Spurious dipole mode in random-phase approximation and in the RPA-based models

The problems related to the existence of the spurious dipole mode (SDM) in the self-consistent nuclear-structure models are considered. A method is formulated that allows to eliminate coupling of the SDM with the physical modes in the extended random-phase approximation (ERPA) theories, in particular, in the time blocking approximation (TBA) which is the model of the ERPA type. It is shown that the application of this method in the realistic TBA calculations of the $E1$ excitations gives the results which are very close to the results of the TBA calculations without using this method if the bare external-field $E1$ operators are replaced by the effective ones.