  The peculiar three-peak structure of the linear polarization profile shown in
the second solar spectrum by the Ba II line at 4554 A has been interpreted as
the result of the different contributions coming from the barium isotopes with
and without hyperfine structure (HFS). In the same spectrum, a triple peak
polarization signal is also observed in the Sc II line at 4247 A. Scandium has
a single stable isotope (^{45}Sc), which shows HFS due to a nuclear spin I=7/2.
We investigate the possibility of interpreting the linear polarization profile
shown in the second solar spectrum by this Sc II line in terms of HFS. A
two-level model atom with HFS is assumed. Adopting an optically thin slab
model, the role of atomic polarization and of HFS is investigated, avoiding the
complications caused by radiative transfer effects. The slab is assumed to be
illuminated from below by the photospheric continuum, and the polarization of
the radiation scattered at 90 degrees is investigated. The three-peak structure
of the scattering polarization profile observed in this Sc II line cannot be
fully explained in terms of HFS. Given the similarities between the Sc II line
at 4247 A and the Ba II line at 4554 A, it is not clear why, within the same
modeling assumptions, only the three-peak Q/I profile of the barium line can be
fully interpreted in terms of HFS. The failure to interpret this Sc II
polarization signal raises important questions, whose resolution might lead to
significant improvements in our understanding of the second solar spectrum. In
particular, if the three-peak structure of the Sc II signal is actually
produced by a physical mechanism neglected within the approach considered here,
it will be extremely interesting not only to identify this mechanism, but also
to understand why it seems to be less important in the case of the barium line.
