We have studied the fine structure of the heavy-hole exciton in CdSe quantu
m dots grown on ZnSe by molecular beam epitaxy. Applying a tilted magnetic
field, all four levels of the ground state are detected simultaneously. The
zero-field separation between the optically forbidden and allowed doublers
ranges between 1.7 and 1.9 meV and is crucially influenced by the finite e
nergy barrier at the heterointerface as well as the existence of a wetting
layer. The energy splitting within the allowed doubler (200 mu eV) is subst
antially larger than for the forbidden states (less than or equal to 20 mu
eV), demonstrating that a dominant contribution arises from the long-ranged
part of the electron-hole exchange interaction. The total set of g factors
is derived. A huge anisotropy for the electron is found. [S0163-1829(99)50
848-5].