Feshbach resonance
In the field of physics, a Feshbach resonance, named after Herman Feshbach, is a feature of many-body systems in which a bound state is achieved if the coupling(s) between at least one internal degree of freedom and the reaction coordinates, which lead to dissociation, vanish. The opposite situation, when a bound state is not formed, is a shape resonance.
Feshbach resonances have become important in the study of the cold atoms systems, both the Fermi gases as well as the Bose–Einstein condensates (BECs). In the context of scattering processes in many-body systems, the Feshbach resonance occurs when the energy of a bound state of an interatomic potential is equal to the kinetic energy of a colliding pair of atoms, which have hyperfine structure coupled via Coulomb or exchange interactions. In experimental settings, the Feshbach resonances provide a way to vary interaction strength between atoms in the cloud by changing scattering length, asc, of elastic collisions. For atomic species that possess these resonances (like K39 and K40), it is possible to vary the interaction strength by applying a uniform magnetic field. Among many uses, this tool has served to explore the region of the BEC (of fermionic molecules) to the BCS (of weakly interacting fermion-pairs) transition in Fermi clouds. For the BECs, Feshbach resonances have been used to study a spectrum of systems from the non-interacting ideal Bose gases to the unitary regime of interactions.
Consider a general quantum scattering event between two particles. In this reaction, there are two reactant particles denoted by A and B, and two product particles denoted by A' and B' . For the case of a reaction (such as a nuclear reaction), we may denote this scattering event by
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