The extracted value of the relic density has reached the few per-cent level
precision. One can therefore no longer content oneself with calculations of
this observable where the annihilation processes are computed at tree-level,
especially in supersymmetry where radiative corrections are usually large.
Implementing full one-loop corrections to all annihilation processes that would
be needed in a scan over parameters is a daunting task. On the other hand one
may ask whether the bulk of the corrections are taken into account through
effective couplings of the neutralino that improve the tree-level calculation
and would be easy to implement. We address this issue by concentrating in this
first study on the neutralino coupling to i) fermions and sfermions and ii) Z.
After constructing the effective couplings we compare their efficiency compared
to the full one-loop calculation and comment on the failures and success of the
approach. As a bonus we point out that large non decoupling effects of heavy
sfermions could in principle be measured in the annihilation process, a point
of interest in view of the latest limit on the squark masses from the LHC. We
also comment on the scheme dependencies of the one-loop corrected results