Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a Li6 mixture which can deviate strongly from the one in a weakly interacting two-component system.