Physical Review A

Roton-Limited Mobility of Ions in Superfluid He4

Rubén G. Barrera, Gordon Baym

Published Oct 1, 1972• 55 citations

Abstract

We calculate the roton-limited mobility of ions in superfluid ${\mathrm{He}}^{4}$ for temperatures below \ensuremath{\sim} 1.7\ifmmode^\circ\else\textdegree\fi{}K. Taking, as a first approximation, a constant ion-roton transition-matrix element, which we treat as an adjustable parameter, we find good agreement with experiment for both positive and negative ions. This model calculation indicates that the most mobile of the recently discovered "exotic" negative carriers is a very light ion.

DOI: 10.1103/physreva.6.1558

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Theoretical modeling of ion mobility in superfluid 4 He

Steven L. Fiedler, David Mateo, Tatevik Aleksanyan +1 more

Physical Review BOct 19, 201226 citations

Mobility of Negative Ions Along Vortices in Rotating Superfluid Helium

Roger L. Douglass

Physical ReviewOct 5, 196856 citations

The mobility of negative ions in superfluid3He

M.M. Salomaa

Contemporary PhysicsMar 1, 198247 citations

Evidence for Roton Pair Creation in Superfluid He4

D. R. Allum, Roger M. Bowley, P. V. E. McClintock

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Ion Motion in Dilute He3 - He4 Solutions at Ultralow Temperatures

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Physical Review AJul 1, 197267 citations

Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

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arXiv:1708.06154Physical review. B./Physical review. BMar 13, 201815 citations

Physical Review A

Roton-Limited Mobility of Ions in Superfluid He4

Rubén G. Barrera, Gordon Baym

Published Oct 1, 1972• 55 citations

Publisher

Abstract

We calculate the roton-limited mobility of ions in superfluid

{\mathrm{He}}^{4}

for temperatures below \ensuremath{\sim} 1.7\ifmmode^\circ\else\textdegree\fi{}K. Taking, as a first approximation, a constant ion-roton transition-matrix element, which we treat as an adjustable parameter, we find good agreement with experiment for both positive and negative ions. This model calculation indicates that the most mobile of the recently discovered "exotic" negative carriers is a very light ion.

DOI: 10.1103/physreva.6.1558

Related papers

Theoretical modeling of ion mobility in superfluid 4 He

Steven L. Fiedler, David Mateo, Tatevik Aleksanyan +1 more

A method for calculating hydrodynamic added mass within the framework of time-dependent bosonic density functional theory (DFT) for superfluid ${}^{4}$ He is developed. As a calibration of the model, it is shown to reproduce the classical hydrodynamic limit for purely repulsive interactions. To model real systems for which experimental data are available, the following ions were considered: Be ${}^{+}$ , K ${}^{+}$ , Ca ${}^{+}$ , Sr ${}^{+}$ , and Ba ${}^{+}$ cations as well as the F${}^{\ensuremath{-}}$, Cl${}^{\ensuremath{-}}$, I${}^{\ensuremath{-}}$, and Br${}^{\ensuremath{-}}$ anions. The DFT model requires the ion-helium pair potential data as input, which were obtained from electron structure calculations by employing coupled clusters theory. The resultant static liquid density profiles as calculated by DFT were found to be in good agreement with previously published quantum Monte Carlo data. The calculated added masses for the positive ions correlated directly with the experimentally observed ion mobility data, by which the ions could be separated into two different categories based on the degree of the first solvent shell following the ion. The calculated added masses for the negative ions were found to be in disagreement with the existing experimental data, suggesting the possibility that other negatively charged species were observed in previous experiments. The negatively charged ions are predicted to have mobilities ($\ensuremath{\mu}$) within the range 0.8--1.0 cm ${}^{2}$ V${}^{\ensuremath{-}1}$ s${}^{\ensuremath{-}1}$ in superfluid helium at 1.3 K with the order $\ensuremath{\mu}$(I${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(Br${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(Cl${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(F${}^{\ensuremath{-}}$).A method for calculating hydrodynamic added mass within the framework of time-dependent bosonic density functional theory (DFT) for superfluid ${}^{4}$He is developed. As a calibration of the model, it is shown to reproduce the classical hydrodynamic limit for purely repulsive interactions. To model real systems for which experimental data are available, the following ions were considered: Be${}^{+}$, K${}^{+}$, Ca${}^{+}$, Sr${}^{+}$, and Ba${}^{+}$ cations as well as the F${}^{\ensuremath{-}}$, Cl${}^{\ensuremath{-}}$, I${}^{\ensuremath{-}}$, and Br${}^{\ensuremath{-}}$ anions. The DFT model requires the ion-helium pair potential data as input, which were obtained from electron structure calculations by employing coupled clusters theory. The resultant static liquid density profiles as calculated by DFT were found to be in good agreement with previously published quantum Monte Carlo data. The calculated added masses for the positive ions correlated directly with the experimentally observed ion mobility data, by which the ions could be separated into two different categories based on the degree of the first solvent shell following the ion. The calculated added masses for the negative ions were found to be in disagreement with the existing experimental data, suggesting the possibility that other negatively charged species were observed in previous experiments. The negatively charged ions are predicted to have mobilities ($\ensuremath{\mu}$) within the range 0.8--1.0 cm${}^{2}$ V${}^{\ensuremath{-}1}$ s${}^{\ensuremath{-}1}$ in superfluid helium at 1.3 K with the order $\ensuremath{\mu}$(I${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(Br${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(Cl${}^{\ensuremath{-}}$) $>$ $\ensuremath{\mu}$(F${}^{\ensuremath{-}}$).

