COHERENCE LENGTHS FOR 3-DIMENSIONAL SUPERCONDUCTORS IN THE BCS-BOSE PICTURE

Following an approach similar to that of Miyake or Randeria, Duan, and Shieh in two dimensions, we study a three-dimensional many-fermion ga s at zero temperature interacting via some short-ranged two-body poten tial. To accommodate a possible singularity (e.g., the Coulomb repulsi on) in the interaction, the potential is eliminated in favor of the tw o-body scattering t-matrix, the low-energy form of which is expressibl e in terms of the s-wave scattering length a(s). The BCS gap equation for s-wave pairing is then solved simultaneously with the number equat ion in order to self-consistently obtain the zero-temperature BCS gap Delta as well as the chemical potential mu, as functions of the dimens ionless coupling variable lambda=k(F)a(s), where k(F) is the Fermi mom entum. Results are valid for arbitrary coupling strength, and in the w eak coupling limit reproduce the standard BCS results. Finally, root-m ean-square pair sizes are obtained as a function of lambda and compare d with experimental values.