  We present a diagrammatic decomposition of the transition pair correlation
function for the uniform electron gas. We demonstrate explicitly that ring and
ladder diagrams are dual counterparts that capture significant long- and
short-ranged interelectronic correlation effects, respectively. Our findings
help to guide the further development of approximate many-electron theories and
reveal that the contribution of the ladder diagrams to the electronic
correlation energy can be approximated in an effective manner using
second-order perturbation theory. We employ the latter approximation to reduce
the computational cost of coupled cluster theory calculations for insulators
and semiconductors by two orders of magnitude without compromising accuracy.
