  We introduce and study the set of radical stable operations of an integral
domain $D$. We show that their set is a complete lattice that is the
join-completion of the set of spectral semistar operations, and we characterize
when every radical operation is spectral (under the hypothesis that $D$ is
rad-colon coherent). When $D$ is a Pr\"ufer domain such that every set of
minimal prime ideals is scattered, we completely classify stable semistar
operations.
