We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation w
e include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported.
The mu + 2H -> nu + n + n, mu + 3He -> nu + 3H, mu + 3He -> nu + n + d and mu + 3He -> nu + n + n + p capture reactions are studied with various realistic potentials under full inclusion of final state interactions. Our results for the two- and three
-body break-up of 3He are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana~IX three-nucleon potential. Most of our results are based on the single nucleon weak current operator. As a first step, we have tested our calculation in the case of the mu + 2H -> nu + n + n and mu + 3He -> nu + 3H reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3He in the break-up channels: 544 1/s and 154 1/s for the n + d and n + n + p channels, respectively. Our results have also been compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.
We compare results from the traditional partial wave treatment of deuteron electro-disintegration with a new approach that uses three dimensional formalism. The new framework for the two-nucleon (2N) system using a complete set of isospin - spin stat
es made it possible to construct simple implementations that employ a very general operator form of the current operator and 2N states.
Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite
set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces.
We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous equations directly
for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.
We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) momentum-space Faddeev calculations of elastic proton-deuteron (pd) scattering and breakup to the case when also a three-nucleon force (3NF) is act
ing. In addition we formulate that approach in the application to electron- and gamma-induced reactions on 3He. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of a 3-dimensional Lippmann-Schwinger equation (LSE). The resulting equations have the same structure as the Faddeev equations which describe pd scattering without 3NF acting. That shows the practical feasibility of both presented formulations.
We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction
. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.
