Hypernuclear Binding Energies and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>-Nucleon Interaction

Abstract

A phenomenological analysis is made of the binding-energy data for light hypernuclei in terms of a two-body $\ensuremath{\Lambda}$-nucleon interaction, in which account is taken of the empirical information available on the structure of light nuclei. It is found that the observed binding energies can be interpreted in terms of a spin-dependent $\ensuremath{\Lambda}$-nucleon interaction; the agreement obtained is adequate for any force-range between 0.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and 0.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm (for Yukawa shape) and any exchange character for this interaction. From observations on $_{\ensuremath{\Lambda}}\mathrm{H}^{4}$ decay it is argued that the $_{\ensuremath{\Lambda}}\mathrm{H}^{4}$, $_{\ensuremath{\Lambda}}\mathrm{He}^{4}$ doublet has zero spin, which requires that the singlet $\ensuremath{\Lambda}$-nucleon interaction be more attractive than the triplet. The well-depth parameter for the singlet $\ensuremath{\Lambda}$-nucleon interaction has values from 0.90 to 0.85 for ranges between 0.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm and 0.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm, the triplet interaction being also attractive but only one-half to one-third as strong. Spin values are assigned to the light hypernuclei, and the angular correlations which could provide a check on these values are discussed. The absorption of ${K}^{\ensuremath{-}}$ mesons in helium discussed; it appears that the selection rules for the production of $A=4$ hypernuclei in this reaction may be confused by the existence of an excited state $_{\ensuremath{\Lambda}}\mathrm{H}^{4*}$, $_{\ensuremath{\Lambda}}\mathrm{He}^{4*}$. A number of uncertainties in the phenomenological analysis of the heavier hypernuclei are pointed out; the present data do not disagree with the conclusions based on the analysis of the lighter and better-known hypernuclei with $A&lt;~5$, but they add little weight to these conclusions.