  Pentagon and triangle shapes in Si-28 and C-12 are discussed in relation with
nuclear density wave. In the antisymmetrized molecular dynamics calculations,
the $K^\pi=5^-$ band in Si-28 and the $K^\pi=3^-$ band in C-12 are described by
the pentagon and triangle shapes, respectively. These negative-parity bands can
be interpreted as the parity partners of the $K^\pi=0^+$ ground bands and they
are constructed from the parity-asymmetric-intrinsic states. The pentagon and
the triangle shapes originate in 7alpha and 3alpha cluster structures,
respectively. In a mean-field picture, they are described also by the static
one-dimensional density wave at the edge of the oblate states. In analysis with
ideal alpha cluster models using Brink-Bloch cluster wave functions and that
with a simplified model, we show that the static edge density wave for the
pentagon and triangle shapes can be understood by spontaneous breaking of axial
symmetry, i.e., the instability of the oblate states with respect to the edge
density wave. The density wave is enhanced in the Z=N nuclei due to the
proton-neutron coherent density waves, while it is suppressed in Z\ne N nuclei.

Nuclear Theory