  We compute tail contributions to the conservative dynamics of a generic
self-gravitating system, for every multipole order, of either electric and
magnetic parity. Such contributions arise when gravitational radiation is
backscattered by the static curvature generated by the source itself and
reabsorbed. Tail processes are relevant for the study of compact binary
dynamics starting from the fourth post-Newtonian order. Within this context, we
resolve a discrepancy recently arised at fifth post-Newtonian order between
Effective Field Theory and self-force results.
