Historical Notes on Feshbach and Shape Resonances

Daniel Kleppner’s Reference Frame piece implies incorrectly that the crossover between Bardeen-Cooper-Schrieffer and Bose–Einstein condensation theory was first studied by Anthony Leggett in 1980. Actually, my early work on this topic was published 11 years before then. ¹

In the mid-1980s, I and colleagues in Australia also found the first example ² of a system that lay on the Bose-gas side of the BCS–Bose gas transition, in a ceramic sample of 3% zirconium-doped strontium titanate (SrTiO₃), although with a pairing temperature much lower than that predicted for the 1969 model used for this material. In three dimensions there is a threshold in the coupling strength for the existence of Bose-gas superconductivity at very low carrier concentrations, and for strengths slightly above the threshold, the pair-binding energy is proportional to the square of the difference of the coupling from the threshold value. Thus, for example, a calculated coupling error that gives a value 5% above threshold instead of 1% above would make a factor of 25 error in the pair-binding energy.

A later attempt ³ to reach the Bose-gas regime in macrocrystalline samples of Zr-doped SrTiO₃ with similar carrier concentrations to those in the ceramic sample mentioned indicated that some nonuniform state prevented the Bose-gas regime being reached. However, there is still much interesting physics awaiting study in this material.