Collisional properties of weakly bound heteronuclear dimers

We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states, and their lifetimes.

Figure 1

The dimer-dimer $s$-wave scattering length $a_{dd}/a$ (solid) and the quantity ${\left(3{\beta }_{dd}\right)}^{1/3}/a$ for $p$-wave scattering (dashed) calculated by using HBO. The dotted line is the result of Eq. (14).

Figure 2

The inelastic rate constant for bosonic dimers with $M/m=28.5$ as a function of the atom-atom scattering length $a$. The solid line corresponds to the case of a real three-body parameter. The results plotted in dashed, dotted, dashed-dotted, and dash-dot-dot lines are obtained by taking into account the light-heavy-heavy relaxation processes. The values of the elasticity parameter ${\eta }_{\ast }=0.1$, 0.5, 1, and $\infty$, respectively (see text). The quantity $a_0$ is the value of $a$ at which the energy of a trimer state equals $E=2{ϵ}_0$ and a new inelastic channel opens. The inset shows the region $a\approx a_0$ in greater detail in order to see the threshold behavior .

Figure 3

The inelastic rate constant for fermionic dimers with the mass ratios $M/m=14.5$ and 22.2. Notations are the same as in Fig. 2.

Figure 4

Dimer-dimer $s$-wave scattering length obtained by the exact four-body method (solid line) and by HBO (dashed line). The inset shows the results of a similar calculation in 1D.