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The association between temperature dependence of liquid 4He scattering law and the phenomena of the Bose condensation
Physica B 276}278 (2000) 465}466
The association between temperature dependence of liquid He scattering law and the phenomena of the Bose condensation I.V. Bogoyavlenskii , A.V. Puchkov, Andrei Skomorokhov * Institute of Physics and Technology, 310108, Kharkov, Ukraine Institute of Physics and Power Engineering, Bondarenko sq.1, 249020, Obninsk, Kaluga Reg., Russia
Abstract In this paper we report the results of investigations of the helium excitation spectrum at the phonon}maxon region of dispersion curve carried out by inelastic neutron scattering to assess the relationship between phenomena of Bose condensation and unique type of the excitations of liquid He. 2000 Elsevier Science B.V. All rights reserved. Keywords: Super#uidity; Low temperature; Liquids
The dynamics in liquid He at low temperatures has already been a subject of interest for many years because helium behaves in a unique way. So excitation in super#uid helium in contrast to the other `simplea liquids remain extremely sharp at wave vectors up to 3.5 As \. Are the sharp excitations then a `signaturea of the super#uid phase, connected in some way to the existence of Bose condensate in super#uid helium, or is He just an extremely cold liquid? The density-quasiparticle picture in the frame of the "eld theory and dielectric function formulation provides [1] a good description of the temperature dependence of neutron scattering data. In this picture, Bose condensate plays an explicit role, and the excitations at the phonon}maxon range of the dispersion curve is interpreted as a joint density/quasiparticle mode strongly coupled via the condensate. Within this description, the phonon at low Q is interpreted as a collective excitation of the zero sound mode (ZS-mode) which is not sensitive to the existence of the Bose-condensate. The sharp maxon peak is interpreted as a quasiparticle excitation of the single-particle mode (SP-mode) which observed in S(Q, u) only bellow ¹ . So the sharp maxon peak is H a unique feature of the condensate and could not be observed in S(Q, u) without one [1].
* Corresponding author. Fax: #7-095-2302326. E-mail address: [email protected] (A. Skomorokhov)
In this paper we report the results of the recent investigations [2] carried by inelastic neutron scattering to assess this relationship. Measurements were performed on the time-of-#ight direct geometry DIN-2PI spectrometer at the Joint Institute for Nuclear Research in Dubna. Initial neutron energy was set about 2 meV and multi-detectors system at angle scattering range 6.3}713 allow us to cover Q range from 0.2 up to 1.15 As \ in one measurements. The Q-dependent resolution widths varied between 0.05 and 0.1 meV (FWHM). The scattering function of He was measured at 11 di!erent temperatures in the range 0.44}2.22 K at SVP. The spectra were corrected for background, detector e$ciency, and interpolated from constant 0 to constant Q. To obtain the one-phonon parameters we used simple subtraction model (SSM) [3]. The multiphonon part of S(Q, u) was determined at lowest experimental temperature and subtracted then from experimental spectra at higher temperatures. The damped harmonic oscillator function (DHO function) was "tted to the resulting one-phonon peak taking into account the instrumental resolution. In the results we obtain data on temperature dependence of S(Q, u) which agree in main with previous detailed study [4]. One-phonon peak is anomalously independent of temperature at the Q less than 0.3 As \. Width of the peak slowly increases with temperature; position and intensity remain constant. We could not "nd any manifestations of the super#uid phase transition in the
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 9 2 - 0
466
I.V. Bogoyavlenskii et al. / Physica B 276}278 (2000) 465}466
Fig. 1. Energy shifts of the one-phonon peak position at SVP and various Q. Curves are simply guides to the eye.
temperature dependence of the one-phonon parameters at this Q-region. At 0.3(Q(0.725 As \ one-phonon parameters demonstrate the essential temperature dependence which is most marked at temperatures near ¹ . H All one-phonon parameters have jump near ¹ . Intensity H and width of peak increase smoothly with temperature up to ¹ and change set of increasing after ¹ . Position H H of the peak have a small dip at ¹"1.9 K and increases just below ¹ (see Fig. 1). Changes of the one-phonon H peak become more marked with Q increasing. And temperature dependence of S(Q, u) at Q"1.15 As \ is quite di!erent from that at the phonon region. Intensity and width of the peak increase with temperature also. Position of the peak remains constant up to 1.6 K, decreases after one and there are no indications of its rise at ¹ (see H Fig. 1).
