21+ and 22+ states in collective nuclei as multiple Q-phonon excitations

In the framework of the e-phonon scheme and the interacting boson model a description of the 2(1)(+) and 2(2)(+) states is obtained. The wave vectors are written as an expansion in multiple e-phonon excitations of the ground state. It is shown that the convergence of this expansion is fast and the main component already provides a good approximation of the wave vector. The accuracy of such a leading-order description exceeds 90% of the wave vector. By taking into account two e-phonon configurations the accuracy of the description of the 2(1)(+) and 2(2)(+) states is increased to 98%. This is true for all collective nuclei with the exception of some rotors where the first excited K=0 band lies below or very close to the gamma band and, due to band mixing, the wave vector of the 2(2)(+) state contains higher Q-phonon excitations. An application to some decay transitions is given.