The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5

Progress of Theoretical PhysicsAug 1, 199342 citations

Helium isotope quantum fluid mixtures

D. S. Betts

The last five years have seen a burst of activity leading to the current view that 3He atoms dissolved in superfluid liquid 4He show remarkable resemblance to a weakly-interacting Fermi gas. This is because the solvent 4He, having vanishingly small entropy, specific heat, viscosity and magnetic susceptibility, behaves almost as if it were a massive vacuum, in which 3He atoms float. So at last a real Fermi ‘gas’ is available and can readily be cooled to temperatures well below its Fermi degeneracy temperature. This model of solute 3He, with its weaknesses and strengths, is the basis of this article.The last five years have seen a burst of activity leading to the current view that 3He atoms dissolved in superfluid liquid 4He show remarkable resemblance to a weakly-interacting Fermi gas. This is because the solvent 4He, having vanishingly small entropy, specific heat, viscosity and magnetic susceptibility, behaves almost as if it were a massive vacuum, in which 3He atoms float. So at last a real Fermi ‘gas’ is available and can readily be cooled to temperatures well below its Fermi degeneracy temperature. This model of solute 3He, with its weaknesses and strengths, is the basis of this article.

Contemporary PhysicsMar 1, 19711 citation

Théorie de la pression osmotique des solutions diluées de 3He dans 4He

Joseph Seiden

On détermine la pression osmotique Π des solutions diluées de 3He dans 4He superfluide par un calcul de perturbation au second ordre en U(r), potentiel d'interaction de deux atomes de 3He dans 4He. Pour des concentrations atomiques de 3He inférieures à 0,5 % et des températures inférieures à 0,1 °K, on montre qu'on peut obtenir des expressions satisfaisantes de Π dans lesquelles U(r) ne figure que par ses second et quatrième « moments », Les valeurs théoriques et expérimentales de Π semblent devoir concorder aux basses températures T << TF (TF, température de Fermi des 3He). Dans la région semi-classique T ≃ TF, l'influence de U(r) sur Π ne peut être mise en évidence que par des expériences à des températures inférieures à 0,1 °K.On détermine la pression osmotique Π des solutions diluées de 3He dans 4He superfluide par un calcul de perturbation au second ordre en U(r), potentiel d'interaction de deux atomes de 3He dans 4He. Pour des concentrations atomiques de 3He inférieures à 0,5 % et des températures inférieures à 0,1 °K, on montre qu'on peut obtenir des expressions satisfaisantes de Π dans lesquelles U(r) ne figure que par ses second et quatrième « moments », Les valeurs théoriques et expérimentales de Π semblent devoir concorder aux basses températures T << TF (TF, température de Fermi des 3He). Dans la région semi-classique T ≃ TF, l'influence de U(r) sur Π ne peut être mise en évidence que par des expériences à des températures inférieures à 0,1 °K.

Journal de physiqueJan 1, 19692 citations

Concentration Dependence of the Effective Mass of 3He Atoms in 3He−4He Mixtures

E. Krotscheck, M. Saarela, K. Schörkhuber +1 more

Recent measurements by Yorozu et al. [S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)] as well as by Simons and Mueller [R. Simons and R. M. Mueller, Czech. J. Phys. Suppl. 46, 201 (1996)] have determined the effective mass of ${}^{3}\mathrm{He}$ atoms in a ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the ${}^{3}\mathrm{He}$ concentration. Using correlated basis function perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.Recent measurements by Yorozu et al. [S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)] as well as by Simons and Mueller [R. Simons and R. M. Mueller, Czech. J. Phys. Suppl. 46, 201 (1996)] have determined the effective mass of ${}^{3}\mathrm{He}$ atoms in a ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the ${}^{3}\mathrm{He}$ concentration. Using correlated basis function perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.

