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تسجيل مستخدم جديدDensity-dependent nn-potential from subleading chiral three-neutron forces: Long-range terms
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تأليف
N. Kaiser
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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.
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We derive from the subleading contributions to the chiral three-nucleon force (long-range terms, published in Phys.,Rev.,C,77, 064004 (2008)) a density-dependent two-nucleon interaction $V_text{med}$ in isospin-symmetric, spin-saturated nuclear matte
r. Following the division of the pertinent 3N-diagrams into two-pion exchange topology, two-pion-one-pion exchange topology and ring topology, we evaluate for these all self-closings and concatenations of nucleon-lines to an in-medium loop. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and $vectau_1!cdot!vectau_2$) and five independent spin-structures are expressed in terms of functions, which are either given in closed analytical form or require at most one numerical integration. In the same way we treat the $2pi$-exchange 3N-force up to fourth order. Our results for $V_text{med}$ are most helpful to implement the long-range subleading chiral 3N-forces into nuclear many-body calculations.
From the subsubleading chiral three-nucleon force [intermediate-range contributions, published in Phys. Rev. C,87, 054007 (2013)] a density-dependent NN-interaction $V_text{med}$ is derived in isospin-symmetric nuclear matter. Following the division
of the pertinent 3N-diagrams into two-pion-one-pion exchange topology and ring topology, one evaluates for these all selfclosings and concatenations of nucleon-lines to an in-medium loop. In the case of the $2pi 1pi$-exchange topology, the momentum- and $k_f$-dependent potentials associated with the isospin-operators ($1$ and $vectau_1 !cdot! vectau_2$) and five independent spin-structures require at most one numerical integration. For the more challenging (concatenations of the) ring diagrams proportional to $c_{1,2,3,4}$, one ends up with regularized double-integrals $int_0^lambda dr,r int_0^{pi/2} dpsi$ from which the $lambda^2$-divergence has been subtracted and the logarithmic piece $sim ln (m_pi/lambda)$ is isolated. The derived semi-analytical results are most helpful to implement the subsubleading chiral 3N-forces into nuclear many-body calculations.
We derive from the subleading contributions to the chiral three-nucleon interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84, 054001 (2011)] their first-order contributions to the energy per particle of isospin-symmetric nuclear
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