Different formulations of <Superscript>3</Superscript>He and <Superscript>3</Superscript>H photodisintegration

Different momentum space Faddeev-like equations and their solutions for the radiative pd-capture and the three-nucleon photodisintegration of ³He are presented. Applications are based on the AV18 nucleon-nucleon and the Urbana IX three-nucleon forces. Meson exchange currents are included using the Siegert theorem. A very good agreement has been found in all cases indicating the reliability of the used numerical methods. Predictions for cross-sections and polarization observables in the pd-capture and the complete three-nucleon breakup of ³He at different incoming-deuteron/photon energies are presented.     

Calculation of A x for the Proton–Deuteron Breakup Reaction at 135 MeV

Observables in proton–deuteron scattering are sensitive probes of the nucleon-nucleon interaction and three-nucleon force effects (3NF). Several facilities in the world, including Kernfysisch Versneller Instituut (KVI), allow a detailed study a few-nucleon interaction below the pion-production threshold exploiting polarized proton and deuteron beams. In this contribution we explored 3NF effects in the break-up scattering process by performing a measurement of differential cross section and the analyzing power, especially the x component of the analyzing power, using a 135 MeV polarized-proton beam impinging on a liquid-deuteron target. The proton–deuteron breakup reaction leads to a final state with three free particles and a rich phase space that allows us to study observables for continuous set of kinematical configurations of the outgoing nucleons. The results are interpreted with the help of state-of-the-art Faddeev calculations.     

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ$\text{Bonn}+\mathrm{\Delta }$ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.     

Calculations of Three-Nucleon Reactions

Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A _y puzzle. The large discrepancy between data and theory for the neutron–neutron quasi-free-scattering cross section in low energy neutron–deuteron breakup requires a modification of the ${^{1}S_0}$ neutron–neutron force. We discuss the consequences that a bound ${^{1}S_0}$ state of two neutrons has on neutron–deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincaré invariant version.     

Analysis of the Effects of Three-nucleon Forces in A = 3, 4 Systems

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N ? d low energy scattering observables.     

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

We extend our approach to incorporate the proton-proton (ppCoulomb force into the three-nucleon (3NFaddeev calculations from elastic proton-deuteron (pdscattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t -matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically that the proton-deuteron (pdbreakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t -matrices.     

Studies of the three-nucleon system dynamics: Cross sections of the deuteron-proton breakup at 130 MeV

The three-nucleon system is the simplest non-trivial testing ground in which the quality of modern nucleon-nucleon interaction models, as well as additional dynamical ingredients referred to as three-nucleon forces, can be probed quantitatively by means of a rigorous technique of solving the Faddeev equations. A large set of high precision, exclusive cross-section data for the $^1{\rm H}({\vec d},pp)n$ breakup reaction at 130?MeV was obtained at KVI, Groningen. It allowed to establish for the first time a clear evidence of the three-nucleon force contributions to the cross sections of the breakup process and to confirm recent predictions of sizable influences of the Coulomb force in this reaction.     

Faddeev Calculations of Breakup Reactions with Realistic Experimental Constraints

We present a method to integrate predictions from a theoretical model of a reaction with three bodies in the final state over the region of phase space covered by a given experiment. The method takes into account the true experimental acceptance, as well as variations of detector efficiency, and eliminates the need for a Monte-Carlo simulation of the detector setup. The method is applicable to kinematically complete experiments. Examples for the use of this method include several polarization observables in dp breakup at 270MeV. The calculations are carried out in the Faddeev framework with the CD Bonn nucleon-nucleon interaction, with or without the inclusion of an additional three-nucleon force.     

Proton-Induced Deuteron Breakup Reaction at 65 MeV: Unspecific Configurations

 Cross sections and vector-analyzing powers for four unspecific configurations of the ²H(p,pp)n breakup reaction at E ^lab _p  = 65MeV were measured in a kinematically complete experiment. Measured observables are compared with rigorous Faddeev calculations using four realistic charge-dependent interaction models, the CD Bonn, Argonne v ₁₈, Nijmegen I, and Nijmegen II potentials with or without inclusion of the Tucson-Melbourne three-nucleon force. Coulomb effects are completely omitted. A satisfactory agreement between theory and experiment has been found. There exist, however, some discrepancies between measured and calculated analyzing-power distributions in certain kinematical regions. The effects of the Tucson-Melbourne three-body force are either negligible or slightly increasing the disagreement. Received May 12, 1999; revised March 3, 2000; accepted for publication April 26, 2000     

Application of EFT at thermal energies

We have evaluated some observables of n-d systems by using pionless effective field theory (EFT( ${\not}\pi$ )) and insertion of the three-body force up to next-to-next to leading order (N²LO). The evaluated data has been compared with experiment and a three-nucleon calculation of the total cross section with modern realistic two- and three-nucleon force AV18/UrbIX potential models.     

Relativistic effects in exclusive pd breakup scattering at intermediate energies

The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. The exclusive breakup reaction at 508 MeV is calculated based on a Malfliet–Tjon type two-body interaction and the cross sections are compared to measured cross sections at this energy. We find that the magnitude of the relativistic effects can be quite large and depends on the configurations considered. In spite of the simple nature of the model interaction, the experimental cross sections are in surprisingly good agreement with the predictions of the relativistic calculations. We also find that although for specific configurations the multiple scattering series converges rapidly, this is in general not the case.     

Measurement of spin-transfer observables in p p-->Lambda Lambda at 1.637 GeV/c

Spin-transfer observables for p p-->Lambda Lambda have been measured using a transversely polarized frozen-spin target and a beam momentum of 1.637 GeV/c. Current models of the reaction near threshold are in good agreement with existing measurements performed with unpolarized particles in the initial state but produce conflicting predictions for the spin-transfer observables Dnn and Knn (the normal-to-normal depolarization and polarization transfer), which are measurable only with polarized target or beam. Measurements of Dnn and Knn presented here are found to be in disagreement with predictions from these models.     

The three-body force in the trinucleons

The status of three-body forces in nuclear physics within the context of the trinucleon system is reviewed. The theoretical approaches of the Hannover. Brazilian, Tuscon-Melbourne, and Urbana-argonne groups to modeling the three-nucleon force are outlined and compared. Results of numerical calculations based upon contemporaryNN forces alone plus those utilizing these three-body interactions are summarized for various bound-state observables and the Fourier transform of the charge density (the charge form factor in the impulse approximation) as well as selected continuum observables. Uncertainties in our experimental knowledge of theNN force, which significantly affect conclusions about the size of nuclear three-body force effects. are discussed.