Three-Body Scattering Hypervolume of Particles with Unequal Masses
- URL: http://arxiv.org/abs/2103.13869v2
- Date: Tue, 31 Aug 2021 13:56:59 GMT
- Title: Three-Body Scattering Hypervolume of Particles with Unequal Masses
- Authors: Zipeng Wang, Shina Tan
- Abstract summary: We analyze the collision of three particles with arbitrary mass ratio at zero collision energy.
We generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008.
We derive some properties of a two-component Bose gas with two-body scattering lengths.
- Score: 8.35070936044077
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $D$ first defined for identical bosons in
2008. We solve the three-body Schr\"{o}dinger 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 $D$
appears at the order $1/B^4$, where $B$ 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 $L$, where the three-body parameter contributes
a term of the order $D/L^6$. 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.
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