arXiv:cond-mat/9802122Physical Review LettersMay 25, 199862 citations

Introduction To Liquid 4HE

H. R. Glyde

Abstract In this chapter we introduce some basic concepts of superfluid 4He that we will draw on in Chapters 8-12. Liquid 4 He has a long and rich history and there are many concepts that are implicit in the field today. We begin with a sketch of the unique mass and heat flow character of superfluid 4He. The assumptions of the two-fluid model used successfully to describe these properties are noted in §7.1. We introduce Bose-Einstein condensation in a Bose gas and the extension of this to interacting superfluid 4 He in §7.2. This leads naturally to the one-body density matrix which is the intermediate scattering function in the impulse approximation,We introduce a number of basic properties such as the static structure factor, the pair correlation function, and the momentum distribution which can be calculated from first principles using Monte Carlo and path integral Monte Carlo (PIMC) methods. We conclude by noting the two current descriptions of the characteristic excitation in superfluid 4He. The first is a density excitation, based on the Landau and Feynman view, with suitable modifications at higher Q to take account of correlations among atoms. In the second, the density excitation is separated into a part due to the excitation of single particles out of the condensate to states above the condensate and a part due to regular density excitations involving only states above the condensate. In the latter picture the condensate appears explicitly in S(Q, ω).Abstract In this chapter we introduce some basic concepts of superfluid 4He that we will draw on in Chapters 8-12. Liquid 4 He has a long and rich history and there are many concepts that are implicit in the field today. We begin with a sketch of the unique mass and heat flow character of superfluid 4He. The assumptions of the two-fluid model used successfully to describe these properties are noted in §7.1. We introduce Bose-Einstein condensation in a Bose gas and the extension of this to interacting superfluid 4 He in §7.2. This leads naturally to the one-body density matrix which is the intermediate scattering function in the impulse approximation,We introduce a number of basic properties such as the static structure factor, the pair correlation function, and the momentum distribution which can be calculated from first principles using Monte Carlo and path integral Monte Carlo (PIMC) methods. We conclude by noting the two current descriptions of the characteristic excitation in superfluid 4He. The first is a density excitation, based on the Landau and Feynman view, with suitable modifications at higher Q to take account of correlations among atoms. In the second, the density excitation is separated into a part due to the excitation of single particles out of the condensate to states above the condensate and a part due to regular density excitations involving only states above the condensate. In the latter picture the condensate appears explicitly in S(Q, ω).

Apr 27, 19951 citation

Bound state of a 3He atom at the interface of crystal and superfluid 4He

Massimo Boninsegni

The bound state of a 3He atom at the interface between coexisting crystalline and superfluid phases of 4He is studied theoretically by means of first principle Quantum Monte Carlo simulations. We consider both the case of a solid/superfluid 4He interface, as well as that of a few solid layers of 4He forming on an attractive substrate. It is observed that the 3He bound state is sharply localized in a well-defined, quasi-2D layer of 4He in the region intermediate between the solid and the liquid. The layer in which the 3He atom resides displays an intriguing interplay of atomic localization and quantum-mechanical exchanges; is not necessarily the first “non-solid” layer, as suggested in previous studies, and it is affected by the attractive strength of the substrate.The bound state of a 3He atom at the interface between coexisting crystalline and superfluid phases of 4He is studied theoretically by means of first principle Quantum Monte Carlo simulations. We consider both the case of a solid/superfluid 4He interface, as well as that of a few solid layers of 4He forming on an attractive substrate. It is observed that the 3He bound state is sharply localized in a well-defined, quasi-2D layer of 4He in the region intermediate between the solid and the liquid. The layer in which the 3He atom resides displays an intriguing interplay of atomic localization and quantum-mechanical exchanges; is not necessarily the first “non-solid” layer, as suggested in previous studies, and it is affected by the attractive strength of the substrate.

arXiv:2203.01264Results in PhysicsMay 14, 20222 citations

{}^{3}\mathrm{He}

atoms in a ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the

{}^{3}\mathrm{He}

concentration. Using correlated basis function perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.