W. Glöckle

The quantum mechanical few-body problem

1. Elements of Potential Scattering Theory.- 1.1 The Moller Wave Operator.- 1.2 The Cross Section.- 1.3 Resolvent Operators and Greens Functions.- 1.4 Asymptotic Behaviour of the Scattering Wave Function.- 1.5 The S-, T-, and K-Matrices.- 1.6 S-Matrix Pole Trajectories.- 1.7 Criteria for Divergence or Convergence of the Neumann Series.- 2. Scattering Theory for the Two-Nucleon System.- 2.1 Density Matrices for the Initial and Final State.- 2.2 The General Spin Observable.- 2.3 The Wolfenstein Parametrisation of the Scattering Amplitude.- 2.4 Examples for Spin Observables.- 2.4.1 Polarisation.- 2.4.2 Asymmetry.- 2.4.3 Depolarisation.- 2.4.4 Spin Correlation Parameters.- 2.5 Partial-Wave Decomposition.- 2.6 Standard S-Matrix Representations.- 2.7 Numerical Methods.- 2.7.1 Coordinate Space.- 2.7.2 Momentum Space.- 2.7.3 Pade Method.- 3. Three Interacting Particles.- 3.1 Channels.- 3.2 The Fundamental Set of Lippmann-Schwinger Equations.- 3.3 Faddeev Equations and Other Coupling Schemes.- 3.3.1 Faddeev Equations.- 3.3.2 Faddeev Equations in Differential Form and the Asymptotic Behaviour of the Faddeev Amplitudes.- 3.3.3 Other Coupling Schemes and Spuriosities.- 3.4 Transition Operators.- 3.4.1 AGS-Equations.- 3.4.2 Unitarity.- 3.4.3 Multiple Scattering Series.- 3.4.4 Identical Particles.- 3.5 Examples of Numerical Studies in Few-Nucleon Scattering.- 3.5.1 Lovelace Equations.- 3.5.2 Kinematical Curves.- 3.5.3 Selected Numerical Studies.- 3.6 The Three-Nucleon Bound State.- 3.6.1 The Faddeev Equations with a Three-Body Force.- 3.6.2 Momentum Space Representation.- 3.6.3 A Technical Remark.- 3.6.4 Physical Remarks About the Triton.- 3.6.5 Appendix: The Recoupling Coefficient in Momentum Space.- 4. Four Interacting Particles.- 4.1 The Fundamental Set of Lippmann-Schwinger Equations.- 4.2 Coupled Equations in Dummy Variables.- 4.3 Yakubovsky Equations.- 4.4 AGS-Equations for Transition Operators.- 4.5 Remarks on Equations of Higher Connectivity.- References.- Reviews, Monographies, and Conferences.

The Three nucleon continuum: Achievements, challenges and applications

Abstract After a brief historic overview the basic equations for three-nucleon (3N) scattering based on general two-nucleon and 3N forces are reviewed and the main steps for their derivation are given. Also the expressions for the various observables, elastic and breakup cross sections, as well as the great variety of spin observables are displayed and derived. The treatment of the 3N Faddeev equations in momentum space and in a partial wave decomposition is outlaid in some detail, the handling of the singularities in the integral kernel described and the algorithms and techniques used to solve the large set of equations in the discretized form are presented. Accuracy tests in form of benchmark calculations, where our results are compared to the ones of other techniques, are given. The bulk part of this review, however, is devoted to the comparison of very many observables in elastic nucleon-deuteron (Nd) scattering and the breakup process to the predictions based on the most modern nucleon-nucleon (NN) forces AV18, Nijmegen93, Nijmegen I and II and a recently updated OBE-potential CD Bonn. Overall the agreement with the data is excellent and there is little room left for the action of a three-nucleon force (3NF). The effects of the π-π, π-ϱ and ϱ-ϱ exchange 3NFs of the Tucson-Melbourne model are studied. They are in general small and in the few cases where discrepancies to data occur using NN forces only, they go into the wrong direction. We propose quite a few measurements, which should help to get more information on the potential energy of three nucleons. Several special topics are discussed: Do certain 3N scattering observables scale with the triton binding energy? Which of the 3N breakup cross sections are totally insensitive to the choice of the NN force and which are very sensitive? How well can one extract the nn scattering length from the 3N breakup? We discuss the outsticking discrepancy of the 3N analyzing power Ay in low energy elastic Nd scattering; the eigen phase shifts and mixing parameters in elastic nd scattering; the simplifications of 3N scattering at high energies and the formulation of the optical potential for elastic nd scattering and its limiting form at high energies. Alternative approaches to solve 3N scattering: in configuration space, using finite rank expansions of NN forces, variational techniques and the hybrid Sendai method are briefly described as well as the proton proton Coulomb force problem in the pd system and the question how to incorporate relativity. Finally some applications are sketched where a 3N final state occurs and where the interaction among the nucleons requires a correct treatment. We mention inelastic electron scattering as well as π-absorption on 3He (3H) and nonmesonic decay of the hypertriton.

