Summation of particle-particle ring diagrams using Green function determinants

Using the Green function determinant's algebraic characteristics, we derive a simplified formula for summing up particle-particle and hole-hole ring diagrams to all orders exactly. The ground-state energy shift of a nuclear system can be obtained simply from the summation of all the differences between the eigenstate energies and the single-particle energies of hole-hole states. We illustrate the application of our formula by calculating the ground-state energy shift for 16O using four versions of Skyrme effective nucleon-nucleon interactions. The contribution from all such higher order ring diagrams is found to be remarkably small compared with that from the corresponding first-order diagram. (orig.)