Three-nucleon Reactions Research Articles

Coulomb Force Effects in Few-Nucleon Systems

Theoretical predictions for sample observables of three-nucleon and four-nucleon reactions are reviewed. The focus is on Coulomb force effects. The calculations are based on the Alt–Grassberger–Sandhas version of the Faddeev equations. The calculations are done in momentum space. The calculational technique used to include the Coulomb repulsion between protons screens the infinite Coulomb tail, renormalizes the results and thereby corrects them for screening. The competition between three-nucleon force and Coulomb force effects as well as the Coulomb domination in special kinematic situations of reactions are discussed. Reactions connected by charge symmetry are reviewed. Special reaction observables are studied, in search for the hadronic violation of charge symmetry in the nuclear interaction and for its competition with the charge-asymmetric Coulomb force.

Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions

We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin T=3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the 1S0 state with isospin T=3/2. For neutron-deuteron elastic scattering the T=3/2 contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called "2/3-1/3" rule.

Calculations of three-nucleon reactions with N3LO chiral forces: achievements and challenges

We discuss the application of the chiral N3LO forces to three-nucleon reactions and point to the challenges which will have to be addressed. Present approaches to solve three-nucleon Faddeev equations are based on a partial-wave decomposition. A rapid increase of the number of terms contributing to the chiral three-nucleon force when increasing the order of the chiral expansion from N2LO to N3LO forced us to develop a fast and effective method of automatized partial-wave decomposition. At low energies of the incoming nucleon below ≈20 MeV, where only a limited number of partial waves is required, this method allowed us to perform calculations of reactions in the three-nucleon continuum using N3LO two- and three-nucleon forces. It turns out that inclusion of consistent chiral interactions, with relativistic 1/m corrections and short-range 2π-contact term omitted in the N3LO three-nucleon force, does not explain the long standing low energy Ay-puzzle. We discuss problems arising when chiral forces are applied at higher energies, where large three-nucleon force effects are expected. It seems plausible that at higher energies, due to a rapid increase of a number of partial waves required to reach convergent results, a three-dimensional formulation of the Faddeev equations which avoids partial-wave decomposition is desirable.

Systematic Study of Three-Nucleon Systems Dynamics in the Cross Section of the Deuteron–Proton Breakup Reaction

An experiment to investigate the 1H(d, pp)n breakup reaction using a deuteron beam of 340, 380 and 400 MeV and the WASA detector has been performed at the Cooler Synchrotron COSY–Julich. The main goal was the detailed study of various aspects of few-nucleon dynamics in the medium energy region, with particular emphasis on relativistic effects and their interplay with three nucleon forces. These effects become more important with increasing available energy in the three nucleon system. Therefore the investigations at high energies are crucial to understand their nature. The almost 4π geometry of the WASA detector gives an unique possibility to study various aspects of dynamics of processes in the three-nucleon reaction. Preliminary results obtained using the WASA detector are presented.

Three-nucleon reactions with chiral dynamics

Faddeev calculations using the chiral three-nucleon force at next-to-next-to- next-to-leading-order show that this force is not able to provide an explanation for the low-energy Ay puzzle. Also the large discrepancies between data and theory for the symmetric-space-star and for the neutron-neutron quasi-free-scattering cross sections in low energy neutron-deuteron breakup cannot be explained by that three-nucleon force. The discrepancy for the neutron-neutron quasi-free-scattering cross section seems to re- quire a modification of the 1 S 0 neutron-neutron force.

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.

Experimental Investigations of Discrepancies in Three-Nucleon Reactions

Experiments on pd scattering, pd capture and pd breakup performed by our Kyushu University group since 1988 are reviewed. Various discrepancies between the experimental results and 3N Faddeev calculations have been found, and systematical measurements of the discrepancies have been made. From discrepancies in pd scattering cross section and in 3N binding energy, 2π-exchange 3N force was determined, and the discrepancies were satisfactorily diminished. There are, however, still many discrepancies awaiting theoretical investigation, as described in this report.

