Tucson Melbourne Research Articles

3N potentials in the Faddeev coordinate space approach to Nd scattering

For studying 3N bound states and Nd scattering, the Tucson Melbourne (TM) and Urbana 3N forces have been derived from the chiral EFT in the momentum representation. The Faddeev equations in configuration space have attractive properties when applied for nd and pd scattering above the twobody threshold. For that reason, we derived components of the TM 3N potential in the coordinate representation.

Nd break-up process with considering 3NF at intermediate energies in a 3D approach

In this work we have applied a three-dimensional approach to solve the three-nucleon Faddeev equation in the Jacobi momenta space. To this end, we have considered the inhomogeneous part of the Faddeev equation as an appropriate approximation for projectile intermediate energies. As an application the Bonn-B and the Tucson–Melbourne two- and three-nucleon forces have been used for calculating the differential cross section for proton–deuteron break-up process. Finally, comparing our results with the experimental data has been performed for 197 MeV and 346 MeV projectile energies.

Complete Set of Deuteron Analyzing Powers for dp Elastic Scattering at Intermediate Energies and Three Nucleon Forces

With the aim of clarifying roles of the 3NFs in nuclei experimental programs with the polarized deuteron beam at intermediate energies are in progress at RIKEN RI Beam Factory. As the first step, we have measured a complete set of deuteron analyzing powers in deuteron–proton elastic scattering at 250 and 294 MeV/nucleon. The obtained data are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson–Melbourne’99, and UrbanaIX three nucleon forces.

Complete Set of Deuteron Analyzing Powers fordpElastic Scattering at Intermediate Energies and Three Nucleon Forces

With the aim of clarifying roles of the 3NFs in nuclei experimental programs with the polarized deuteron beam at intermediate energies are in progress at RIKEN RI Beam Factory. As the first step, we have measured a complete set of deuteron analyzing powers in deuteron–proton elastic scattering at 250 and 294 MeV/nucleon. The obtained data are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson–Melbourne’99, and UrbanaIX three nucleon forces.

S-Factor of the 3H(α,γ)7Li Reaction at Astrophysical Energies

The astrophysical S-factor for α-3H radiative capture is calculated at astrophysical energies. We construct conserved two- and three-body electromagnetic currents, using minimal substitution in the explicit momentum dependence of the two- and three-nucleon interactions. The realistic Argonne υ18 two-nucleon and Urbana IX or Tucson—Melbourne three-nucleon interactions are considered for calculation. By extrapolation of results for the astrophysical S-factor at zero energy, the energy in the order of 1 keV and less is found to be S(0) = 0.107(0.112) keV·b, with(without) three-body interactions in satisfactory agreement with other theoretical results and experimental data.

TRITON BREAKUP AND FORMATION AT VERY LOW ENERGIES

Different theoretical models for two- and three-body electromagnetic currents are constructed using meson-exchange mechanisms and minimal substitution in the momentum dependence of two- and three-nucleon interactions. We review the use of effective field theory (EFT) to compute electromagnetic reactions in three-nucleon systems at very low energies. We first explain how EFT theory can be extended to incorporate the photon into the three-nucleon systems when also a three-nucleon force is acting. We also explain the predictions of the resulting EFT for neutron–deuteron radiative capture process at very low energies. In this work, a number of low-energy photonuclear observables, including neutron–deuteron radiative capture reactions and triton photodisintegration, are calculated in order to make a comparative study of the pion-less EFT results with the models based on the realistic Argonne v18(AV18) two-nucleon and Urbana IX or Tucson–Melbourne three-nucleon interactions. The calculated cross-section of neutron–deuteron radiative capture and photon polarization parameter of 3 H are in satisfactory agreement with the available experimental data.

TOWARDS A THREE-DIMENSIONAL SOLUTION FOR 3N BOUND STATES WITH 3NFs

After a brief discussion about the necessity of using the 3D approach, we present the non partial wave (PW) formalism for 3N bound state with the inclusion of 3N force (3NF). As an example the evaluation of 3NF matrix elements, which appear in the obtained coupled three-dimensional integral equations, for 2π-exchange Tucson–Melbourne 3NF show how would be this formalism efficient and less cumbersome in comparison with the PW formalism.

Pd scattering at 250 MeV and three-nucleon forces

We have measured angular distributions of the differential cross-section, the analyzing power 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) 2π-exchange model, a modification thereof (TM′) closer to chiral symmetry, and the Urbana IX model.

