Semiclassical quantization of strongly chaotic vibrations in an M-7-like cluster - art. no. 056223

We report semiclassical energy spectra of vibrational state of a cluster co mposed of seven identical atoms like Ar-7 in terms of our previously develo ped semiclassical wave function, which we call the action-decomposed functi on. The classical dynamics of this vibrational state is strongly chaotic an d undergoes a large amplitude motion due to structural isomerization, which demands a long run of trajectory calculation. Permutation of identical par ticles should also be taken into account as a quantum effect, since a singl e molecular shape can be shared by many permutational isomers. Furthermore, chaos causes a spurious divergence in the amplitude factor of a correlatio n function in the initial value representation, which arises from the ampli tude factor (Prefactor) of a semiclassical wave function, while the final-s tate representation is suffered from the well-known divergence arising at c austics. Both approaches therefore face tremendous difficulty in a long-tim e calculation of the correlation functions. We challenge to extract some li mited number of spectral lines from such chaotic dynamics. We further apply a correlation function that is free of such a troublesome amplitude factor . Numerical results from all these schemes are reported.