Higher-order corrections to collective particle-hole excitations using green function techniques

Using Green function techniques, we determine higher-order corrections to the Tamm-Dancoff and Random Phase Approximation equations. In particular, we find that the second-order corrections to the Tamm-Dancoff equations consist of a t-matrix term and a core-polarization term. If we truncate our configuration space, we obtain an additional second-order correction from the particle-hole ladder term. We carry out numerical calculations of these second-order corrections for the negative-parity excited states of ⁴He using the Tabakin separable potential.