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 $1,, vecsigma_1!cdot!vecsigma_2,, vecsigma_1!cdot!vec q, vecsigma_2!cdot!vec q,, i( vecsigma_1!+!vecsigma_2)!cdot ! (vec q!times ! vec p,),, (vecsigma_1!cdot!vec p,vecsigma_2!cdot!vec p+vecsigma_1!cdot!vec p,, vecsigma_2!cdot!vec p,)$ and $ vecsigma_1!cdot ! (vec q!times ! vec p,)vecsigma_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.
تحميل البحث