Simple model for analyzing Efimov energy and three-body recombination of three identical bosons with van der Waals interactions

Abstract

We construct a simple model to calculate the trimer bound state energy ${E}_{T}^{(n)}$ and three-body recombination rate ${K}_{3}^{0}$ of three identical bosons with van der Waals interaction without using any two- or three-body fitting parameter. Using this simple model, we investigate the influence of the van der Waals finite-range effect on ${E}_{T}^{(n)}$ and ${K}_{3}^{0}$. Our calculation shows that the finite-range effect leads to the ground trimer state energy ${E}_{T}^{(0)}$ not crossing the atom-dimer threshold, and the scaled three-body recombination rate ${K}_{3}^{0}/{a}^{4}$ deviating from the universal three-body theory. The results of our simple model agree within a few percent with other theoretical works with van der Waals interaction and also the experimental data.