Three-body scattering hypervolume for bosons with two-body repulsive Gaussian potentials

Shangguo Zhu, Shina Tan

P. M. A. Mestrom, V. E. Colussi, T. Secker +1 more

The elastic scattering properties of three bosons at low energy enter the many-body description of ultracold Bose gases via the three-body scattering hypervolume $D$. We study this quantity for identical bosons that interact via a pairwise finite-range potential. Our calculations cover the regime from strongly repulsive potentials towards attractive potentials supporting multiple two-body bound states and are consistent with the few existing predictions for $D$. We present a numerical confirmation of the universal predictions for $D$ in the strongly interacting regime, where Efimov physics dominates, for a local nonzero-range potential. Our findings highlight how $D$ is influenced by three-body quasibound states with strong $d$-wave or $g$-wave characteristics in the weakly interacting regime.

V. Polkanov, Orest Hryhorchak, V. Pastukhov

Zipeng Wang, Shina Tan

We study the zero-energy collision of three identical spin-polarized fermions with short-range interactions in one dimension. We derive the asymptotic expansions of the three-body wave function when the three fermions are far apart or one pair and the third fermion are far apart, and the three-body scattering hypervolume ${D}_{F}$ appears in the coefficients of such expansions. If the two-body interaction is attractive and supports two-body bound states, ${D}_{F}$ acquires a negative imaginary part related to the amplitudes of the outgoing waves describing the departure of the resultant bound pair and the remaining free fermion. For weak interaction potentials, we derive an approximate formula of the hypervolume by using the Born expansion. For the square-barrier and the square-well potentials and the Gaussian potential, we solve the three-body Schr\"odinger equation to compute ${D}_{F}$ numerically. We also calculate the shifts of energy and of pressure of spin-polarized one-dimensional Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate in one dimension.

Zipeng Wang, Shina Tan

We study the zero-energy collision of three identical spin-polarized fermions with short-range interactions in one dimension. We derive the asymptotic expansions of the three-body wave function when the three fermions are far apart or one pair and the third fermion are far apart, and the three-body scattering hypervolume $D_F$ appears in the coefficients of such expansions. If the two-body interaction is attractive and supports two-body bound states, $D_F$ acquires a negative imaginary part related to the amplitudes of the outgoing waves describing the departure of the resultant bound pair and the remaining free fermion. For weak interaction potentials, we derive an approximate formula of the hypervolume by using the Born expansion. For the square-barrier and the square-well potentials and the Gaussian potential, we solve the three-body Schrödinger equation to compute $D_F$ numerically. We also calculate the shifts of energy and of pressure of spin-polarized one-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate in one dimension.

Richard J. Eden, L. D. Fadeev