Hindrance Factors for Beta Decays of Heavy Nuclei

The schematic model proposed by Brown and Bolsterli, and applied to the giant dipole resonance, is extended to the $\beta$ and $\gamma$ transitions of heavy nuclei. Special emphasis is placed on the extent to which forbidden $\beta$ decays of heavy nuclei are hindered because of possible giant resonances corresponding to those found in the electromagnetic transitions. A new method of calculating hindered forbidden nuclear matrix elements is proposed on the basis of the schematic model. It is shown that the hindrance factor due to the giant resonance effect is roughly 4 for the first-forbidden $\beta$ transitions. Systematics of unique first-forbidden transitions are examined from this viewpoint.