Interaction of a phonon with an odd quasi particle and l-forbidden β transitions

The l-forbidden β transitions of odd spherical nuclei are considered. The density matrix of phonons of the odd-odd nuclear core is built and the Hamiltonian of the interaction between an odd quasiparticle and a phonon is written in the framework of finite Fermi-system theory. The explicit form of the wave functions of the ground state of the mother and daughter nuclei is found using the variation procedure. Only the components ''one quasiparticle'' and ''one quasiparticle + phonon'' are considered when the wave function is being chosen. The reduced nuclear matrix element of the l-forbidden β transition is obtained in the above approximation. If the state ''quasi-particle + phonon'' is included, then the terms responsible for l unaltering β decay appear in the transition matrix element. For l-forbidden β transitions of nuclei 65Ni, 65Zn, 65Ga, 69Ge, 67Cu the calculated values of lgfot are in better agreement with experiment than the onequasiparticle value