Effect of dipole interaction on collective modes $ in^{3} $He-A
Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Tewordt, L. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1977 |
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| Schlagwörter: |
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| Anmerkung: |
© Plenum Publishing Corporation 1977 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of low temperature physics - Kluwer Academic Publishers-Plenum Publishers, 1969, 29(1977), 1-2 vom: Okt., Seite 119-147 |
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| Übergeordnetes Werk: |
volume:29 ; year:1977 ; number:1-2 ; month:10 ; pages:119-147 |
| Links: |
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| DOI / URN: |
10.1007/BF00659092 |
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| Katalog-ID: |
OLC2036746799 |
|---|
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| 245 | 1 | 0 | |a Effect of dipole interaction on collective modes $ in^{3} $He-A |
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| 520 | |a Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. | ||
| 650 | 4 | |a Nuclear Magnetic Resonance | |
| 650 | 4 | |a Dipole Interaction | |
| 650 | 4 | |a Spin Wave | |
| 650 | 4 | |a Collective Mode | |
| 650 | 4 | |a Transverse Spin | |
| 700 | 1 | |a Schopohl, N. |4 aut | |
| 700 | 1 | |a Vollhardt, D. |4 aut | |
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10.1007/BF00659092 doi (DE-627)OLC2036746799 (DE-He213)BF00659092-p DE-627 ger DE-627 rakwb eng 530 VZ Tewordt, L. verfasserin aut Effect of dipole interaction on collective modes $ in^{3} $He-A 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1977 Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin Schopohl, N. aut Vollhardt, D. aut Enthalten in Journal of low temperature physics Kluwer Academic Publishers-Plenum Publishers, 1969 29(1977), 1-2 vom: Okt., Seite 119-147 (DE-627)129546267 (DE-600)218311-0 (DE-576)014996642 0022-2291 nnns volume:29 year:1977 number:1-2 month:10 pages:119-147 https://doi.org/10.1007/BF00659092 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_70 GBV_ILN_170 GBV_ILN_2006 GBV_ILN_2185 GBV_ILN_2192 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4323 GBV_ILN_4700 AR 29 1977 1-2 10 119-147 |
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10.1007/BF00659092 doi (DE-627)OLC2036746799 (DE-He213)BF00659092-p DE-627 ger DE-627 rakwb eng 530 VZ Tewordt, L. verfasserin aut Effect of dipole interaction on collective modes $ in^{3} $He-A 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1977 Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin Schopohl, N. aut Vollhardt, D. aut Enthalten in Journal of low temperature physics Kluwer Academic Publishers-Plenum Publishers, 1969 29(1977), 1-2 vom: Okt., Seite 119-147 (DE-627)129546267 (DE-600)218311-0 (DE-576)014996642 0022-2291 nnns volume:29 year:1977 number:1-2 month:10 pages:119-147 https://doi.org/10.1007/BF00659092 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_70 GBV_ILN_170 GBV_ILN_2006 GBV_ILN_2185 GBV_ILN_2192 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4323 GBV_ILN_4700 AR 29 1977 1-2 10 119-147 |
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10.1007/BF00659092 doi (DE-627)OLC2036746799 (DE-He213)BF00659092-p DE-627 ger DE-627 rakwb eng 530 VZ Tewordt, L. verfasserin aut Effect of dipole interaction on collective modes $ in^{3} $He-A 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1977 Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin Schopohl, N. aut Vollhardt, D. aut Enthalten in Journal of low temperature physics Kluwer Academic Publishers-Plenum Publishers, 1969 29(1977), 1-2 vom: Okt., Seite 119-147 (DE-627)129546267 (DE-600)218311-0 (DE-576)014996642 0022-2291 nnns volume:29 year:1977 number:1-2 month:10 pages:119-147 https://doi.org/10.1007/BF00659092 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_70 GBV_ILN_170 GBV_ILN_2006 GBV_ILN_2185 GBV_ILN_2192 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4323 GBV_ILN_4700 AR 29 1977 1-2 10 119-147 |
