Model boson-fermion mixture within the self-consistent-field approximation

Abstract

We study the ground state properties of a boson-fermion mixture interacting via a hard-core repulsive potential with an attractive tail at zero temperature. We use the self-consistent field approach to calculate the ground state partial structure factors and the effective interactions between the species. We compare our results with the experimental data on liquid 3 He-4 He mixtures to find qualitative agreement. Collective modes and dynamic structure factors for the mixture are also discussed.

Structure of a model one-dimensional liquid 3He–4He mixture

“…These calculations along with some earlier reports [2] have shown that the self-consistent field method of Singwi, Tosi, Land, and Sjölander (STLS) [3] which was originally devised to treat the short-range correlation effects in Coulomb liquids is also capable of handling systems interacting via short-range potentials. We have recently extended the approach of Ng and Singwi [1] to study a bosonfermion mixture and found that our results are in good qualitative agreement with realistic 3 He- 4 He mixtures [4].…”

“…An interesting observation is that the behavior of V 0 g αβ (a 0 ) is largely independent of the 3 He mole fraction in the range 0.001 < x < 0.1. In our previous calculations [4] for higher-dimensional systems, we had found noticeable x-dependence. To relate our dimensionless results to the physical situation, we take a 0 ≈ 2.2 Å and obtain n 0 ≈ 0.23 Å −1 .…”

“…The self-consistent field method (or the STLS approximation) renormalizes the bare hard-core potentials to yield reasonable ground state structure factors. We find that the STLS method provides a reasonable qualitative description of liquid 3 He- 4 He mixtures which may be useful in the analysis of static and dynamical properties. Static structure factors and collective modes can be qualitatively correctly described by a simple hard-core interaction model.…”

“…There has been some experimental interest in 1D quantum liquids following the suggestion [6] and subsequent realization [7,8] of confining He in carbon nanotubes. On the theoretical side, the ground state properties of 1D liquid 4 He have recently been investigated by the variational hypernetted-chain calculations [9] and quantum Monte Carlo methods [10,11].…”

“…Our main motivation is to study the 1D liquid 3 He- 4 He mixture since a dilute solution of 3 He atoms in liquid 4 He form a fascinating quantum liquid as an example of interacting boson-fermion mixture [5]. There has been some experimental interest in 1D quantum liquids following the suggestion [6] and subsequent realization [7,8] of confining He in carbon nanotubes.…”