Three-Body Scattering Hypervolume of Particles with Unequal Masses
arXiv:2103.13869 · doi:10.1103/PhysRevA.103.063315
Abstract
We analyze the collision of three particles with arbitrary mass ratio at zero collision energy, assuming arbitrary short-range potentials, and generalize the three-body scattering hypervolume first defined for identical bosons in 2008. We solve the three-body Schrödinger equation asymptotically when the three particles are far apart or one pair and a third particle are far apart, deriving two asymptotic expansions of the wave function, and the parameter appears at the order , where is the overall size of the triangle formed by the particles. We then analyze the ground state energy of three such particles with vanishing or negligible two-body scattering lengths in a large periodic volume of side length , where the three-body parameter contributes a term of the order . From this result we derive some properties of a two-component Bose gas with negligible two-body scattering lengths: its energy density at zero temperature, the corresponding generalized Gross-Pitaevskii equation, the conditions for the stability of the two-component mixture against collapse or phase separation, and the decay rates of particle densities due to three-body recombination.
arXiv comment10 pages, no figure
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