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. 
Geetha Gopakumar, Chiranjib Sur, Bhanu Pratap Das, Rajat K. Chaudhuri,   D. Mukherjee and Kimihiko Hirao