2025/01/09 by Jiansen Zhang, Zhang, Jiansen, Zipeng Wang +3 · 1 citation
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Atomic and Subatomic Physics Research #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2501.05194
We study the zero-energy collision of three fermions, two of which are in the spin-down (\downarrow) state and one of which is in the spin-up (\uparrow) state. Assuming that the two-body and the three-body interactions have a finite range, we find a parameter, D, called the three-body scattering hypervolume. We study the three-body wave function asymptotically when three fermions are far apart or one spin-\uparrow (spin-\downarrow) fermion and one pair, formed by the other two fermions, are far apart, and derive three asymptotic expansions of the wave function. The three-body scattering hypervolume D appears in the coefficients of such expansions at the order of B-5, where B=√((s12+s22+s32)/2) is the hyperradius of the triangle formed by the three fermions (we assume that the three fermions have the same mass), and s1,s2,s3 are the sides of the triangle. We compute the T-matrix element for three such fermions colliding at low energy in terms of D in the absence of two-body interactions. When the interactions are weak, we calculate D approximately using the Born expansion. We also analyze the energy shift of three two-component fermions in a large periodic cube due to D and generalize this result to the many-fermion system. D also determines the three-body recombination rates in two-component Fermi gases, and we calculate the three-body recombination rates in terms of D and the density and temperature of the gas.