Measurement of the Kinetic Energy and Lattice Constant in hcp Solid Helium at Temperatures 0.07–0.4 K

Adams, Mark A.; Mayers, J.; Kirichek, O.; Down, R. B. E.

doi:10.1103/physrevlett.98.085301

Cited by 41 publications

(46 citation statements)

References 27 publications

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“…A condensate fraction has not been observed in crystalline solid helium 40,68,69 at these pressures, even when the surface area is large. 69 An upper limit of n 0 ≤ 0.3 % has been set.…”

Section: -67mentioning

confidence: 85%

Atomic momentum distribution and Bose-Einstein condensation in liquid4He under pressure

et al. 2011

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Neutron scattering measurements of the dynamic structure factor, S(Q, ω), of liquid 4 He as a function of pressure at high momentum transfer, Q, are presented. At high Q the dynamics of single atoms in the liquid is observed. From S(Q, ω) the atomic momentum distribution, n(k), the Bose-Einstein condensate fraction, n0, and the Final State broadening function are obtained. The shape of n(k) differs from a classical, Maxwell-Boltzmann distribution with higher occupation of low momentum states in the quantum liquid. The width of n(k) and the atomic kinetic energy, K , increase with pressure but the shape of n(k) remains approximately independent of pressure. The present observed and Monte Carlo calculations of K agree within error. The condensate fraction decreases from n0 = 7.25 ± 0.75% at SVP (p ≃ 0) to n0 = 3.2 ± 0.75% at pressure p = 24 bar, a density dependence that is again reproduced by MC calculations within observed error. The Final State function is the contribution to S(Q, ω) arising from the interaction of the struck atom with its neighbors following the scattering. The FS function broadens with increasing pressure reflecting the increased importance of FS effects at higher pressure.

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“…A condensate fraction has not been observed in crystalline solid helium 40,68,69 at these pressures, even when the surface area is large. 69 An upper limit of n 0 ≤ 0.3 % has been set.…”

Section: -67mentioning

confidence: 85%

Atomic momentum distribution and Bose-Einstein condensation in liquid4He under pressure

et al. 2011

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“…Observation of BEC in solid helium would be an unambiguous verification of superflow but, as yet, has not been observed [17][18][19] . To better understand BEC in dense systems we have measured 20 the condensate fraction in liquid 4 He at low temperature as a function of pressure up to solidification, p = 25.3 bar.…”

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confidence: 90%

Bose-Einstein condensation in liquid4He near the liquid-solid transition line

et al. 2012

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We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, n0(T ), and the atomic momentum distribution, n ⋆ (k), of liquid 4 He as a function of temperature at pressure p =24 bar. Both the temperature dependence of n0(T ) and of the width of n ⋆ (k) are determined. The n0(T ) can be represented by n0(T ) = n0 (0)γ ] with a small n0(0) = 2.80 ± 0.20 % and large γ = 13 ± 2 for T < T λ indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the n ⋆ (k). The narrowing accounts for 65 % of the drop in kinetic energy below T λ and reveals an important coupling between BEC and k > 0 states. The experimental results are well reproduced by Path Integral Monte Carlo calculations.

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“…h i is the particle momentum along theq direction, and J IA ðy;qÞ is the neutron Compton Profile (NCP) [5]. 1 When the sample is isotropic, the particle momentum distribution only depends on the modulus of p, and theq direction is immaterial, so the NCP is simply J IA ðyÞ ¼ 2p R 1 y j j pnðpÞdp. The kinetic energy is directly proportional to the second moment of the NCP…”

Section: Methodsmentioning

confidence: 99%

“…Measurements of momentum distributions are a matter of widespread interest because of their connection to the theories of Bose/Fermi liquids, anharmonic solids [1], and in the case of water, to provide valuable experimental evidence relating to the hydrogen-bond potential energy surfaces [2][3][4]. The most direct method to measure the momentum distribution is Deep Inelastic Neutron Scattering [5,6], with experimental methods mainly developed at the ISIS pulsed neutron source and following a theoretical study by Gunn et al [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

2013

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a b s t r a c tBy means of Deep Inelastic Neutron Scattering we determined the temperature dependence of the proton kinetic energy in polycrystalline ice Ih between 5 K and 271 K. We compare our results with predictions form Path Integral quantum simulations and semiclassical quasi-harmonic models with phasedependent frequencies. The latter show the best agreement with the experiment if the librational contribution is properly taken into account. The kinetic energy increase with temperature in ice is also found to be approximately a factor $ 5 smaller than in the case of liquid water above room temperature, highlighting the role played by anharmonic quantum fluctuations in the two phases.

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Measurement of the Kinetic Energy and Lattice Constant in hcp Solid Helium at Temperatures 0.07–0.4 K

Cited by 41 publications

References 27 publications

Atomic momentum distribution and Bose-Einstein condensation in liquid4He under pressure

Atomic momentum distribution and Bose-Einstein condensation in liquid4He under pressure

Bose-Einstein condensation in liquid4He near the liquid-solid transition line

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

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