  The computational cost of ab initio nuclear structure calculations is
rendered particularly acute by the presence of (at least) three-nucleon
interactions. This feature becomes especially critical now that many-body
methods aim at extending their reach beyond mid-mass nuclei. Consequently,
state-of-the-art ab initio calculations are typically performed while
approximating three-nucleon interactions in terms of effective, i.e.
system-dependent, zero-, one- and two-nucleon operators. While straightforward
in doubly closed-shell nuclei, existing approximation methods based on
normal-ordering techniques involve either two- and three-body density matrices
or a symmetry-breaking one-body density matrix in open-shell systems. In order
to avoid such complications, a simple, flexible, universal and accurate
approximation technique involving the convolution of the initial operator with
a sole symmetry-invariant one-body matrix is presently formulated and tested
numerically. Employed with a low-resolution Hamiltonian, the novel
approximation method is shown to induce errors below $2-3\%$ across a large
range of nuclei, observables and many-body methods.