We suppose that temperature dependence of peak position at 0.3(Q(0.725 As \ with a dip bellow ¹ can be viewed as indication of strong hybridization H between ZS and SP modes (if suppose that ZS energy for normal He lies above SP energy for super#uid He). Note, we "nd peculiarity in S(Q, u) in this Q range [5] that can be treated as indication ZS-SP hybridization also according prediction Glyde}Gri$n model [6]. Temperature independence of one phonon peak at Q(0.3 As \ and its smooth dependence up to ¹ at H Q"1.15 As \ indicate that there are no evidence SPmode at Q(0.3 As \ and ZS-mode at Q"1.15 As \. Wave vector range 0.3(Q(0.725 As \ is probably a range where SP and ZS modes exist simultaneously. Note that previous detailed study of S(Q, u) identify dip in u(Q, ¹) just bellow ¹ at all Q(1.4 As \, that not H agree with our data completely. This disappointment may be caused by some arbitrariness of determination of the multiphonon part of S(Q, u). The Russian Federation Program `Actual Investigation of Condensed Mattera supported this research.
References [1] Henry Glyde, J. Low-Temp. Phys. 93 (1993) 862. [2] I.V. Bogoyavlenskii, A.V. Puchkov, A. Skomorokhov, Annual Report 1998, FLNP JINR, in press. [3] A. Miller, D. Pines, P. Noziers, Phys. Rev. 127 (1962) 1452. [4] K.H. Andersen, W.G. Srtiling, J. Phys.: Condens Matter 6 (1994) 5805. [5] I.V. Bogoyavlenskii, A.V. Puchkov, A. Skomorokhov, Physica B, in press. [6] A. Gri$n, E.C. Svensson, Physica B 165&166 (1990) 487.
The association between temperature dependence of liquid He scattering law and the phenomena of the Bose condensation I.V. Bogoyavlenskii , A.V. Puchkov, Andrei Skomorokhov * Institute of Physics and Technology, 310108, Kharkov, Ukraine Institute of Physics and Power Engineering, Bondarenko sq.1, 249020, Obninsk, Kaluga Reg., Russia
Abstract In this paper we report the results of investigations of the helium excitation spectrum at the phonon}maxon region of dispersion curve carried out by inelastic neutron scattering to assess the relationship between phenomena of Bose condensation and unique type of the excitations of liquid He. 2000 Elsevier Science B.V. All rights reserved. Keywords: Super#uidity; Low temperature; Liquids
The dynamics in liquid He at low temperatures has already been a subject of interest for many years because helium behaves in a unique way. So excitation in super#uid helium in contrast to the other `simplea liquids remain extremely sharp at wave vectors up to 3.5 As \. Are the sharp excitations then a `signaturea of the super#uid phase, connected in some way to the existence of Bose condensate in super#uid helium, or is He just an extremely cold liquid? The density-quasiparticle picture in the frame of the "eld theory and dielectric function formulation provides [1] a good description of the temperature dependence of neutron scattering data. In this picture, Bose condensate plays an explicit role, and the excitations at the phonon}maxon range of the dispersion curve is interpreted as a joint density/quasiparticle mode strongly coupled via the condensate. Within this description, the phonon at low Q is interpreted as a collective excitation of the zero sound mode (ZS-mode) which is not sensitive to the existence of the Bose-condensate. The sharp maxon peak is interpreted as a quasiparticle excitation of the single-particle mode (SP-mode) which observed in S(Q, u) only bellow ¹ . So the sharp maxon peak is H a unique feature of the condensate and could not be observed in S(Q, u) without one [1].
