Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDensity-dependent nn-potential from subleading chiral three-neutron forces: Long-range terms
123
0
0.0
(
0
)
Authors
N. Kaiser
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 matter. 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 matter and pure neutron matter in an analytical way. For the variety of short-range and long-range terms that constitute the subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the results for 2-ring diagrams can be given in terms of elementary functions of the ratio Fermi-momentum over pion mass, one ends up in most cases for the closed 1-ring diagrams with one-parameter integrals. The same treatment is applied to the subsubleading chiral three-nucleon interactions as far as these have been constructed up to now.
The energy- and density-dependent single-particle potential for nucleons is constructed in a medium of infinite isospin-symmetric nuclear matter starting from realistic nuclear interactions derived within the framework of chiral effective field theory. The leading-order terms from both two- and three-nucleon forces give rise to real, energy-independent contributions to the nucleon self-energy. The Hartree-Fock contribution from the two-nucleon force is attractive and strongly momentum dependent, in contrast to the contribution from the three-nucleon force which provides a nearly constant repulsive mean field that grows approximately linearly with the nuclear density. Together, the leading-order perturbative contributions yield an attractive single-particle potential that is however too weak compared to phenomenology. Second-order contributions from two- and three-body forces then provide the additional attraction required to reach the phenomenological depth. The imaginary part of the optical potential, which is positive (negative) for momenta below (above) the Fermi momentum, arises at second-order and is nearly inversion-symmetric about the Fermi surface when two-nucleon interactions alone are present. The imaginary part is strongly absorptive and requires the inclusion of an effective mass correction as well as self-consistent single-particle energies to attain qualitative agreement with phenomenology.
We study the effect of the nucleon-nucleon-lambda (NN$Lambda$) three-body force on neutron stars. In particular, we consider the NN$Lambda$ force recently derived by the J{u}lich--Bonn--Munich group within the framework of chiral effective field theory at next-to-next-to-leading order. This force, together with realistic nucleon-nucleon, nucleon-nucleon-nucleon and nucleon-hyperon interactions, is used to calculate the equation of state and the structure of neutron stars within the many-body non-relativistic Brueckner-Hartree-Fock approach. Our results show that the inclusion of the NN$Lambda$ force leads to an equation of state stiff enough such that the resulting neutron star maximum mass is compatible with the largest currently measured ($sim 2 M_odot$) neutron star masses. Using a perturbative many-body approach we calculate also the separation energy of the $Lambda$ in some hypernuclei finding that the agreement with the experimental data improves for the heavier ones when the effect of the NN$Lambda$ force is taken into account.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
