Bound state properties of Borromean halo nuclei: 6He and 11Li

The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schrodinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.

https://iopscience.iop.org/article/10.1088/0034-4885/73/3/036301/pdf

The R-matrix theory

Application of the Hyperspherical Formalism to the Trinucleon Bound State Problems

The Lagrange-mesh method

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh–Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A = 3 and 4 nuclear systems. When the wavefunction of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this review, the main aspects of the method are discussed together with its application to the A = 3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon–nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high-momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this review is twofold. The first is to present a complete description of the HH method for bound and scattering states, also including detailed formulae for the computation of the matrix elements of the NN and 3N interactions. The second is to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

http://iopscience.iop.org/article/10.1088/0954-3899/35/6/063101/pdf

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

The transformation from one set of Jacobi co-ordinates to another for hyperspherical functions is closely related to the Talmi-Moshinsky transformation for two particles in an oscillator well. The corresponding coefficients are calculated analytically.

J. Raynal

Papers

Transformation coefficients in the hyperspherical approach to the three-body problem