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A Numerical Coupled-Cluster Procedure Applied to the Closed-Shell Atoms Be and Ne

A coupled-cluster procedure, applicable to closed-shell as well as open-shell atoms, is described, and results from calculations on the closed-shell atoms Be and Ne are presented. The procedure is based on numerical solution of coupled radial pair equations, which can be iterated to self-consistency. The coupling between different pair excitations is considered in two steps. The first step, called intra-shell coupling, includes the interaction between excitations differing in the final states as well as in the mlms values of the electrons being excited. In the second step, the inter-shell coupling, also the residual interaction between excitations involving different nl shells is considered. While the former coupling is quite important, it has been found that the latter contributes only about 1% to the correlation energy. Single and triple excitations are neglected in the present work, but quadrupole excitations are included by means of the exponential ansatz of the coupled-cluster procedure. According to our results for Be, 98.6% of the experimental correlation energy is obtained with complete pair-pair coupling, which is consistent with the estimated value of about 1.5% for the contribution of single and triple excitations. With only intra-shell coupling the result is in almost exact agreement with the experimental value due to cancellations between single/triple excitations and inter-shell couplings. Similar results are obtained for Ne. The results of the present work are compared and discussed in relation to earlier many-body calculations on these systems.