Effect of Quadrupole Vibrations onl-ForbiddenM1Transitions

The effect of quadrupole vibrations on $l$-forbidden $M1\mathrm{}$ transitions is computed using the wave functions resulting from the shell model with a residual pairing plus $P^{\mathrm{}\left(2\right)\mathrm{}}$ force. These wave functions for low states of an odd nucleus are a linear combination of a spin $j$ quasiparticle and spin $j^{\prime }$ quasiparticles coupled to 2+ phonons to angular momentum $j$. The one-phonon components of the wave functions allow $l$-forbidden $M1\mathrm{}$ transitions to proceed both via the single particle and collective $M1\mathrm{}$ operators. The calculation shows that this quadrupole coupling can explain most of the observed transition rate in a number of cases, while in a few cases, particularly for the odd-$N$ nuclei fast transitions occur which are still unexplained. In addition, it is shown that the $E2\mathrm{}$ contribution to these transitions while expected to be enhanced to several times single particle in most cases, nevertheless usually makes only a very small contribution to the total rate.