Quantum third virial coefficient of a fractional-statistics gas

A quantum calculation of the third virial coefficient of a two-dimensional gas obeying fractional statistics is performed by diagonalizing the three-body Hamiltonian in a harmonic-oscillator potential with a large fermionic basis. The numerical results for the virial coefficient ${\mathit{A}}_3$ as a function of the flux strength α (α=0 for fermions, α=1 for bosons) are reliable in the range 0≤α≤0.25. $A sub 3— increases quadratically with α for very small α, but higher powers contribute substantially for large α.