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10.1007/BF00659092 doi (DE-627)OLC2036746799 (DE-He213)BF00659092-p DE-627 ger DE-627 rakwb eng 530 VZ Tewordt, L. verfasserin aut Effect of dipole interaction on collective modes $ in^{3} $He-A 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1977 Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin Schopohl, N. aut Vollhardt, D. aut Enthalten in Journal of low temperature physics Kluwer Academic Publishers-Plenum Publishers, 1969 29(1977), 1-2 vom: Okt., Seite 119-147 (DE-627)129546267 (DE-600)218311-0 (DE-576)014996642 0022-2291 nnns volume:29 year:1977 number:1-2 month:10 pages:119-147 https://doi.org/10.1007/BF00659092 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_70 GBV_ILN_170 GBV_ILN_2006 GBV_ILN_2185 GBV_ILN_2192 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4323 GBV_ILN_4700 AR 29 1977 1-2 10 119-147 |
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10.1007/BF00659092 doi (DE-627)OLC2036746799 (DE-He213)BF00659092-p DE-627 ger DE-627 rakwb eng 530 VZ Tewordt, L. verfasserin aut Effect of dipole interaction on collective modes $ in^{3} $He-A 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1977 Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin Schopohl, N. aut Vollhardt, D. aut Enthalten in Journal of low temperature physics Kluwer Academic Publishers-Plenum Publishers, 1969 29(1977), 1-2 vom: Okt., Seite 119-147 (DE-627)129546267 (DE-600)218311-0 (DE-576)014996642 0022-2291 nnns volume:29 year:1977 number:1-2 month:10 pages:119-147 https://doi.org/10.1007/BF00659092 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_70 GBV_ILN_170 GBV_ILN_2006 GBV_ILN_2185 GBV_ILN_2192 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4323 GBV_ILN_4700 AR 29 1977 1-2 10 119-147 |
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English |
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Enthalten in Journal of low temperature physics 29(1977), 1-2 vom: Okt., Seite 119-147 volume:29 year:1977 number:1-2 month:10 pages:119-147 |
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Enthalten in Journal of low temperature physics 29(1977), 1-2 vom: Okt., Seite 119-147 volume:29 year:1977 number:1-2 month:10 pages:119-147 |
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Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin |
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Tewordt, L. @@aut@@ Schopohl, N. @@aut@@ Vollhardt, D. @@aut@@ |
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The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. 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530 VZ Effect of dipole interaction on collective modes $ in^{3} $He-A Nuclear Magnetic Resonance Dipole Interaction Spin Wave Collective Mode Transverse Spin |
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effect of dipole interaction on collective modes $ in^{3} $he-a |
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Effect of dipole interaction on collective modes $ in^{3} $He-A |
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Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. © Plenum Publishing Corporation 1977 |
| abstractGer |
Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. © Plenum Publishing Corporation 1977 |
| abstract_unstemmed |
Abstract A general theory for the correlation functions of $ superfluid^{3} $He which takes into account rigorously the magnetic dipole interaction is developed. The resulting equations are solved for the Anderson-Brinkman-Morel (ABM) state and for wave vectorsq oriented parallel to the energy gap axis. Then the dispersion relations of low-frequency modes, including Fermi liquid corrections and damping due to pair breaking, are calculated in the zero-temperature and zero-field limit. There are two real frequency modes arising from each of the longitudinal and transverse spin density correlation functions: a spin wave and an orbit wave,both exhibiting a frequency gap where that of the spin wave is somewhat modified in comparison to the unperturbed longitudinal nuclear magnetic resonance frequency ΩL/ABM.The orbit wave is damped much more strongly than the spin wave. Further, there are two real frequency modes arising from the density correlation function: the sound wave, having a frequency gap of the order ΩL/ABM, and an orbit wave, exhibiting a gap in wave number of order ΩL/ABM/vF.—The NMR frequency undergoes a small splitting, which is the result of the splitting of the energy gap due to the dipole interaction. One of the two gaps still has nodes.—In addition to these low-frequency modes our equations yield resonances at frequencies of the order of the gap frequency $ Δ_{0} $/ħ, i.e., at ω=1.22 $ Δ_{0} $/ħ and at ω=1.58 $ Δ_{0} $/ħ. The damping and the oscillator strengths of these resonances are calculated. © Plenum Publishing Corporation 1977 |
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