Theory of photoassociation of ultra-cold trimers

We present a general theory for the formation of ultracold trimers by photoassociation from an excited atom and a ground state diatomic molecule in an ultracold mixed gas containing atoms and molecules. The excited atom has a non-zero quadrupole moment, and interacts with the dimer by a quadrupole-quadrupole long-range interaction, which is attractive enough to bind trimers. We have also applied the general formalism for the multipole and dispersion asymptotic interactions to the calculation of long-range coefficients of interaction between an alkali atom (Li or Cs) in its ground or its first excited state and a molecule (Li$_2$ or Cs$_2$) in an excited rotational state. The suggested photoassociation theory can easily be generalized to the formation of tetramers from identical dimers by an RF field.