  Coannihilation processes provide an important additional mechanism for
reducing the density of stable relics in the Universe. In the case of the
stable lightest neutralino of the MSSM, and in particular the Constrained MSSM
(CMSSM), the coannihilation with sleptons plays a major role in opening up
otherwise cosmologically excluded ranges of supersymmetric parameters. In this
paper, we derive a full set of exact, analytic expressions for the
coannihilation of the lightest neutralino with the sleptons into all two--body
tree--level final states in the framework of minimal supersymmetry. We make no
simplifying assumptions about the neutralino nor about sfermion masses and
mixings other than the absence of explicit CP--violating terms and
inter--family mixings. The expressions should be particularly useful in
computing the neutralino WIMP relic abundance without the approximation of
partial wave expansion. We illustrate the effect of our analytic results with
numerical examples and demonstrate a sizeable difference with approximate
expressions available in the literature.
