  By using the Continuum RPA (CRPA) method, the incoherent transition strength
of the exotic mu - e conversion in the 208Pb and 40Ca nuclei is investigated.
The question whether excited nuclear states lying high in the continuum give an
important contribution to the incoherent rate is addressed. The admixture of
spurious components in the rate coming from 1- excitations is investigated in
detail by using the self-consistent CRPA with Skyrme interactions as well as a
less consistent version and by employing two ways to remove the spurious
strength: the use of effective operators or simply the exclusion of the
spurious state appearing close to zero energy. In all cases, the correction
achieved is quite large.
