Energy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions

From the subleading contributions to chiral three-nucleon (3N) interaction [published in Phys. Rev. C 77, 064004 (2008) and 84, 054001 (2011)], their first-order energy per particle of isospin-symmetric nuclear matter pure neutron are derived an analytical way. For variety short-range long-range terms that constitute 3N force pertinent closed 3-ring, 2-ring, 1-ring diagrams evaluated. While 3-ring vanish by a spin-trace results for 2-ring can be given elementary functions ratio Fermi momentum over pion mass, one ends up most cases with one-parameter integrals. The same treatment is applied subsubleading interactions as far these have been constructed now.