Momentum-space calculations for three-nucleon scattering including a three-nucleon force

The formalism to include a three-nucleon force into three-nucleon continuum calculations is presented. First numerical results, obtained in momentum space, are shown. The two- and three-nucleon forces have been restricted to act only in the¹ S ₀ and³ S ₁-³ D ₁ partial-wave states. As two-nucleon interaction the Bonn-B potential and as three-nucleon interaction the Tucson-Melbourne two-pion exchange model has been used.     

Axial observables in d-->p--> breakup and the three-nucleon force

We have measured three axial polarization observables in d-->p--> breakup with a polarized 270 MeV deuteron beam on a polarized proton target. Axial observables are zero by parity conservation in elastic scattering but can be easily observed in the breakup channel at the present energy. Based on a symmetry argument, the sensitivity of these observables to the three-nucleon force might be enhanced. Calculations without three-nucleon force are in fair agreement with our measurement, indicating that the expected sensitivity of axial observables to the three-nucleon force is not confirmed. Including a three-nucleon force in the calculation does not improve the agreement with the data.     

Relativity in the three-nucleon system

A Poincaré-invariant formulation of the three-body system is used. The two-body force embedded in the three-particle Hilbert space is generated out of the high-precision NN forces by solving a nonlinear equation. The solution of the relativistic 3N Faddeev equation for ³H reveals less binding energy than for the nonrelativistic one. The effect of the Wigner spin rotation on the binding energy is very small.     

The three-nucleon system

A brief review is given of the recent progress made in the study of the three-nucleon problem with local interactions. In particular, it is pointed out that the presence of meson exchange currents can contribute significantly to the³He charge form factor at high momentum transfer.Invited talk at the symposium Theory of lightest nuclei, Liblice, Czechoslovakia, May 1974.     

Off-shell effects in the three-nucleon system

The triton binding energy and the neutron-deuteron doublet scattering length have been studied with phase-equivalent rank-2 separable potentials in S-waves. The potentials have been constructed from the phase shifts using the solution of the inverse scattering problem. Large off-shell effects are connected with the appearance of additional nodes in the deuteron or the low-energy singlet wave functions.     

Nucleon-nucleon interaction in the three-nucleon system

The three-nucleon system is reconsidered. The Faddeev equations are given leading to a set of integral equations. Solving these integral equations, suitable forms are considered for the nucleon-nucleon interaction. In the bound state of three-nucleon system, the form of the nuclear forces from the nucleon-nucleon interaction is important. In the present calculations, we consider the nuclear forces resulting from the nucleon-nucleon interaction by the exchange of a scalar meson, a pseudoscalar meson, and a massless vector meson. With this different meson exchange nucleon-nucleon interaction, the binding energy of the three-nucleon system is calculated by solving the Faddeev integral equations giving a value of 8.452 MeV.     

pd scattering at 250 MeV and three-nucleon forces

We have measured angular distributions of the differential cross-section, the analyzingpower and all of the spin transfer coefficients K _y ^y, K _x ^x, K _z ^x, K _x ^z, and K _z ^z for the pd elastic scattering at 250 MeV. These are the first measurements of a complete set of proton polarization observables for pd elastic scattering at intermediate energies. The present data are compared with theoretical predictions based on exact solutions of the three-nucleon Faddeev equations and modern realistic nucleon-nucleon potentials combined with three-nucleon forces (3NF), namely the Tucson-Melbourne (TM) 2 -exchange model, a modification thereof (TM) closer to chiral symmetry, and the Urbana IX model.Received: 30 September 2002, Published online: 22 October 2003PACS: 21.45. + v Few-body systems - 21.30.-x Nuclear forces - 24.70. + s Polarization phenomena in reactions     

Near-barrier fusion, breakup and scattering for the Be + Sm system

Fusion, breakup and scattering for the ⁹Be + ¹⁴⁴Sm system at near barrier energies are investigated by different approaches. We show that at energies above the barrier there is a small complete fusion suppression when compared with predictions from a double folding potential and with a similar tightly bound system. At sub-barrier energies there is no significant deviation from the predictions using coupled channel calculations that do not include the breakup channel. The energy dependence of the optical potential does not show the usual threshold anomaly found in tightly bound systems. From a simultaneous analysis of fusion and scattering data we estimate the distance where breakup starts to occur.     

