Effective interaction of three resonantly interacting particles and the force range

The effect of the force range ${\mathit{r}}_0$ on an effective long-range interaction in a system of three resonantly interacting particles is considered. By employing a boundary-condition approach, it is explicitly shown that the account of the force range gives rise to a correction ${\mathit{r}}_0$/${\mathit{R}}^3$ in the effective long-range interaction. The correction is universal (i.e., independent of detail structure of the force), and is attractive for symmetric $0^{+}$ three-particle states. The effect of the correction on the well-known correlation between the three-particle binding energy and the particle-pair scattering length is calculated.