  The long-range terms of the subleading chiral three-nucleon force [published
in Phys.\,Rev.\,C77, 064004 (2008)] are specified to the case of three
neutrons. From these $3n$-interactions an effective density-dependent
neutron-neutron potential $V_\text{med}$ in pure neutron matter is derived.
Following the division of the pertinent 3n-diagrams into two-pion exchange,
two-pion-one-pion exchange and ring topology, all self-closings and
concatenations of two neutron-lines to an in-medium loop are evaluated. The
momentum and $k_n$-dependent potentials associated with the spin-operators
$1,\, \vec\sigma_1\!\cdot\!\vec\sigma_2,\, \vec\sigma_1\!\cdot\!\vec q\,
\vec\sigma_2\!\cdot\!\vec q,\, i( \vec\sigma_1\!+\!\vec\sigma_2)\!\cdot \!
(\vec q\!\times \! \vec p\,),\, (\vec\sigma_1\!\cdot\!\vec
p\,\vec\sigma_2\!\cdot\!\vec p+\vec\sigma_1\!\cdot\!\vec p\,'\,
\vec\sigma_2\!\cdot\!\vec p\,')$ and $ \vec\sigma_1\!\cdot \! (\vec q\!\times
\! \vec p\,)\vec\sigma_2\!\cdot \! (\vec q\!\times \! \vec p\,)$ are expressed
in terms of functions, which are either given in closed analytical form or
require at most one numerical integration. The subsubleading chiral 3N-force is
treated in the same way. The obtained results for $V_\text{med}$ are helpful to
implement the long-range chiral three-body forces into advanced neutron matter
calculations.
