As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both, novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF.
We introduce new values of the strength constants (i.e., $a$, $b$, $c$, and $d$ coefficients) of the Tucson-Melbourne (TM) 2$π$ exchange three nucleon potential. The new values come from contemporary dispersion relation analyses of meson factory $π$N 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.
A recently developed procedure for a partial wave decomposition of a three-nucleon force is applied to the pi-pi, pi-rho and rho-rho components of the Tucson-Melbourne three-nucleon potential. The resulting matrix elements for the pi-pi and pi-rho components are compared with the values obtained using the standard approach to the partial wave decomposition, in which the pi-rho expressions for the matrix elements are also derived and presented. Several numerical tests and results for the triton binding energy and the correlation function prove the reliability and efficiency of the new method.
In Faddeev calculations of ^3Hwe study the dependence of the binding on the three nucleon force. We adopt the 2 pi -exchange Tucson-Melbourne three-nucleon force and investigate phenomenologically the dependence on the strength of the individual three-body force operators (a -, b -, c - and d -terms). While the a -term provides a tiny contribution the b - and d -terms provides a tiny contribution the b - and d -terms are important to gain the experimental binding energy. We find two solutions for the c -term, one around the value used in the Tucson-Melbourne model and a new one close to zero, …
We present high precision benchmark calculations for the triton binding energy using the most recent, phase equivalent realistic nucleon-nucleon (NN) potentials and the Tuscon-Melbourne pi-pi three-nucleon force (3NF). That 3NF is included with partial waves up to a total two-body angular momentum of j_max=6. It is shown that the inclusion of the 3NF slows down the convergence in the partial waves and j_max=5 is needed in order to achieve converged results within a few keV. We adjust the cut-off parameter Lambda in the form factors of the Tuscon-Melbourne 3NF separately for the different NN po…
The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne $π$ and $ρ$ exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the $πNN$ cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure $π$ exchange. The $ρ$ exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton bin…
In the last decade, for studying 3$N$ bound states and $Nd$ scattering the Tucson-Melbourne (TM) and Urbana 3$N$ force derived from the chiral EFT have been applied. We plan to use the TM 3$N$ force for studying the $Nd$ scattering on the basis of the Faddeev equations in configuration space. In the given paper, we present our final formulas for components of the TM 3$N$ potential obtained in the coordinate space.
Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon interactions and the Tucson-Melbourne three-nucleon force adjusted to the triton binding energy. Predictions based on NN forces only underestimate nucleon-deuteron data in the minima at higher energies starting around 60 MeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly.
We present new calculations of the $α$-particle which are based on the most modern nucleon-nucleon interactions alone and combined with the Tucson-Melbourne or the Urbana IX three-nucleon interaction. Results for the binding energies and some properties of the wavefunction are given. On that phenomenological level little room is left for the action of a possible four-nucleon force.
After a brief discussion about the necessity of using the 3D approach, we present the non 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.
Recent advances in the study of the p-d radiative and mu-3he weak capture processes are presented and discussed. The three-nucleon bound and scattering states are obtained using the correlated-hyperspherical-harmonics method, with realistic Hamiltonians consisting of the Argonne v14 or Argonne v18 two-nucleon and Tucson-Melbourne or Urbana IX three-nucleon interactions. The electromagnetic and weak transition operators include one- and two-body contributions. The theoretical accuracy achieved in these calculations allows for interesting comparisons with experimental data.
After a brief review of the role three-nucleon forces play in the few-nucleon systems, the chiral-perturbation-theory approach to these forces is discussed. Construction of the (nominal) leading- and subleading-order Born terms and pion-rescattering graphs contributing to two-pion-exchange three-nucleon forces is reviewed, and comparisons are made of the types of such forces that are used today. It is demonstrated that the short-range $c$-term of the Tucson-Melbourne force is unnatural in terms of power counting and should be dropped. The class of two-pion-exchange three-nucleon forces then be…
The contribution of a $ππ$-exchange three-body force to the three-nucleon binding energy is calculated in terms of a $πN$ amplitude. The latter is based on a meson-theoretical model of $πN$ interaction developed by the Jülich group. Similar to a previous study based on simple phenomenological $πN$ potentials a very small effect of the resulting three-body force is found. Possible origins of the two-orders-of-magnitude descrepancy between the present result and the values obtained for the Tucson-Melbourne three-body force are investigated. Evidence is provided that this discrepancy is most like…
The longitudinal and transversal asymmetries of the total $\vec{n}\vec{d}$ cross section are calculated. Four modern nucleon-nucleon interactions: AV18, CD Bonn, NijmI and NijmII, give different predictions for these observables. When the three-nucleon Hamiltonian is supplemented by the $2π$-exchange Tucson-Melbourne three-nucleon force (3NF), individually adjusted with each particular NN potential to reproduce the experimental triton binding energy, all predictions practically coincide. We propose to check this scaling behavior experimentally in order to get a clear signal for 3NF effects in …
