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From the Coulomb to Effective Interaction: Application to Bose—Einstein Condensation

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Abstract

An expression for the short-range effective interaction potential of “quasinuclei” is derived based on the “pure” Coulomb interaction model. This model represents the equilibrium Coulomb system (CS) of interacting electrons and identical nuclei using the adiabatic approximation for nuclei and an arbitrarily strong (in general) interaction for the electronic subsystem (degenerate or nondegenerate). Based on general properties of the Coulomb interaction, it is shown that the Fourier component of the effective pair potential between “quasinuclei” is discontinuous at the wave vector q = 0 in the case of the weak interaction between electronic and nuclear subsystems. This discontinuity is important for Bose-condensed systems such as Hell and rarefied alkali-metal gases at temperatures lower than that of the Bose condensation transition when a macroscopic number of quasiparticles with momentum q = 0 exist. It is shown that there can be a spectral gap for single-particle excitations, which disappears in the normal state.

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Acknowledgments

The author is grateful to E.M. Apfelbaum, V. B. Bobrov, A.M. Ignatov, G.A. Martynov, and P.P.J.M. Schram for helpful discussions.

This study was supported by the Russian Foundation for Basic Research, project no. 17-02-00573.

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Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, 13/19 Izhorskaya St., Moscow, 127412, Russia

    S. A. Trigger

  2. Prokhorov General Physics Institute, Russian Academy of Sciences, 38 Vavilova St., Moscow, 119991, Russia

    S. A. Trigger

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  1. S. A. Trigger
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Correspondence to S. A. Trigger.

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Russian Text © The Author(s), 2019, published in Kratkie Soobshcheniya po Fizike, 2019, Vol. 46, No. 6, pp. 32–37.

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Trigger, S.A. From the Coulomb to Effective Interaction: Application to Bose—Einstein Condensation. Bull. Lebedev Phys. Inst. 46, 206–209 (2019). https://doi.org/10.3103/S1068335619060058

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  • DOI: https://doi.org/10.3103/S1068335619060058

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