It is well known that at long wavelengths $\lambda$ an s-wave scatterer can have a scattering cross section $\sigma$ on the order of ${\lambda }^2$, much larger than its physical size, as measured by the range of its potential. Very interesting phenomena can arise when two or more identical scatterers are placed close together, well within one wavelength. We show that, for a pair of identical scatterers, an extremely narrow p-wave “proximity” resonance develops from a broader s-wave resonance of the individual scatterers. A new s-wave resonance of the pair also appears. The relation of these proximity resonances (so called because they appear when the scatterers are close together) to the Thomas and Efimov effects is discussed.

• Received 30 July 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.4122