Faddeev equations for elastic Nd scattering have been solved using modern NN forces combined with the Tucson-Melbourne two-pion exchange three-nucleon force, with a modification thereof closer to chiral symmetry and the Urbana IX three-nucleon force. Theoretical predictions for the differential cross section and several spin observables using NN forces only and NN forces combined with three-nucleon force models are compared to each other and to the existing data. A wide range of energies from 3 to 200 MeV is covered. Especially at the higher energies striking three-nucleon force effects are fo…
We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 hbarOmega we show that realistic nucleon-nucleon interactions, like e.g. the CD-Bonn, under predict the experimental cross sections by more than a factor of two. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time,the TM'(99) in…
Effective Field Theory(EFT) is, the unique, model independent and systematic low-energy version of QCD for processes involving momenta below the pion mass. A low-energy photo-nuclear observable in three-body systems, photon polarization parameter at thermal neutron energies is calculated by using pionless EFT up to next-to-next to leading order(N$^2$LO). In order to make a comparative study of this model, we compared our results for photon polarization parameter with the realistic Argonne $v_{18}$ two-nucleon and Urbana IX or Tucson-Melbourne three-nucleon interactions. Three-body currents giv…
A detailed study of the 4He longitudinal response function R_L(ω,q) is performed at different kinematics, with particular emphasis on the role of three-nucleon forces. The effects shown are the results of an ab initio calculation where the full four-body continuum dynamics is considered via the Lorentz integral transform method. The contributions of the various multipoles to the longitudinal response function are analyzed and integral properties of the response are discussed in addition. The Argonne V18 nucleon-nucleon interaction and two different three-nucleon force models (Urbana IX, Tucson…
The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are discussed in detail. We present results of first applications to 6,7Li, 6He, 7,8,10Be, 10,11,12B, 12N and 10,11,12,13C using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence…
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 NN forces are used alone or when the two pion-exchange Tucson-Melbourne 3NF was combined with each of them. In addition AV18 was combin…
We investigate the sensitivity of the non-exclusive nucleon induced deuteron breakup reaction to the three-nucleon interaction and distributions of three-nucleon force effects in inclusive spectra. To this end we solve the three-nucleon Faddeev equation at a number of incoming nucleon laboratory energies using the CD Bonn nucleon-nucleon interaction alone or combined with the 2π-exchange Tucson-Melbourne three-nucleon force. Based on these solutions energy spectra of an outgoing nucleon, at a specified detection angle as well as spectra integrated over that angle, are calculated. By integratin…
Total photonuclear absorption cross sections of $^3$H and $^3$He are studied using realistic NN and NNN forces. Final state interactions are fully included. Two NN potential models, the AV14 and the r-space Bonn-A potentials, are considered. For the NNN forces the Urbana-VIII and Tucson-Melbourne models are employed. We find the cross section to be sensitive to nuclear dynamics. Of particular interest in this work is the effect which NNN forces have on the cross section. The addition of NNN forces not only lowers the peak height but increases the cross section beyond 70 MeV by roughly 15%. Cro…
Trinucleon longitudinal response functions R_L(q,omega) are calculated for q values up to 500 MeV/c. These are the first calculations beyond the threshold region in which both three-nucleon (3N) and Coulomb forces are fully included. We employ two realistic NN potentials (configuration space BonnA, AV18) and two 3N potentials (UrbanaIX, Tucson-Melbourne). Complete final state interactions are taken into account via the Lorentz integral transform technique. We study relativistic corrections arising from first order corrections to the nuclear charge operator. In addition the reference frame depe…
Different models for conserved two- and three-body electromagnetic currents are constructed from two- and three-nucleon interactions, using either meson-exchange mechanisms or minimal substitution in the momentum dependence of these interactions. The connection between these two different schemes is elucidated. A number of low-energy electronuclear observables, including (i) $np$ radiative capture at thermal neutron energies and deuteron photodisintegration at low energies, (ii) $nd$ and $pd$ radiative capture reactions, and (iii) isoscalar and isovector magnetic form factors of $^3$H and $^3$…
We measured the cross sections of the $^2$H(p,pp)n breakup reaction at E$_p$=16 MeV in three kinematical configurations: the np final-state interaction (FSI), the co-planar star (CST), and an intermediate-star (IST) geometry. The cross sections are compared with theoretical predictions based on the CD Bonn potential alone and combined with the updated 2$π$-exchange Tucson-Melbourne three-nucleon force (TM99'), calculated without inclusion of the Coulomb interaction. The resulting excellent agreement between data and pure CD Bonn predictions in the FSI testifies to the smallness of three-nucleo…
The proton to proton polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'} and the proton to deuteron polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'}, K_x^{y'z'}, K_y^{z'z'}, K_z^{y'z'}, K_y^{x'z'} and K_y^{x'x'-y'y'} have been measured in d(\vec p, \vec p)d and d(\vec p, \vec d)p reactions at E^{lab}_p = 22.7 MeV, respectively. The data have been compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi) phenomenological nucleon-nucleon potentials combined with model three-nucleon force…
