Calculation of the Self-Consistent Phonon Spectrum of hcp<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Gillis, N. S.; Kœhler, Thomas; Werthamer, N. R.

doi:10.1103/physrev.175.1110

Cited by 103 publications

(20 citation statements)

References 13 publications

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“…7). Using self-consistent phonon theory, Gillis et al, 8 for example, calculated a phonon dispersion curve for hcp 4He which was in satisfactory agreement with neutron scattering and sound velocity data.…”

Section: Introductionmentioning

confidence: 76%

“…The sound velocity in hcp 4He also depends on the crystal orientation. Therefore we have measured the frequency shift Av, which is connected with the sound velocity by (8), to get some information about the crystal orientation. Since it is difficult to resolve these small shifts with sufficient accuracy by a Fabry-Perot interferometer, we used an optical heterodyne method.…”

Section: The Optical Arrangementmentioning

confidence: 99%

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Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

1976

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Section: Introductionmentioning

confidence: 76%

Section: The Optical Arrangementmentioning

confidence: 99%

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

1976

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“…In (b), the intensities are calculated from the inelastic structure factor following ref. [20] with an additional common scaling factor. energy mode is a propagating vacancy excitation.…”

Section: Resultsmentioning

confidence: 99%

“…Figure 2 shows the dispersions of these excitations, as obtained by fitting Gaussians to the data. The lowest energy mode is an acoustic phonon and we argue that the sharp intermediate [20]. In (b), the intensities are calculated from the inelastic structure factor following ref.…”

Section: Resultsmentioning

confidence: 99%

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

et al. 2008

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There has been a resurgence of interest in the properties of solid helium due to the recent discovery of non-classical rotational inertia (NCRI) in solid 4 He by Chan and coworkers below 200 mK which they have interpreted as a transition to a 'supersolid' phase. We have carried out a series of elastic and inelastic neutron scattering measurements on single crystals of hcp 4 He at temperatures down to 60 mK. While we have found no direct evidence of any change in the excitation spectrum at low temperatures, we have found that the excitation spectrum of solid 4 He shows several interesting features, including extra branches in addition to the phonon branches. We interpret these extra branches as single particle excitations due to propagating vacancy waves, which map on to the famous 'roton minimum' long known in the excitation spectrum of superfluid liquid 4 He. The results show that in fact solid 4 He shares several features in common with the superfluid.

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“…The version of the SCPT used by Horton et al -known as the improved self-consistent phonon theory (ISC) -was formulated by Gillis, Koehler and Werthamer [11] and is in fact only the first-order approximation of the SCPT (so-called pseudoharmonic approximation), in which only the fourth-order term in the anharmonic part of the Hamiltonian is incorporated, while the reduced second-order approximation of the SCPT (RSOSCPT) developed by Plakida and Siklós [12] incorporates also the thirdorder anharmonic term, which leads to the convergence of the self-consistent method also in the case of quantum crystals. So we think that it is worth improving the method of Plakida and Siklós and rejecting some of the simplifying assumptions taken by them.…”

Section: Introductionmentioning

confidence: 99%

Dynamic and thermodynamic properties of solid helium in the reduced all‐neighbours approximation of the self‐consistent phonon theory

Malinowska-Adamska

Słoma

Tomaszewski

2003

Physica Status Solidi (b)

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The results of studies of physical properties of solid helium obtained with the help of the reduced allneighbours approximation of the self-consistent phonon theory are presented. The results of calculation of the temperature and pressure variations of the quantities describing the dynamics and thermodynamics of solid He-3 and He-4 obtained in terms of the (exp, m) Buckingham, the (n, m) Lennard-Jones and the (exp, exp) Morse renormalized potentials are given and compared with experimental and other theoretical data.Работа содержит результаты исследования физических свойств кристаллов гелия в приближении всех соседей второго порядка самосогласованной теории фононного поля. Численные расчёты зависимостей динамических и термодинамических свойств кристаллов He-3 и He-4 от температуры и внешнего давления, полученные с помощью межатомных самосогласованных потенциалов: (exp, m) Букингама, (n, m) Леннарда-Джонса и (exp, exp) Морзе показали правильную физическую зависимость и хорошо совпадают с експериментальными данными.

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Calculation of the Self-Consistent Phonon Spectrum of hcpHe4

Cited by 103 publications

References 13 publications

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

Dynamic and thermodynamic properties of solid helium in the reduced all‐neighbours approximation of the self‐consistent phonon theory

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