2007/09/17 by Shina Tan · 91 citations
Physics and Astronomy · #Amplitude #Atomic and Subatomic Physics Research #Bose gas #Bose–Einstein condensate #Boson #Cold Atom Physics and Bose-Einstein Condensates #Function (biology) #Ground state #Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Range (aeronautics) #Scattering #Scattering amplitude #Scattering length #Wave function #Work (physics) #cond-mat.stat-mech #hep-lat #nucl-th
paper · pdf · doi:10.1103/physreva.78.013636
published in Physical Review A 78(1) (American Physical Society) · 24 pages, no figure
arxiv created 2007/09/17 · openalex publication_date 2008/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. Asymptotic expansions of this wave function at large interparticle distances are derived, from which is defined a quantity D named three-body scattering hypervolume, which is an analog of the two-body scattering length. Given any finite-range interactions, one can thus predict the effective three-body force from a numerical solution of the Schr"odinger equation. In this way, the constant D for hard-sphere bosons is computed, leading to the first complete result for the ground-state energy per particle of a dilute Bose-Einstein condensate (BEC) of hard spheres to order \ensuremathρ2, where \ensuremathρ is the number density. Effects of D are also demonstrated in the three-body energy in a finite box of size L, which is expanded to the order L^\ensuremath-7, and in the three-body scattering amplitude in vacuum. The three-body scattering amplitude calculated in this paper disagrees with an earlier calculation in the literature, because of the omission of the two-body effective range in that earlier work. Another key prediction is the condensate fractions of dilute BECs, which also disagree with an earlier work in the literature based on the effective field theory (EFT), as a result of short-range physics. An EFT prediction of the BEC ground-state energy, however, is corroborated.