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The problem of hyperon-nucleon interaction is a key problem in the physics of hypernuclei. An extremely scarce experimental database of direct hyperon-nucleon interaction stimulates interest in studying bound hyperon-nucleon systems. From the point of view of studying spin-spin and spin- orbit components of N interaction and charge symmetry in hypernuclei the 7He and 9Be nuclei are of particular interest as examples of the p-shell nuclei. On the other hand these hyperon-nucleon systems may exhibit new properties in relation to nucleon-nucleus systems due to exclusion of the Pauli between hyperon and nucleons.

The 7He hypernucleus was considered within the 5He +n+n cluster model (Fig. 1).


Fig. 1 Cluster model 5He+n+n for 7He hypernucleus. Spin projection of particles are shown by arrows.

The hyperon-nucleon interaction is described by a one-boson-exchange potential that is constructed on the basis of the NSC97f model. Phenomenological potentials are used to describe the α and αN interactions. For the 5He interaction, used is a folding-model potential.

Our findings are:

  • The calculations using OBE simulating potential for NSC97f model of NY-interaction give the 7He binding energy (5.35 MeV) which is close to the preliminary experimental value (5.4 MeV).
  • We discussed the receipt for extracting hyperon binding energy from the three-body calculation. The value obtained in previous calculation by E. Hiyama et al. has to be corrected. The new corrected value agrees with our consideration.
  • We shown that the variant of the method of analytical continuation in a coupling constant with three-body pseudo-potential can be applied for evaluation of energies of low-lying levels of the hypernuclei.
  • We have found that the ground band of the 7He spectrum can be classified as an analog of the 6He ground band (see Fig. 2).


Fig. 2 Low-lying levels of 7He hypernucleus. For comparison the spectrum of 6He is depicted. Total orbital momentum of each level is shown.

An α-cluster model is applied to study low-lying spectrum of the 9Be hypernucleus. The spin-orbit α interaction is given by modified Scheerbaum potential.

For 9 Be nucleus findings are:

  • It is possible to find a set of phenomenological potentials to reproduce the ground state + binding energy and excitation energy of the 5/2+ and 3/2+ states, simultaneously.
  • Our calculations reproduce well the experimental data for excitation energies and therefore improve the previous alpha-cluster calculations (see Fig. 3).
  • It is shown that the spectrum of 9Be can be classified as an analog of 9Be spectrum with the exception of several "genuine hypernuclear states" (see Fig. 4). This agrees qualitatively with previous studies (see Fig. 5).
  • It is shown that “glue role of Lambda-hyperon” is only effective for ground band (total orbital momentum is zero) of the spectrum (see Fig. 4).
  • Energy space of spin-flip doublet (9/2+,7/2+) was predicted by our model

3.4 Fig. 4 Low-lying levels of 9Be and 9Be spectrum.
Fig. 5 Low-lying levels of 9Be hypernucleus. Results of our calculation are noted by Cal.1. Calculations by T. Yamada, K. Ikeda, T. Motoba, H. Bando (PRC 38, 854 (1988)) are Cal. 2. Orbital momentum of each level is shown.