BCS theory in several other ways [@Annett-99]. This led to a resurgence of interest in the BCS to Bose crossover [@Micnas-Ranninger-Robaskiewicz-90; @Gyorffy-Staunton-Stocks-91; @Zwerger-92; @Alexandrov-Rubin-93; @Haussmann-93; @Pistolesi-Strinati-94; @Haussmann-94; @Pistolesi-Strinati-96; @SaDeMelo-Randeria-Engelbrecht-93; @Engelbrecht-Randeria-SaDeMelo-97; @Babaev-Kleinert-98; @Babaev-Kleinert-99; @Andrenacci-Pieri-Strinati-99; @Chen-Kosztin-Levin-00; @Ohashi-Griffin-02], particularly in models with exotic pairing [@Randeria-Duan-Shieh-90; @Zwerger-97; @Engelbrecht-Nazarenko-Randeria-98; @DenHertog-99; @Andrenacci-Perali-Pieri-Strinati-99; @Jon-James-2000; @Soares-Kokubun-RodriguezNunez-Rendon-02; @Quintanilla-Gyorffy-Annett-Wallington-02]. On the other hand little attention has been given to the physics of the crossover in the context of the original discussions of exotic pairing [@Balian-64; @Anderson-Brinkman-74], namely when a central attraction, in a continuum, leads to Cooper pairing with $ l>0 $. In fact this is a specially interesting case since the two-body ground state is guaranteed, under quite general conditions, [@Landau-Lifshitz-QM] to have $ l=0 $, making exotic pairing necessarily a many-body effect. Some obvious questions arise: What type of isotropic interactions lead to exotic pairing, and under what conditions? Is exotic pairing possible in the Bose-Einstein (BE) limit, when the BCS ground state is a condensate of non-overlapping pairs [@Eagles-69; @Pincus-et-al-73; @Leggett-80; @Nozieres-SchmittRink-85]? Moreover the recent achievement of Fermi degeneracy in magnetically trapped, ultra-low temperature gases has stimulated speculations that superfluidity [@Bruun-Castin-Dum-Burnett-99; @Combescot-01; @Holland-Kokkelmans-Chiofalo-Walser-01] and indeed the BCS-Bose crossover [@Ohashi-Griffin-02] may be observable in these systems. Understanding the 