The hypernucleus 5ΛHe in a two frequency model

Our previously developed two-frequency folded-diagram method is applied to calculate the binding energy of 5 Λ He 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 ℏ ω N for a nucleon in 5 Λ He is set constant according to an empirical formula, while that for a hyperon ℏ ω Y remains as a parameter. The G-matrix elements are calculated exactly by using an exact Pauli exclusion operator. We then obtain the Λ's single particle energy in 5 Λ He as a function of ℏ ω Λ . A stable ℏ ω Λ 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 ℏ ω N 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.