1 ntroduction A description based on rotational, vibrational and smgle par-tiele degrees of freedom has proved to be adequatefor many nuelei. The vibrational modes ean be deseribed either with colleetive variables or as linear combinations of elementary exeitations. Both methods yield the same result in the adiabatic limito The eolleetive and intrinsie degrees of freedom can be mixed through residual terms of the Hamiltonian, sueh as the Coriolis foree and the rotation-vibration interaetion.

more »

... s leads to a mixing of the sta tes belongíng to the rotational band of the ground state with. those belongíng to bands of the vibrational state. The aim of this paper is to show that, in the adiabatic limit,. this mixing ís the same whether we ehoose to consider the vibrations. as colleetive modes or as superposition of intrinsic excitations. 1) The nuclear Hamiltonian We assume a single particle Hamiltonian with axial symmetry (the Hartree field) plus residual two body interactions: H = Hsp + Hp + H q (1) Here Hp represents the short range part of the interaction which preserves the axial symmetry and is supposed to be día-gonalised with H sp to give a spectra of elementary excitations. The term H q is the quadrupole force, whose strength is given by a parameter K and which tends to deform the field.