  The inferred value of the relic density from cosmological observations has
reached a precision that is akin to that of the LEP precision measurements.
This level of precision calls for the evaluation of the annihilation cross
sections of dark matter that goes beyond tree-level calculations as currently
implemented in all codes for the computation of the relic density. In
supersymmetry radiative corrections are known to be large and thus must be
implemented. Full one-loop radiative corrections for many annihilation
processes have been performed. It is important to investigate whether the bulk
of these corrections can be parameterised through an improved Born
approximation that can be implemented as a selection of form factors to a
tree-level code. This paper is a second in a series that addresses this issue.
After having provided these form factors for the annihilation of the
neutralinos into fermions, which cover the case of a bino-like LSP (Lightest
Supersymmetric Particle), we turn our attention here to a higgsino-like dark
matter candidate through its annihilation into $ZZ$. We also investigate the
cases of a mixed LSP. In all cases we compare the performance of the form
factor approach with the result of a full one-loop correction. We also study
the issue of the renormalisation scheme dependence. An illustration of the
phenomenon of non decoupling of the heavy sfermions that takes place for the
annihilation of the lightest neutralino into $ZZ$ is also presented.