The three-nucleon system near the N-d threshold

The three-nucleon system is studied at energies a few hundred keV above the N-d threshold. Measurements of the tensor analyzing powers T₂₀ and T₂₁ for p-d elastic scattering at E_c.m. = 432 keV are presented together with the corresponding theoretical predictions. The calculations are extended to very low energies since they are useful for extracting the p-d scattering lengths from the experimental data. The interaction considered here is the Argonne V18 potential plus the Urbana three-nucleon potential. The calculation of the asymptotic D- to S-state ratio for ³H and ³He, for which recent experimental results are available, is also presented.     

Bag-model inspired nucleon-nucleon potentials and the three-nucleon system

Several examples of short-range energy-dependentN-N potentials derived in the quark-compound-bag (QCB) model are presented. They all satisfy the classical causality condition. We show that for radii of theN-N interactions ofb1.4 fm thes-wave QCB potentials reproduce fairly well the trinucleon binding energy and other three-nucleon observables.     

The three-nucleon system with the Reid and Gammel-Brueckner potentials

We report preliminary results for an extension of our calculations to the Reid and Gammel-Brueckner nucleon-nucleon potentials. The results for the Reid potential appear to disagree with those of some other calculations.     

How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length

We show that chiral symmetry and gauge invariance enforce relations between the short-distance physics that occurs in a number of electroweak and pionic reactions on light nuclei. Within chiral perturbation theory, this is manifested via the appearance of the same axial isovector two-body contact term in pi(-)d --> nngamma, p-wave pion production in NN collisions, tritium beta decay, pp fusion, nud scattering, and the hep reaction. Using a Gamow-Teller matrix element obtained from calculations of pp fusion as input, we compute the neutron spectrum obtained in pi(-)d --> nngamma. With the short-distance physics in this process controlled from pp --> de(=)nu(e), the theoretical uncertainty in the nn scattering length extracted from pi(-)d --> nngamma is reduced by a factor larger than 3, to approximately < or = 0.05 fm.     

Virtual breakup effects in elastic scattering of polarized deuterons

Elastic scattering of polarized deuterons at E_d = 56 MeV is investigated for ¹⁶O, ⁴⁰Ca, ⁵⁸Ni, ¹¹⁸Sn and ²⁰⁸Pb target nuclei by the use of folding interactions. Effects of virtual breakup of the deuteron to S- and D-states in the continuum region are taken into account by the CDCC method and are found to make indispensable contributions to cross sections and analyzing powers, where continuum-continuum couplings are substantial. The contribution of the D-state admixture in the ground state is important for the tensor analyzing powers. The calculated results agree well with experimental data. The invariant-amplitude method and the second-order sum rule study clarify the characteristic feature of the spin dependence of the effective interactions due to the virtual breakup. The near-side/far-side decomposition of scattering amplitudes illuminates the difference of the reaction mechanism between light and heavy target nuclei. The investigation for the ²⁰⁸Pb target at E_d = 21.5 MeV gives important information on the energy dependence of the effective interactions. The use of different parameter sets for the input nucleon-target optical potentials shows that the detailed results depend significantly on the choice of the parameter sets.     

Analysis of three-nucleon scattering using Faddeev equations up to third order

The Faddeev equations for three nucleons are iterated up to third order using separable interactions: the Tabakin potential for the first order and the Yamaguchi potential for the other orders. This method is applied to the quasi-free scattering ²H(p, 2p)n and ²H(s, np)p. Apparent convergence of the rescattering series is obtained for incident lab energies $\text{E}{}_{\mathrm{<mtext>lab</mtext>}}\text{? 40}\text{MeV}$ and the shape and magnitude of the experimental results are thus reproduced.     

Exchange magnetic moment form factor of the three-nucleon system

The exchange magnetic moment form factor of ³H and ³He is derived from experiment, regarding the D state probability P_D as free parameter. The isoscalar part is roughly constant. The rms radius corresponding to the isovector part increases as P_D increases.     

Precise measurement of dp elastic scattering at 270 MeV and three-nucleon force effects

The cross section, the deuteron vector A(d)(y) and tensor analyzing powers A(ij), the polarization transfer coefficients K(y('))(ij), and the induced polarization P(y(')) were measured for the dp elastic scattering at 270 MeV. The cross section and A(d)(y) are well reproduced by Faddeev calculations with modern data-equivalent nucleon-nucleon forces plus the Tucson-Melbourne three-nucleon force. In contrast, A(ij), K(y('))(ij), or P(y(')) are not described by such calculations. These facts indicate the deficiencies in the spin dependence of the Tucson-Melbourne force and call for extended three-nucleon force models.