Relation between shrinkage effect and compression of rotational spectrum in ⁷ΛLi hypernucleus

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It has been shown experimentally that the ⁶Li nucleus shrinks by adding a Λ particle while its spectrum is also compressed. We discuss the compatibility of these two effects, contrasting also with a relation between the shrinkage effect and the stability of the spectrum in the ⁹ΛBe hypernucleus. To this end, we employ two-body d-⁵ΛHe and α-⁵ΛHe cluster models for the ⁷ΛLi and ⁹ΛBe hypernuclei, respectively. We first argue that a Gaussian-like interaction between two clusters leads to a stabilization of the spectrum against an addition of a Λ particle, even though the intercluster distance is reduced. In the case of ⁷ΛLi, the spin-orbit interaction between the intercluster motion and the deuteron spin has to be considered also. We show that the shrinkage effect makes the expectation value of the spin-orbit potential larger, lowering the excitation energy for the ⁶Li(3+)⊗ Λ(1/2+) level.