STUDIES AT RCNP CYCLOTRON RELATED TO CHIRAL SYMMETRY IN NUCLEAR PHYSICS

Nuclear physics programs recently carried out at the RCNP cyclotron facility have been discussed with emphasis on the two subjects in relation to the chiral symmetry. One is the three-nucleon reactions at intermediate energies and effects of the three-nucleon force, which may be consistently understood in the chiral effective field theory. Another is the high-resolution measurements of spin-isospin excitations and a possibility for explaining the fine-structures in giant resonances by the chiral mean field model.

Treatment of the Coulomb interaction in three-nucleon reactions

The Coulomb interaction between the two protons is included in the calculation of three-nucleon hadronic and electromagnetic reactions using screening and renormalization approach. Calculations are done using integral equations in momentum space. The reliability of the method is demonstrated. The Coulomb effect on observables is discussed.

Study of the Coulomb effect in the photodisintegration of 3He

The Coulomb interaction between the two protons is included in the description of three-nucleon electromagnetic reactions using the screening and renormalization approach. Calculations are done using integral equations in momentum space. The Coulomb effect on observables is discussed.

Momentum-space treatment of the Coulomb interaction in three-nucleon reactions with two protons

The Coulomb interaction between the two protons is included in the calculation of proton-deuteron elastic scattering, radiative proton-deuteron capture and two-body electromagnetic disintegration of ${}^3\mathrm{He}$. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn + $\Delta$ to a coupled-channel two-baryon potential, allowing for single virtual $\Delta$-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. Convergence of the procedure is found already at moderate screening radii. The reliability of the method is demonstrated. The Coulomb effect on observables is seen at low energies for the whole kinematic regime. In proton-deuteron elastic scattering at higher energies the Coulomb effect is confined to forward scattering angles; the $\Delta$-isobar effect found previously remains unchanged by Coulomb. In electromagnetic reactions Coulomb competes with other effects in a complicated way.

A “4π-type” study of the reaction p(d, pp)n at Ed = 26.5 MeV

Experimental data on the three-nucleon reaction p(d, pp)n at E d = 26.5 MeV obtained with the multidetector system BOL, covering most of the phase space, are presented. The data are compared with Faddeev calculations using a local S-wave potential for the nucleon-nucleon interaction. The calculated cross sections, which are in general not sensitive to the precise choice of the nucleon-nucleon potential, agree well with the data over the major part of phase space. We have, though, discovered a region in phase space with a strong discrepancy. In the same region, around a neutron c.m. angle of 140°, the calculations are sensitive to the N-N potential. Theoretical and experimental angular distributions in the p-n recoil c.m. subsystem for proton- neutron energies below 0.5 MeV agree in absolute magnitude, both being isotropic. For larger relative energies, a discrepancy develops, part of which might be related to missing higher par- tial wave components in the N-N interaction, rather than to Coulomb or S-wave scattering effects. The total breakup cross section has been deduced from the data as 169 ± 36 mb.

The angular distribution of final state interacting n-p pairs in the reaction p+d → p+p+n

Abstract The three-particle reaction p+d → p+p+n has been investigated systematically at a deuteron bombarding energy of 52.3 MeV. Kinematically complete experiments have been carried out by detecting the two protons in coincidence. The kinematical conditions were chosen predominantly to observe the effect of the n-p final state interaction. All the data are analysed in terms of the Watson-Migdal model of final state interactions. At specific kinematical conditions the impulse approximation turns out to be a more general and better description. An angular distribution was obtained for the production of singlet and triplet final state interacting n-p pairs with zero relative energy in the n-p subsystem. A relation is derived which connects the measured angular distribution for triplet final state interaction in the three-nucleon reaction quantitatively with the angular distribution of elastic p-d scattering. The systematic study proves that values of the nucleon-nucleon scattering lengths can be extracted with a high degree of reliability from three-particle reactions under properly chosen kinematical conditions.

Proton-proton final-state interaction in the three-nucleon reaction p+d → p+p+n

The three-nucleon reaction p+d → p+n+n has been investigated at a deuteron bombarding energy of 52.3 MeV. A kinematically complete experiment was carried out with the aim to observe the proton-proton final-state interaction. By using the Watson-Migdal model a proton-proton scattering length of a pp = −7.5 ± 0.5 fm is extracted from the measurements.