We consider the two-nucleon system at next-to-next-to-next-to-leading order (N
3LO) in chiral effective field theory. The two-nucleon potential at N
3LO consists of one-, two- and three-pion ...exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin-breaking and relativistic corrections. We employ spectral function regularization for the multi-pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low-energy constants (LECs) related to pion–nucleon vertices are taken consistently from studies of pion–nucleon scattering in chiral perturbation theory. The total of 26 four-nucleon LECs has been determined by a combined fit to some
np and
pp phase shifts from the Nijmegen analysis together with the
nn scattering length. The description of nucleon–nucleon scattering and the deuteron observables at N
3LO is improved compared to the one at NLO and NNLO. The theoretical uncertainties in observables are estimated based on the variation of the cut-offs in the spectral function representation of the potential and in the regulator utilized in the Lippmann–Schwinger equation.
We employ the chiral nucleon–nucleon potential derived in Nucl. Phys. A 637 (1998) 107 to study bound and scattering states in the two-nucleon system. At next-to-leading order, this potential is the ...sum of renormalized one-pion and two-pion exchange and contact interactions. At next-to-next-to-leading order, we have additional chiral two-pion exchange with low-energy constants determined from pion–nucleon scattering. Alternatively, we consider the
Δ(1232) as an explicit degree of freedom in the effective field theory. The nine parameters related to the contact interactions can be determined by a fit to the
np S- and P-waves and the mixing parameter
ϵ
1 for laboratory energies below 100 MeV. The predicted phase shifts and mixing parameters for higher energies and higher angular momenta are mostly well described for energies below 300 MeV. The S-waves are described as precisely as in modern phenomenological potentials. We find a good description of the deuteron properties.
The potentials V (v) in the nonrelativistic (relativistic) nucleon–nucleon (NN) Schrödinger equation are related by a quadratic equation. That equation is numerically solved, thus providing phase ...equivalent v-potentials related for instance to the high precision NN potentials, which are adjusted to NN phase shift and mixing parameters in a nonrelativistic Schrödinger equation. The relativistic NN potentials embedded in a three-nucleon (3N) system for total NN momenta different from zero are also constructed in a numerically precise manner. They enter into the relativistic interacting 3N mass operator, which is needed for relativistic 3N calculations for bound and scattering states.
We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting ...scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory.
Nuclear forces in the chiral limit Epelbaum, E.; Meißner, Ulf-G.; Glöckle, W.
Nuclear physics. A,
02/2003, Letnik:
714, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We investigate the behaviour of the nuclear forces as a function of the light quark masses (or, equivalently, pion mass) in the framework of chiral effective field theory at next-to-leading order. ...The nucleon–nucleon force is described in terms of one and two-pion exchange and local short distance operators, which depend explicitly and implicitly on the quark masses. The pion propagator becomes Coulomb-like in the chiral limit and thus one has significant scattering in all partial waves. The pion–nucleon coupling depends implicitly on the quark masses and we find that it becomes stronger in the chiral limit. There is a further quark mass dependence in the
S-wave four-nucleon couplings, which can be estimated by means of dimensional analysis. We find that nuclear physics in the chiral limit becomes natural. There are no new bound states, the deuteron binding energy is
B
D
CL=9.6±1.9
+1.8
−1.0 MeV, and the
S-wave scattering lengths take values of a few fm,
a
CL
(
1S
0)=−4.1±1.6
+0.0
−0.4
fm and
a
CL
(
3S
1)=1.5±0.4
+0.2
−0.3
fm. We also discuss the extrapolation to larger pion masses pertinent for the extraction of these quantities from lattice simulations.
We present new calculations of the alpha particle which are based on the most modern nucleon-nucleon interactions alone and combined with the Tucson-Melbourne or the Urbana IX three-nucleon ...interaction. Results for the binding energies and some properties of the wave function are given. On that phenomenological level little room is left for the action of a possible four-nucleon force.
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