Three-nucleon force effects in the FSI configuration of the d(n, nn)p breakup reaction

We investigated three-nucleon (3N) force effects in the final state interaction (FSI) configuration of the d(n, nn)p breakup reaction at the incoming nucleon energy E n = 200 MeV. Although 3N force effects for the elastic nucleon-deuteron scattering cross section at comparable energies are located predominantly in the region of intermediate and backward angles, the corresponding 3N force effects for the integrated FSI configuration breakup cross section are found also at forward scattering angles

Orthogonal polynomial approach to calculate the two-nucleon transition operator in three dimensions

We give a short report on the possibility to use orthogonal polynomials (OP) in calculations that involve the two-nucleon (2N) transition operator. The presented work adds another approach to the set of previously developed methods (described in Phys. Rev. C 81, 034006 (2010); Few-Body Syst. 53, 237 (2012); K. Topolnicki, PhD thesis, Jagiellonian University (2014)) and is applied to the transition operator calculated at laboratory kinetic energy 300MeV. The new results for neutron-neutron and neutron-proton scattering observables converge to the results presented in Few-Body Syst. 53, 237 (2012) and to results obtained using the Arnoldi algorithm (Y. Saad, Iterative methods for sparse linear systems (SIAM Philadelphia, PA, USA 2003)). The numerical cost of the calculations performed using the new scheme is large and the new method can serve only as a backup to cross-check the previously used calculation schemes

Achievements and challenges in understanding nucleon-deuteron reactions

Results on three-nucleon (3N) elastic scattering below the pion production threshold are discussed with an emphasis on a need for a three-nucleon force (3NF). The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with (semi) phenomenological nucleon-nucleon (NN) potentials only and data point to the need for 3NF’s. This notion is supported by the fact that another possible reason for the discrepancies in elastic nucleondeuteron (Nd) scattering, relativistic effects, turned out to be small. Results based on a new generation of chiral NN forces (up to N4LO) alone or combined with N2LO 3NF support predictions found with standard interactions. To resolve higher energy discrepancies found in nucleon-deuteron (Nd) reactions requires application of a chiral 3NF up to at least N3LO order of chiral expansion

Momentum space 3N Faddeev calculations of hadronic and electromagnetic reactions with proton-proton Coulomb and three-nucleon forces included

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 acting. 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.Comment: 12 page

The general operator form for the total-momentum-dependent nucleon-nucleon potential

In this paper we describe a procedure to obtain the general operator form of two-nucleon (2N) potentials and apply it to the case of the 2N potential that has an additional dependence on the total momentum of the system. This violates Galilean invariance but terms including the total momentum appear in some relativistic approaches. In operator form, the potential is expressed as a linear combination of a fixed number of known spin-momentum operators and scalar functions of momenta. Since the scalar functions effectively define the potentials, using the operator form significantly reduces the number of parameters that are needed in numerical implementations. The proposed operator form explicitly obeys the usual symmetries of rotational invariance, particle exchange, time reflection and parity

Approximate three-dimensional wave function and the T-matrix for the sharply cut off Coulomb potential

For a sharply cut-off Coulomb potential we derive analytically the asymptotic form of the threedimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid for any type of screening. We obtain also the asymptotic form of the corresponding three-dimensional half-shell t-matrix. Our results are fully supported by the numerical solutions of the three-dimensional Lippmann-Schwinger equation

Perturbative treatment of three-nucleon force contact terms in three-nucleon Faddeev equations

We present a perturbative approach to solving the three-nucleon continuum Faddeev equation. This approach is particularly well suited to dealing with variable strengths of contact terms in a chiral three-nucleon force. We use examples of observables in the elastic nucleon-deuteron scattering as well as in the deuteron breakup reaction to demonstrate high precision of the proposed procedure and its capability to reproduce exact results. A significant reduction of computer time achieved by the perturbative approach in comparison to exact treatment makes this approach valuable for fine-tuning of the three-nucleon Hamiltonian parameters

A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations

We present recently introduced novel approach to include the proton-proton (pp) Coulomb force into the momentum space three-nucleon (3N) Faddeev calculations. It is based on a standard formulation for short range forces and relies on a screening of the long-range Coul omb interaction. In order to avoid all uncertainties connected with an application of the partial wave expansion, unsuitable when working with long-range forces, we apply directly the 3-dimensional pp screened Coulomb t-matrix. That main new ingredient, the 3-dimensional screened pp Coulomb t-matrix, is obtained by a numerical sol ution of the 3-dimensional Lippmann-Schwinger (LS) equation. Using a simple dynamical model for the nuclear part of the interaction we demonstrate the feasibility of that approach. The physical elastic pd scattering amplitude has a well defined screening limit and does not require renormalisation. Well converged elastic pd cro ss sections are obtained at finite screening radii. Also the proton-deuteron (pd) breakup observables can be determ ined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd e lastic scattering, the screening limit exists only after renormalisation of the pp t-matrices

An application of chiral forces with the semi-local regularization in momentum space to the deuteron photodisintegration process

A recent paper by P. Reinert et al. [Eur. Phys. J. A54, 86 (2018)] showed a possibility of improving chiral nucleon-nucleon potential models by employing a semi-local regularization in momentum space. The authors derived nucleon-nucleon potentials with this kind of regularization completely up to the fifth order of the chiral expansion and considered additionally some contact interactions which appear at the sixth order. Such a chiral interaction has never been applied to study electromagnetic processes in two- or three-nucleon systems. Here we continue our research of photodisintegration processes, now using the improved chiral force. In particular, we discuss our predictions for the deuteron photodisintegration reaction in the photon energy range up to 100 MeV. The results of our calculations reveal that the new potential yields predictions characterized by a weaker dependence on the regularization parameter and faster convergence with respect to the chiral expansion order compared to the older chiral potentials