2024/02/03 by Junjie Liang, Liang, Junjie, Shina Tan +1 · 1 citation
Medicine · Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Crystallography and Radiation Phenomena #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Radiation Therapy and Dosimetry
paper · pdf · doi:10.48550/arxiv.2402.02202
openalex publication_date 2024/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter D is defined. The dimension of D is length squared, and we call D three-body scattering area. We find that the ground state energy per particle of a zero-temperature dilute Bose gas with these interactions is approximately (ℏ2 D )/(6m)ρ2, where ρ is the number density of the bosons, m is the mass of each boson, and ℏ is Planck's constant over 2π. Such a Bose gas is stable at D≥ 0 in the thermodynamic limit, and metastable at D<0 in the harmonic trap if the number of bosons is less than Ncr≈ 3.6413 √((ℏ)/(mω|D|)), where ω is the angular frequency of the harmonic trap. If the two-body interaction supports bound states, D typically acquires a negative imaginary part, and we find the relation between this imaginary part and the amplitudes of the pair-boson production processes. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of D.