Physical Review BOct 19, 201226 citations

Mobility of Negative Ions Along Vortices in Rotating Superfluid Helium

Roger L. Douglass

The mobility of negative ions trapped on linear vortices in rotating superfluid helium has been measured by a time-of-flight technique in the temperature range $0.8\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<1.6\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. Measurements could not be extended below 0.8\ifmmode^\circ\else\textdegree\fi{}K because, contrary to the present theory, the ion escape rate became too large. No evidence of direct trapping of positive ions by vortex lines was observed down to 0.4\ifmmode^\circ\else\textdegree\fi{}K. The trapped-ion mobility is interpreted in terms of scattering of the ion by thermal distributions of quantized vortex waves and rotons localized about the vortex axis.The mobility of negative ions trapped on linear vortices in rotating superfluid helium has been measured by a time-of-flight technique in the temperature range $0.8\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<1.6\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. Measurements could not be extended below 0.8\ifmmode^\circ\else\textdegree\fi{}K because, contrary to the present theory, the ion escape rate became too large. No evidence of direct trapping of positive ions by vortex lines was observed down to 0.4\ifmmode^\circ\else\textdegree\fi{}K. The trapped-ion mobility is interpreted in terms of scattering of the ion by thermal distributions of quantized vortex waves and rotons localized about the vortex axis.

Physical ReviewOct 5, 196856 citations

The mobility of negative ions in superfluid3He

M.M. Salomaa

This article reviews recent experimental and theoretical work on the mobility of negative ions in the superfluid A and B phases of liquid 3He. In the normal Fermi liquid at temperatures below ∼ 50 mK and also in the superfluid close to the superfluid transition temperature, Tc , the mobility of a negative ion may simply be considered as limited by the elastic scattering of 3He quasiparticles. This explains the constancy of the ion mobility in the normal phase. However, underlying the rapid increase of the measured mobility in the superfluid phases there is a subtle quantum-mechanical scattering effect. Detailed solutions of the 3He quasiparticle—negative ion scattering process in the pair-correlated state provide a simple physical picture of an energy-dependent forward-peaking phenomenon. This yields quantitative theoretical results for the ion mobility in the quasi-isotropic B phase and for the ion mobility tensor in the anisotropic A phase which agree with the experimental data.This article reviews recent experimental and theoretical work on the mobility of negative ions in the superfluid A and B phases of liquid 3He. In the normal Fermi liquid at temperatures below ∼ 50 mK and also in the superfluid close to the superfluid transition temperature, Tc , the mobility of a negative ion may simply be considered as limited by the elastic scattering of 3He quasiparticles. This explains the constancy of the ion mobility in the normal phase. However, underlying the rapid increase of the measured mobility in the superfluid phases there is a subtle quantum-mechanical scattering effect. Detailed solutions of the 3He quasiparticle—negative ion scattering process in the pair-correlated state provide a simple physical picture of an energy-dependent forward-peaking phenomenon. This yields quantitative theoretical results for the ion mobility in the quasi-isotropic B phase and for the ion mobility tensor in the anisotropic A phase which agree with the experimental data.

Contemporary PhysicsMar 1, 198247 citations

Evidence for Roton Pair Creation in Superfluid He4

D. R. Allum, Roger M. Bowley, P. V. E. McClintock

We have measured the drift velocity $\overline{v}$ of negative ions through superfluid $^{4}\mathrm{He}$ for temperatures $T<0.45$ K, under a pressure of 25 bar, for electric fields $20<E<2.6\ifmmode\times\else\texttimes\fi{}{10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1}$. From the observed form of $\overline{v}(E)$ , we deduce that roton emission from an ion traveling faster than the Landau critical velocity is governed by hitherto unrecognized selection rules whereby the rotons can be created only in pairs.We have measured the drift velocity $\overline{v}$ of negative ions through superfluid $^{4}\mathrm{He}$ for temperatures $T<0.45$ K, under a pressure of 25 bar, for electric fields $20<E<2.6\ifmmode\times\else\texttimes\fi{}{10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1}$. From the observed form of $\overline{v}(E)$, we deduce that roton emission from an ion traveling faster than the Landau critical velocity is governed by hitherto unrecognized selection rules whereby the rotons can be created only in pairs.

