Asymptotical approximation of interconnection of nucleons' quadrupole and cluster motion in atomic nucleus

Atomic nuclei display different kinds of collective motion. The well known example - is the collective model arising from valent nucleons motion. The other a special kind of collective motion is cluster mode. If a collective model has quadrupole character, then cluster one has dipole character. In the boson formalism this model is describing by dynamic symmetry U(6) direct X U(4). The common Hamiltonian symmetrical to U(6) direct X U(4) group has a form H=Hd+Hp+Vpd. In the paper the asymptotical wave function for dipole states connected with (N-1) bosons of s- and d-types is presented. In this case the problem for Hamiltonian eigenvalues is solving by analytical way. With use Elliot method and wave functions asymptotical form the operators for matrix elements of E2-, E1-, M1-transitions are cited