The hypernucleus 5ΛHe in a two frequency model Original Research Article

Our previously developed two-frequency folded-diagram method is applied to calculate the binding energy of 5ΛHe starting with Nijmegen YN potentials NSC89 and NSC97(a-f). Since the masses of a hyeron and a nucleon are different and so may be their binding energies in a hypernucleus, wave functions of a hyperon and a nucleon are treated with different frequencies. The frequency ℏωN for a nucleon in 5ΛHe is set constant according to an empirical formula, while that for a hyperon ℏωY remains as a parameter. The G-matrix elements are calculated exactly by using an exact Pauli exclusion operator. We then obtain the Λʹs single particle energy in 5ΛHe as a function of ℏωΛ. A stable ℏωΛ can be found at the saturate minimum. Results from various modes of the realistic Nijmegen NSC89 and NSC97 YN potentials are compared to each other. Calculations by switching ℏωN to other values are also done. The result from NSC97f is found to be closest to the experimental value. Possible implications of the results are discussed.