* Corresponding author. Fax: #7-095-2302326. E-mail address: [email protected] (A. Skomorokhov)
In this paper we report the results of the recent investigations [2] carried by inelastic neutron scattering to assess this relationship. Measurements were performed on the time-of-#ight direct geometry DIN-2PI spectrometer at the Joint Institute for Nuclear Research in Dubna. Initial neutron energy was set about 2 meV and multi-detectors system at angle scattering range 6.3}713 allow us to cover Q range from 0.2 up to 1.15 As \ in one measurements. The Q-dependent resolution widths varied between 0.05 and 0.1 meV (FWHM). The scattering function of He was measured at 11 di!erent temperatures in the range 0.44}2.22 K at SVP. The spectra were corrected for background, detector e$ciency, and interpolated from constant 0 to constant Q. To obtain the one-phonon parameters we used simple subtraction model (SSM) [3]. The multiphonon part of S(Q, u) was determined at lowest experimental temperature and subtracted then from experimental spectra at higher temperatures. The damped harmonic oscillator function (DHO function) was "tted to the resulting one-phonon peak taking into account the instrumental resolution. In the results we obtain data on temperature dependence of S(Q, u) which agree in main with previous detailed study [4]. One-phonon peak is anomalously independent of temperature at the Q less than 0.3 As \. Width of the peak slowly increases with temperature; position and intensity remain constant. We could not "nd any manifestations of the super#uid phase transition in the
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 9 2 - 0
466
I.V. Bogoyavlenskii et al. / Physica B 276}278 (2000) 465}466
Fig. 1. Energy shifts of the one-phonon peak position at SVP and various Q. Curves are simply guides to the eye.
temperature dependence of the one-phonon parameters at this Q-region. At 0.3(Q(0.725 As \ one-phonon parameters demonstrate the essential temperature dependence which is most marked at temperatures near ¹ . H All one-phonon parameters have jump near ¹ . Intensity H and width of peak increase smoothly with temperature up to ¹ and change set of increasing after ¹ . Position H H of the peak have a small dip at ¹"1.9 K and increases just below ¹ (see Fig. 1). Changes of the one-phonon H peak become more marked with Q increasing. And temperature dependence of S(Q, u) at Q"1.15 As \ is quite di!erent from that at the phonon region. Intensity and width of the peak increase with temperature also. Position of the peak remains constant up to 1.6 K, decreases after one and there are no indications of its rise at ¹ (see H Fig. 1).
We suppose that temperature dependence of peak position at 0.3(Q(0.725 As \ with a dip bellow ¹ can be viewed as indication of strong hybridization H between ZS and SP modes (if suppose that ZS energy for normal He lies above SP energy for super#uid He). Note, we "nd peculiarity in S(Q, u) in this Q range [5] that can be treated as indication ZS-SP hybridization also according prediction Glyde}Gri$n model [6]. Temperature independence of one phonon peak at Q(0.3 As \ and its smooth dependence up to ¹ at H Q"1.15 As \ indicate that there are no evidence SPmode at Q(0.3 As \ and ZS-mode at Q"1.15 As \. Wave vector range 0.3(Q(0.725 As \ is probably a range where SP and ZS modes exist simultaneously. Note that previous detailed study of S(Q, u) identify dip in u(Q, ¹) just bellow ¹ at all Q(1.4 As \, that not H agree with our data completely. This disappointment may be caused by some arbitrariness of determination of the multiphonon part of S(Q, u). The Russian Federation Program `Actual Investigation of Condensed Mattera supported this research.
References [1] Henry Glyde, J. Low-Temp. Phys. 93 (1993) 862. [2] I.V. Bogoyavlenskii, A.V. Puchkov, A. Skomorokhov, Annual Report 1998, FLNP JINR, in press. [3] A. Miller, D. Pines, P. Noziers, Phys. Rev. 127 (1962) 1452. [4] K.H. Andersen, W.G. Srtiling, J. Phys.: Condens Matter 6 (1994) 5805. [5] I.V. Bogoyavlenskii, A.V. Puchkov, A. Skomorokhov, Physica B, in press. [6] A. Gri$n, E.C. Svensson, Physica B 165&166 (1990) 487.