Random Phase Approximation For allowed and Parity Non-conserving Electric Dipole Transition Amplitudes and its connection with Many-Body Perturbation Theory and Coupled Cluster Theory

The connections between the Random Phase Approximation (RPA) and Many-Body Perturbation Theory (MBPT) and its all order generalisation, the Coupled- Cluster Theory (CCT) have been explored. Explicit expressions have been derived for the electric dipole amplitudes for allowed and forbidden transitions induced by the parity non-conserving neutral weak interaction. The Goldstone diagrams associated with the RPA terms in both cases are shown to arise in MBPT and CCT and the numerical verification of this relationship is made for the allowed electric dipole transitions.