Extension of Proton-Deuteron Phase-Shift Analysis to E p=22.7 MeV and 4 P J Phase Shifts

A previously reported proton-deuteron phase-shift analysis has been extended by more than a factor of two to a proton energy of E_p=22.7MeV. Three-nucleon phase-shift and mixing parameters calculated with the Argonne v₁₈ nucleon-nucleon potential for proton-deuteron and deuteron-proton elastic scattering were used as starting values. It was found that the experimental ⁴P_J three-nucleon phase shifts are at variance with the calculated ones throughout the entire energy range investigated and do not approach the theoretical values at higher energies.     

Trinucleons as multi-quark systems

A new approach to the three-nucleon system is suggested, in which it is assumed that the short-range interaction of nucleon clusters within the trinucleons is described in terms of wave functions of virtual multi-quark configurations. It is shown that the effective three-nucleon Hamiltonian contains three-body forces arising from the dynamics of overlapping bags in the trinucleons. They may, however, be eliminated by a proper redefinition of the nucleon component in a nine-quark wave function. We derive the integral equation for the three-nucleon wave function which has the form of the standard Faddeev equation but requires the phase-equivalent redefinition of the initial form of nucleon-nucleon potential in the quark-compound-bag method.     

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.     

Temperature dependence of upper critical fields for clean superconductors of the second kind

TheD ₁₃ pion-nucleon scattering phase-shifts are calculated using the Khuri representation suitably modified in order to exhibit explicitly the isolated nucleon pole in theu-channel. The results of the calculation are compared with the phase-shift analysis ofRoper.     

The two-pion-exchange three-nucleon potential and nuclear matter

We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be ? 1.90 ± 0.2 MeV.     

3H at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion

The chiral three-nucleon force (3NF) at next-to-next-to-next-to leading order (N³LO) is used to calculate the triton wave function and the doublet nucleon–deuteron scattering length. This allows us to fix the values of the low-energy constants which are free parameters of the theory. The obtained values of these parameters, the expectation values of the kinetic energy, two- and three-body potentials and individual contributions of different parts of 3NF are given.     

Three-Body Dynamics in One Dimension: A Test Model for the Three-Nucleon System with Irreducible Pionic Diagrams

 We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using simple two-body potentials that reproduce the deuteron binding, we obtain that the three-body system binds at about 7.5 MeV. We then consider two types of residual pionic corrections in the dynamical equation; one related to the 2π-exchange three-body diagram, the other to the 1π-exchange three-body diagram. We find that the first contribution can produce an additional binding effect of about 0.9 MeV. The second term produces smaller binding effects, which are, however, dependent on the uncertainty in the off-shell extrapolation of the two-body t-matrix. This presents interesting analogies with what occurs in three dimensions. The paper also discusses the general three-particle quantum scattering problem, for motion restricted to the full line. Received March 5, 2002; accepted July 19, 2002     

Proton-induced deuteron breakup reaction2H(p,pp)n

The screening and renormalization approach allows for a mathematically correct incorporation, in three-body scattering theory, of the long-ranged Coulomb interaction between charged particles. It is based on first calculating the transition amplitudes using screened Coulomb potentials. Then, after renormalization the zero-screening limit, leading to the amplitudes pertaining to unscreened Coulomb potentials, is performed numerically. Within this formalism the proton-induced breakup of deuterons is investigated, with the Coulomb repulsion between the two protons taken into account. Kinematically complete differential cross sections in various kinematic configurations are calculated and compared with the results of an identical calculation but for the neutron-induced reaction. In this way information on the size of the Coulomb effects in the proton-deuteron reaction can be extracted. Comparison is made with experimental data at 13.0 MeV projectile energy. In addition, the quality of approximate ways of including the Coulomb interaction is studied.Dedicated to Prof. Werner Sandhas on the occasion of his 60th birthday     

S-ware πN scattering effects in the nuclear three-body force

We examine the contributions of the off-mass-shell,s-wave N scattering amplitude terms in the Tucson-Melbourne two-pion-exchange three-body force to the trion binding energy. While thea andc terms are not as important as thep-wave terms, they comprise a nonnegligible part of the three-nucleon force which produces nonperturbative effects in the triton wave function.     

Momentum space 3N Faddeev calculations of hadronic and electromagnetic reactions with proton-proton Coulomb and three-nucleon forces included

We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) momentum space Faddeev calculations of elastic proton-deuteron (pd) scattering and breakup to the case when also a three-nucleon force (3NF) is acting. In addition, we formulate that approach in the application to electron- and g \gamma -induced reactions on ³He . The main new ingredient is a 3-dimensional screened pp Coulomb t -matrix obtained by a numerical solution of a 3-dimensional Lippmann-Schwinger equation (LSE). The resulting equations have the same structure as the Faddeev equations which describe pd scattering without 3NF acting. That shows the practical feasibility of both presented formulations.     

Δ(3, 3) excitations and effective three-nucleon forces in finite nuclei

Contributions from three-body terms with intermediate Δ(3,3) isobar excitations to the ground state energies of nuclei are investigated. These terms can either be understood as three-body clusters in a many-body theory including isobar excitations explicitly or as contributions to an effective three-nucleon force. For the example ¹⁶O the resulting contribution is attractive and its value is typically about ?0.5 MeV per nucleon. This is smaller than the typical values of 1 MeV per nucleon repulsion obtained from the modifications of the effective two-body nucleon-nucleon interaction in nuclei due to intermediate Δ(3, 3) configurations. The gain in energy from the three-body terms including Δ(3,3) configurations, however, is of the same importance as the contribution from three-body terms including nucleons only.     

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.     

A spin-isospin-dependent 3N scattering formalism in a 3D Faddeev scheme

We introduce a spin-isospin-dependent three-dimensional approach for the formulation of the three-nucleon scattering. The Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude T to momentum-helicity representations of the two-body t -matrix and the deuteron wave function. Finally, the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.     

Calculation of proton-deuteron phase parameters including the coulomb force

A previously proposed exact method for including the Coulomb force in three-body collisions is applied to proton-deuteron scattering. We present phase shifts for angular momenta up to L = 9, from elastic threshold to 50 MeV proton laboratory energy. Separable rank-one potentials are taken for the nuclear interactions. A charge-independent and a charge-symmetric choice, while leading to different neutron-deuteron and proton-deuteron phase parameters, nevertheless yield practically the same Coulomb corrections. We investigate, moreover, the question of P-wave resonances. A critical comparison of our results with those obtained in a coordinate-space formalism is performed. Furthermore, proposals for an approximate inclusion of the Coulomb potential are tested, and found unsatisfactory.     

The real part of the amplitude of proton-deuteron scattering at an energy 3 GeV

Measurement of the differential cross-sections of the proton-deuteron scattering at 3 GeV is described. Measurement was performed in the region of angles 2.5° to 11.5°. Analysis of the experimental data shows that besides the imaginary scattering amplitude a real part of the scattering amplitude is also required to describe proton-deuteron scattering at 3 GeV energy; the magnitude of the real part is 28% of the imaginary part.Behová 7, Praha 1, Czechoslovakia.We gratefully acknowledge the assistance of the JINR staff and their valuable services.