On the convergence of multi-channel effective interactions

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Abstract

A detailed analysis of convergence properties of the Andreozzi-Lee-Suzuki iteration method, which is used for the calculation of low-momentum effective potentials Vlowk is presented. After summarizing different modifications of the iteration method for one-flavor channel we introduce a simple model in order to study the generalization of the iteration method to multi-flavor channels. The failure of a straightforward generalization is discussed. The introduction of a channel-dependent cutoff cures the conceptual and technical problems. This novel method has already been applied successfully for realistic hyperon-nucleon interactions.

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Soft-core baryon-baryon one-boson-exchange models. II. Hyperon-nucleon potential

P. Maessen, Th. Rijken, J. J. de Swart (1989)

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Soft-core hyperon-nucleon potentials

Y. Yamamoto, V. Stoks, Th. Rijken (1998)

A new Nijmegen soft-core OBE potential model is presented for the low-energy YN interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. An important innovation with respect to the original soft-core potential is the assignment of the cut-off masses for the baryon-baryon-meson (BBM) vertices in accordance with broken SU(3)\(_F\), which serves to connect the NN and the YN channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the \(^3P_0\) model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. We present six hyperon-nucleon potentials which describe the available YN cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the \(\Sigma N\) and \(\Lambda N\) channels. For the scalar-meson mixing angle we obtained values \(\theta_S=37\) to 40 degrees, which points to almost ideal mixing angles for the scalar \(q\bar{q}\) states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of \(\Lambda\) hypernuclei.