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 investigate how strong a hypothetical 1S0 bound state of two neutrons would affect different observables in the neutron-deuteron reactions. To that aim we extend our momentum space scheme of solving three-nucleon Faddeev equations to incorporate i
n addition to the deuteron also the 1S0 dineutron bound state. We discuss effects induced by dineutron on the angular distribution of the neutron-deuteron elastic scattering and cross sections of the deuteron breakup. A comparison to the available data for neutron-deuteron total cross sections and elastic scattering angular distributions cannot decisively exclude a possibility that the two neutrons can form 1S0 bound state. However, the strong modifications of a final-state-interaction peak of the neutron-deuteron breakup when changing from negative to positive values of the neutron-neutron scattering length seems to exclude existence of dineutron.
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.
Large discrepancies between quasi-free neutron-neutron (nn) cross section data from neutron-deuteron (nd) breakup and theoretical predictions based on standard nucleon-nucleon (NN) and three-nucleon (3N) forces are pointed out. The nn 1S0 interaction
is shown to be dominant in that configuration and has to be increase to bring theory and data into agreement. Using the next-to-leading order (NLO) 1S0 interaction of chiral perturbation theory (chiPT) we demonstrate that the nn QFS cross section only slightly depends on changes of the nn scattering length but is very sensitive to variations of the effective range parameter. In order to account for the reported discrepancies one must decrease the nn effective range parameter by about 12 % from its value implied by 19charge symmetry and charge independence of nuclear forces.
The six-nucleon problem for the bound state is formulated in the Yakubovsky scheme. Hints for a numerical implementation are provided.
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.