Feasibility study of a three-nucleon force in the no-core shell model:3Hbinding energy

We investigate the three-nucleon system with a realistic nucleon-nucleon potential and the Tucson-Melbourne (TM) two-pion exchange three-body interaction using a translationally invariant harmonic oscillator basis. In the calculations, the no-core shell-model two-body effective interaction replaces the nucleon-nucleon potential, while the three-nucleon interaction is added without any renormalization. We study the convergence of the approach by changing the basis size. Also the dependence of the binding energies on the TM cutoff parameter $\ensuremath{\Lambda}$ is examined. The results show promise for the construction of three-body effective interactions including a three-nucleon interaction, for use in future ab initio no-core shell-model nuclear structure calculations for $A>3$ systems.

Cross section and complete set of proton spin observables inp→delastic scattering at 250 MeV

The angular distributions of the cross section, the proton analyzing power, and all proton polarization transfer coefficients of $\stackrel{\ensuremath{\rightarrow}}{p}d$ elastic scattering were measured at 250 MeV. The range of center-of-mass angles was $10\ifmmode^\circ\else\textdegree\fi{}--165\ifmmode^\circ\else\textdegree\fi{}$ for the cross section and the analyzing power, and about $10\ifmmode^\circ\else\textdegree\fi{}--95\ifmmode^\circ\else\textdegree\fi{}$ for the polarization transfer coefficients. These are the first measurements of a complete set of proton polarization observables for $\stackrel{\ensuremath{\rightarrow}}{p}d$ 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) $2\ensuremath{\pi}$-exchange model, a modification thereof ${(\mathrm{T}\mathrm{M}}^{\ensuremath{'}}$) closer to chiral symmetry, and the Urbana IX model. Large effects of the three-nucleon forces are predicted. The inclusion of the three-nucleon forces gives a good description of the cross section at angles below the minimum. However, appreciable discrepancies between the data and predictions remain at backward angles. For the spin observables the predictions of the TM 3NF model deviate strongly from the other two 3NF models, which are close together, except for ${K}_{y}^{{y}^{\ensuremath{'}}}.$ In the case of the analyzing power all 3NF models fail to describe the data at the upper half of the angular range. In the restricted measured angular range the polarization transfer coefficients are fairly well described by the ${\mathrm{TM}}^{\ensuremath{'}}$ and Urbana IX 3NF models, whereas the TM 3NF model mostly fails. The transfer coefficient ${K}_{y}^{{y}^{\ensuremath{'}}}$ is best described by the Urbana IX but the theoretical description is still insufficient to reproduce the experimental data. These results call for a better understanding of the spin structure of the three-nucleon force and very likely for a full relativistic treatment of the three-nucleon continuum.

Three-nucleon force effects in nucleon induced deuteron breakup. I. Predictions of current models

An extensive study of three-nucleon force effects in the entire phase space of the nucleon-deuteron breakup process, for energies from above the deuteron breakup threshold up to 200 MeV, has been performed. $3N$ Faddeev equations have been solved rigorously using the modern high precision nucleon-nucleon potentials AV18, CD Bonn, Nijm I, II, and Nijm 93, and also adding $3N$ forces. We compare predictions for cross sections and various polarization observables when $\mathrm{NN}$ forces are used alone or when the $2\ensuremath{\pi}$-exchange Tucson-Melbourne (TM) three nucleon force (3NF) was combined with each of them. In addition AV18 was combined with the Urbana IX 3NF and CD Bonn with the ${\mathrm{TM}}^{\ensuremath{'}}$ 3NF, which is a modified version of the TM 3NF, more consistent with chiral symmetry. Large but generally model dependent 3NF effects have been found in certain breakup configurations, especially at the higher energies, both for cross sections and spin observables. These results demonstrate the usefulness of the kinematically complete breakup reaction in testing the proper structure of $3N$ forces.

Reworking the Tucson-Melbourne Three-Nucleon Potential

We introduce new values of the strength constants (i.e., a, b, c, and d coefficients) of the Tucson-Melbourne (TM) 2π-exchange three-nucleon potential. The new values come from contemporary dispersion-relation analyses of meson-factory πN-scattering data. We make variational Monte-Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range–π-range part of the potential due to the c coefficient and discuss the effect on the triton binding energy.

Triton binding energy and three-nucleon potential

The method of continued fractions proposed by Horacek and Sasakawa is applied to calculate the binding energy of the triton. By this method, the Faddeev equation is solved very quickly. We solved it with 34 channels for the super-soft core (TRS), Paris (PARIS) and Argonne (AV) potentials with Tucson-Melbourne (TM) three-nucleon potential. The binding energy obtained from these realistic two-nucleon potentials without a threenucleon potential is at most 7.7 MeV. If we include the TM three-nucleon potential taking a cutoff mass of Λ=800 MeV for the dipole πNN form factor, the triton is overbound (9.3 ≈ 9.7 MeV), whereas for Λ=700 MeV, we get binding energies which almost agree with the experimental value; TRS+TM, 8.47; PARIS + TM, 8.32; AV+TM, 8.42 MeV.