Charlotte Elster

Resonance saturation for four nucleon operators

In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of nucleon-nucleon scattering. We show that the so-determined numerical values have a remarkable similarity to values extracted from phenomenological one-boson-exchange models in a low momentum expansion. We also extract these values from various modern high accuracy nucleon-nucleon potentials and find again the same similarity. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.

Two-Body T-Matrices Without Angular-Momentum Decomposition: Energy and Momentum Dependences

Abstract. The two-body T-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon-type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in forward direction. In contrast, the corresponding partial-wave contributions, whose number increases with increasing energy, become more and more oscillatory with increasing energy. The angular and momentum dependence of the full amplitude is studied and displayed on as well as off the energy shell as function of positive and negative energies. The behaviour of the T-matrix in the vicinity of bound-state poles and resonance poles in the second energy sheet is studied. It is found that the angular dependence of T exhibits very characteristic properties in the vicinity of those poles, which are given by the Legendre function corresponding to the quantum number either of the bound state or the resonance (or virtual) state. This behaviour is illustrated along numerical examples.

Three-Body Scattering Below Breakup Threshold: An Approach without using Partial Waves

Abstract. The Faddeev equation for three-body scattering below the three-body breakup threshold is directly solved without employing a partial-wave decomposition. In the simplest form it is a three-dimensional integral equation in four variables. From its solution the scattering amplitude is obtained as function of vector Jacobi momenta. Based on Malfliet-Tjon-type potentials differential and total cross sections are calculated. The numerical stability of the algorithm is demonstrated and the properties of the scattering amplitude discussed.

Model Study of Three-Body Forces in the Three-Body Bound State

Abstract. The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.

Nucleon–nucleon scattering in a three-dimensional approach

Two-nucleon scattering at intermediate energies of a few hundred MeV requires quite a few angular momentum states in order to achieve convergence of e.g. scattering observables. This is even more true for the scattering of three or more nucleons upon each other. An alternative approach to the conventional one, which is based on angular momentum decomposition, is to work directly with momentum vectors, specifically with the magnitudes of momenta and the angles between them. We formulate and numerically illustrate [1] this alternative approach for the case of NN scattering using two realistic interaction models, the Argonne AV18 [2] and the Bonn-B [3] potentials. The momentum vectors enter directly into the scattering equation, and the total spin of the two nucleons is treated in a helicity representation with respect to the relative momenta q of the two nucleons. The momentum-helicity states are given as

The Nd Break-Up Process in Leading Order in a Three-Dimensional Approach

A three-dimensional approach based on momentum vectors as variables for solving the three nucleon Faddeev equation in first order is presented. The nucleon-deuteron break-up amplitude is evaluated in leading order in the NN T-matrix, which is also generated directly in three dimensions avoiding a summation of partial wave contributions. A comparison of semi-exclusive observables in the d(p,n)pp reaction calculated in this scheme with those generated by a traditional partial wave expansion shows perfect agreement at lower energies. At about 200 MeV nucleon laboratory energies deviations in the peak of the cross section appear, which may indicate that special care is required in a partial wave approach for energies at and higher than 200 MeV. The role of higher order rescattering processes beyond the leading order in the NN T-matrix is investigated with the result, that at 200 MeV rescattering still provides important contributions to the cross section and certain spin observables. The influence of a relativistic treatment of the kinematics is investigated. It is found that relativistic effects become important at projectile energies higher than 200 MeV.

THE PROTON-DEUTERON BREAK-UP PROCESS IN A THREE-DIMENSIONAL APPROACH

The pd break-up amplitude in the Faddeev scheme is calculated by employing a three-dimensional method without partial wave decomposition (PWD). In the first step and in view of higher energies only the leading term is evaluated and this for the process d(p,n)pp. A comparison with the results based on PWD reveals discrepancies in the cross section around 200 MeV. This indicates the onset of a limitation of the partial wave scheme. Also around 200 MeV relativistic effects are clearly visible and the use of relativistic kinematics shifts the cross section peak to where the experimental peak is located. The theoretical peak height, however, is wrong and calls first of all for the inclusion of rescattering terms, which are shown to be important in a nonrelativistic full Faddeev calculation in PWD.

Elastic Scattering of

Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction

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He based on a Cluster Description

He(p,p)