  The notion of rational spin double affine Hecke algebras (sDaHa) and rational
double affine Hecke-Clifford algebras (DaHCa) associated to classical Weyl
groups are introduced. The basic properties of these algebras such as the PBW
basis and Dunkl operator representations are established. An algebra
isomorphism relating the rational DaHCa to the rational sDaHa is obtained. We
further develop a link between the usual rational Cherednik algebra and the
rational sDaHa by introducing a notion of rational covering double affine Hecke
algebras.
