  We use diagrammatic perturbation theory to construct an effective shell-model
operator for the neutrinoless double-beta decay of 82Se. The starting point is
the same Bonn-C nucleon-nucleon interaction that is used to generate the
Hamiltonian for recent shell-model calculations of double-beta decay. After
first summing high-energy ladder diagrams that account for short-range
correlations and then adding diagrams of low order in the G matrix to account
for longer-range correlations, we fold the two-body matrix elements of the
resulting effective operator with transition densities from the recent
shell-model calculation to obtain the overall nuclear matrix element that
governs the decay. Although the high-energy ladder diagrams suppress this
matrix element at very short distances as expected, they enhance it at
distances between one and two fermis, so that their overall effect is small.
The corrections due to longer-range physics are large, but cancel one another
so that the fully corrected matrix element is comparable to that produced by
the bare operator. This cancellation between large and physically distinct
low-order terms indicates the importance of a reliable nonperturbative
calculation.
