper limit to the quantities involved it becomes difficult to draw definite conclusions from the experimental data.

Dietrich et al. Ill/, scaled the roton linewidth in pure 4 ~ e at different pressures, to a uni- versal curve, T(T-T (P)). It would be interesting

A

to know whether this method should be applied to the case of 3 ~ e - 4 ~ e mixture, as the A point is depressed by addition of the 3 ~ e . In the present case of a 6 % mixture, T is lowered by about

A

80 mK. The accuracy of the existing data is cer- tainly not yet sufficient to answer this question.

of the two roton pair state and what we have plot- ted in the figure is l' = 112 Tpair. The interpre- tation of the Raman scattering data in mixtures at temperatures below 1 K is complicated because the contribution to the roton linewidth contains, as well as roton-roton interactions, interactions in-

(4)

References

/I/ Landau, L.D., and Pomeranchuk, I.Ya., Dokl. Akad. Nauk. USSR, 59 (1948) 669

-

/2/ Hilton, P., Scherm, R., Stirling, W., J. Low Temp. Phys.

27 (1977) 851

-

131 Ruvalds, J., Slinkmann, J., Rajagopal, A.K., Bagchi, A., Phys. Rev.

B

2

(1977) 2047

/ 4 / Khalatnikov, I.M., "An Introduction to the Theory of Superfluidity"

Bedjamin, New York (1 965)

/5/ Greytak,T.J., Yan, J., Proc. of the ^12thIntern. Conf. on Low Temp.

Physics, Kyoto (1970)

/ 6 / Rowe, J.M., Price, D.L., Ostrowski, G.F., Phys. Rev. Lett.

31 (1973) 510

-

/7/ Woerner, R.L., Rockwell, D.A., Greytak, T.J., Phys. Rev. Lett.

30 (1973) 1114

-

/8/ Surko, C.M., and Slusher, R.E., Phys. Rev. Lett.

30 (1973) 1 1 1 1

-

/9/ Murray, C.A., Woerner, R.L., Greytak, T.J., J. Phys. C., 8 (1 975) L90

-

/lo/ Bagchi, A., Ruvalds, J., Phys. Rev. A., 8 (1973) 1973

-

/11/ Dietrich, O.W., Graf, E., Huang, C.,Passell, L., Phys. Rev. A, 5 (1972) 1377