Scissor modes in triaxial metal clusters

We study the scissor mode (orbital $M1\mathrm{}$ excitations) in small Na clusters, triaxial metal clusters ${\mathrm{Na}}_{12}$ and ${\mathrm{Na}}_{16}$ and the close-to-spherical ${\mathrm{Na}}_9^{+},$ all described in density-functional theory with detailed ionic background. The scissor modes built on spin-saturated ground and spin-polarized isomeric states are analyzed in virtue of both macroscopic collective and microscopic shell-model treatments. It is shown that the mutual destruction of Coulomb and the exchange-correlation parts of the residual interaction makes the collective shift small and the net effect can depend on details of the actual excited state. The cross-talk with dipole and spin-dipole modes is studied in detail. In particular, a strong cross-talk with spin-dipole negative-parity mode is found in the case of spin-polarized states. Triaxiality and ionic structure considerably complicate the scissor response, mainly at the expense of stronger fragmentation of the strength. Nevertheless, even in these complicated cases the scissor mode is mainly determined by the global deformation. The detailed ionic structure destroys the spherical symmetry and can cause finite $M1\mathrm{}$ response (transverse optical mode) even in clusters with zero global deformation. But its strength turns out to be much smaller than for the genuine scissor modes in deformed systems.