Predicting the three-body parameter across Feshbach resonances of any width
In plain words
The position of the first Efimov molecule is measured by a number (the three-body parameter), found to be close to 9.7 times a basic atomic length. The task is a theory that predicts it for every atom and resonance, including narrow ones.
Precise statement
For identical bosons near an isolated s-wave Feshbach resonance with van der Waals length $r_{\mathrm{vdW}}$, resonance strength $s_{\mathrm{res}}$ and background scattering length $a_{\mathrm{bg}}$, predict a_-^(1)/r_vdW, the scattering length of the first three-body loss resonance. Answer: a model reproducing all measured values (Cs, K-39, Li-7, Rb-85) within experimental error, including the deviation from -9.7 for $s_{\mathrm{res}} < 1$.
What would settle it
A multichannel three-body calculation that matches every measured a_-^(1) within error bars, plus a new measurement at a narrow resonance that it predicts in advance.
Status in the literature
Theory traced the value to a universal three-body barrier near $R \sim 2 r_{\mathrm{vdW}}$ (Wang et al., PRL 2012), but measurements at resonances of different widths scatter by roughly 15 to 30% around the universal value.
See also
- Related A renormalizable power counting for chiral nuclear forces
- Related Finite-range corrections to the Efimov scaling factor 22.7
- Related Is a separate four-body parameter needed for Efimov-linked tetramers?
- Related Universality of the three-body parameter in heavy-heavy-light atom mixtures
- Related Observation of the super Efimov tower in two-dimensional p-wave fermions