<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow/> <mml:mrow> <mml:mo>Λ</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msubsup> <mml:mi>He</mml:mi> </mml:math> (1⁻, 2⁻) spin doublet in a Λ + n + α cluster model

Abstract

Abstract The spin singlet and spin triplet states of the helium-6-lambda hypernucleus are studied in configuration space as a three-body problem, using the hyperspherical method. This hypernucleus is treated as a Λ + n + α cluster model. Since the α particle core has a spin of 0, this is an ideal hypernucleus from which to understand spin dependence in hyperon-nucleon potentials. In this paper, the hyperon-nucleon potential considered is the GLM-YN0 Λ-n potential, which is a simulation of the NSC97f potential obtained through inverse scattering theory. Due to violations of the cluster structure, two-body potentials underbind the helium-6-lambda hypernucleus. This issue is addressed by including a three-body force to complement these two-body forces. A three-body force, whose strength is spin dependent, is used to guide predictions of the spin triplet state of helium-6-lambda which is not yet known experimentally.