Three-body cluster effects on Λ single-particle energies in 17ΛO and 41ΛCa

A method to obtain microscopic descriptions of Lambda hypernuclei is formulated in the framework of the unitary-model-operator approach. A unitarily transformed Hamiltonian is introduced and given in a cluster expansion form. The structure of three-body cluster terms are discussed, in particular, with regard to the Lambda single-particle energy. The Lambda single-particle energies including the three-body cluster contributions are calculated for the 0s(1/2), 0p(3/2) and 0p(1/2) states in O-17(Lambda), and for the 0s(1/2), 0p(3/2), 0p(1/2), 0d(5/2) 0d(3/2) and 1s(1/2) states in Ca-41(Lambda), using the Nijmegen soft-core (NSC), NSC97a-f, and the Julich (A) over tilde (J (A) over tilde) and J (B) over tilde hyperon-nucleon interactions. It is found that tilt: three-body cluster terms bring about sizable effects in the magnitudes of the Lambda single-particle energies, but affect the Lambda spin-orbit splittings only little.