The R-matrix method on a Lagrange mesh is a very simple approximation of the R-matrix method with a basis. By analysing an exactly solvable example, we observe that the mesh approximation does not reduce the accuracy of the R-matrix bound-state energies and phase shifts. This property is obtained with two different meshes, the shifted Legendre and shifted Jacobi meshes, which correspond to equivalent polynomial bases. Their comparison shows that the orthogonality of the Lagrange basis functions is not as crucial as was previously assumed: the Legendre mesh, which corresponds to a nonorthogonal Lagrange basis, is at least as accurate as the Jacobi mesh based on an orthogonal basis. We also emphasize the surprising origin of a known property of the R-matrix method: the results are much more accurate with basis functions without uniform boundary conditions because the quality of the matching is realized by a few highly excited eigenfunctions, with weak physical content, of the sum of the Hamiltonian and Bloch operators.

Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively-charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the 16 O+n, 16 O+p and 12 C+α nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.

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Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-⌳ plus ␣ system in a three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-⌳ separation energy ⌬B ⌳⌳ = 1.41 MeV, which is consistent with the recent empirical value, ⌬B ⌳⌳ exp = 1.01± 0.20 MeV, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.