Physical Review LettersMay 31, 197675 citations

Ion Motion in Dilute He3 - He4 Solutions at Ultralow Temperatures

Moyses Kuchnir, John B. Ketterson, Pat R. Roach

Measurements of the velocity of charge carriers in several dilute solutions of $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$ in the temperature range 0.017-1.0 K are reported. The low-field negative-ion mobility shows a ${T}^{\ensuremath{-}\frac{1}{2}}$ dependence below 0.08 K characteristic of hard-sphere scattering. A maximum is observed in the mobility in the vicinity of 0.4 K. This can be interpreted in terms of a $^{3}\mathrm{He}$ condensation on the bubble surface. The positive-ion mobility is nearly temperature independent below 0.7 K. This has recently been interpreted in terms of a momentum-dependent polarization scattering. The field dependence of the positive-carrier velocity shows a discontinuity in the vortex-ring regime. The discontinuity can be shown to result from a size-dependent drag coefficient and a maximum is observed for very small rings (\ensuremath{\sim}16 \AA{}).Measurements of the velocity of charge carriers in several dilute solutions of $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$ in the temperature range 0.017-1.0 K are reported. The low-field negative-ion mobility shows a ${T}^{\ensuremath{-}\frac{1}{2}}$ dependence below 0.08 K characteristic of hard-sphere scattering. A maximum is observed in the mobility in the vicinity of 0.4 K. This can be interpreted in terms of a $^{3}\mathrm{He}$ condensation on the bubble surface. The positive-ion mobility is nearly temperature independent below 0.7 K. This has recently been interpreted in terms of a momentum-dependent polarization scattering. The field dependence of the positive-carrier velocity shows a discontinuity in the vortex-ring regime. The discontinuity can be shown to result from a size-dependent drag coefficient and a maximum is observed for very small rings (\ensuremath{\sim}16 \AA{}).

Physical Review AJul 1, 197267 citations

Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

Alberto Villois, Hayder Salman

We study the motion of an electron bubble in the zero-temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schr\"odinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^{4}\mathrm{He}$ at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.We study the motion of an electron bubble in the zero-temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schr\"odinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^{4}\mathrm{He}$ at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.

arXiv:1708.06154Physical review. B./Physical review. BMar 13, 201815 citations

We calculate the roton-limited mobility of ions in superfluid

{\mathrm{He}}^{4}

A method for calculating hydrodynamic added mass within the framework of time-dependent bosonic density functional theory (DFT) for superfluid

{}^{4}

He is developed. As a calibration of the model, it is shown to reproduce the classical hydrodynamic limit for purely repulsive interactions. To model real systems for which experimental data are available, the following ions were considered: Be

{}^{+}

, K

{}^{+}

, Ca

{}^{+}

, Sr

{}^{+}

, and Ba

{}^{+}

cations as well as the F${}^{\ensuremath{-}}$, Cl${}^{\ensuremath{-}}$, I${}^{\ensuremath{-}}$, and Br${}^{\ensuremath{-}}$ anions. The DFT model requires the ion-helium pair potential data as input, which were obtained from electron structure calculations by employing coupled clusters theory. The resultant static liquid density profiles as calculated by DFT were found to be in good agreement with previously published quantum Monte Carlo data. The calculated added masses for the positive ions correlated directly with the experimentally observed ion mobility data, by which the ions could be separated into two different categories based on the degree of the first solvent shell following the ion. The calculated added masses for the negative ions were found to be in disagreement with the existing experimental data, suggesting the possibility that other negatively charged species were observed in previous experiments. The negatively charged ions are predicted to have mobilities ($\ensuremath{\mu}$) within the range 0.8--1.0 cm

{}^{2}

V${}^{\ensuremath{-}1}$ s${}^{\ensuremath{-}1}$ in superfluid helium at 1.3 K with the order $\ensuremath{\mu}$(I${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(Br${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(Cl${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(F${}^{\ensuremath{-}}$).

We have measured the drift velocity

\overline{v}

of negative ions through superfluid

^{4}\mathrm{He}

for temperatures

T<0.45

K, under a pressure of 25 bar, for electric fields $20<E<2.6\ifmmode\times\else\texttimes\fi{}{10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1}$. From the observed form of

\overline{v}(E)

, we deduce that roton emission from an ion traveling faster than the Landau critical velocity is governed by hitherto unrecognized selection rules whereby the rotons can be created only in pairs.

Measurements of the velocity of charge carriers in several dilute solutions of

^{3}\mathrm{He}

^{4}\mathrm{He}

in the temperature range 0.017-1.0 K are reported. The low-field negative-ion mobility shows a ${T}^{\ensuremath{-}\frac{1}{2}}$ dependence below 0.08 K characteristic of hard-sphere scattering. A maximum is observed in the mobility in the vicinity of 0.4 K. This can be interpreted in terms of a

^{3}\mathrm{He}

condensation on the bubble surface. The positive-ion mobility is nearly temperature independent below 0.7 K. This has recently been interpreted in terms of a momentum-dependent polarization scattering. The field dependence of the positive-carrier velocity shows a discontinuity in the vortex-ring regime. The discontinuity can be shown to result from a size-dependent drag coefficient and a maximum is observed for very small rings (\ensuremath{\sim}16 \AA{}).

^{4}\mathrm{He}

at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.