The Two-nucleon system at next-to-next-to-next-to-leading order

Abstract We consider the two-nucleon system at next-to-next-to-next-to-leading order (N 3 LO) in chiral effective field theory. The two-nucleon potential at N 3 LO consists of one-, two- and three-pion exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin-breaking and relativistic corrections. We employ spectral function regularization for the multi-pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low-energy constants (LECs) related to pion–nucleon vertices are taken consistently from studies of pion–nucleon scattering in chiral perturbation theory. The total of 26 four-nucleon LECs has been determined by a combined fit to some np and pp phase shifts from the Nijmegen analysis together with the nn scattering length. The description of nucleon–nucleon scattering and the deuteron observables at N 3 LO is improved compared to the one at NLO and NNLO. The theoretical uncertainties in observables are estimated based on the variation of the cut-offs in the spectral function representation of the potential and in the regulator utilized in the Lippmann–Schwinger equation.

Nuclear forces from chiral Lagrangians using the method of unitary transformation I : Formalism

Abstract We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory.

Cross Section Minima in Elastic Nd Scattering: Possible Evidence for Three-Nucleon Force Effects

Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon (NN ) 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 60thinspMeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly. {copyright} {ital 1998} {ital The American Physical Society}

Improving the convergence of the chiral expansion for nuclear forces - I: Peripheral phases

Abstract.We study the two-pion exchange potential at next-to-next-to-leading order in chiral effective field theory. We propose a new cut-off scheme for the pion loop integrals based on spectral-function regularization. We show that this method allows for a consistent implementation of constraints from pion-nucleon scattering. It leads to a much improved description of the partial waves with angular momentum

The hypernuclei (4)(lambda)He and (4)(lambda)H: challenges for modern hyperon-nucleon forces.

l \geq 2

Elastic scattering and break-up processes in then-d system

as compared to the calculation utilizing dimensional regularization.

The α particle based on modern nuclear forces

The hypernuclei (4)(Lambda)He and (4)(Lambda)H provide important information on the hyperon-nucleon interaction. We present accurate Faddeev-Yakubovsky calculations for the Lambda separation energies of the 0(+) ground and the 1(+) excited states based on the Nijmegen SC YN interactions. We explicitly take the Sigma admixture into account. Mass differences of the baryons and the charge dependence of the interaction are considered. The results show that the Nijmegen models cannot predict all separation energies simultaneously hinting to failures of the current interaction models. It is pointed out that the differences of the Lambda separation energies of (4)(Lambda)He and (4)(Lambda)H are interesting observables to probe the YN interaction models.

Resonance saturation for four nucleon operators

A method to solve the AGS equations in momentum space is presented. The two-nucleon transition operators are generated with the new Bonn potential restricted to the states1S0,3S1-3D1,3P0,1P1,3P1,3P2-3F2,1D2 and3D2. Cross sections and analyzing powers for elastic and break-up processes are calculated at a neutron laboratory energyEn=10.3 MeV.