Sum rule in a consistent relativistic random-phase approximation

A fully consistent relativistic random-phase approximation (RRPA) is studie d in the sense that the relativistic mean-field (RMF) wavefunction of nucle us and the particle-hole residual interactions in the RRPA are calculated f rom the same effective Lagrangian. A consistent treatment of RRPA within th e RMF approximation, i.e., no sea approximation, has to include also the pa irs formed from the Dirac states and occupied Fermi states, which is essent ial for satisfying the current conservation. The inverse energy-weighted su m rule for the isoscalar giant monopole mode is investigated in the constra ined RMF. It is found that the sum rule is fulfilled only in the case where the Dirac state contributions are included.