SU(3) symmetry and scissors mode vibrations in nuclei Original Research Article

We show that a nearly perfect SU(3) symmetry emerges from an extended projected shell model. Starting from a deformed potential we construct separate bases for neutron and proton collective rotational states by exact angular momentum projection. These rotational states are then coupled by diagonalizing a residual pairing plus quadrupole interaction. The states obtained exhibit a one-to-one correspondence with an SU(3) spectrum up to high angular momentum and excitation, and their wave functions have a near-maximal overlap with the SU(3) states. They can also be classified as rotational bands built on spin-1ℏ phonon excitations, which correspond to a geometrical scissors mode and its generalizations. This work is a direct demonstration that numerical angular momentum projection theory extends the Elliottʹs original idea to heavy nuclear systems.