ΛN spin-orbit splittings in Λ9Be and Λ13C studied with one-boson-exchange ΛN interactions

Movitated by the on-going gamma-ray experiment at the Alternating Gradient Synchrotron at Brookhaven National Laboratory, we discuss the energy splittings of the 5/2(1)(+)-3/2(1)(+) doublet in Be-9(Lambda) and the 3/2(1)(-)- 1/2(1)(-) doublet in C-13(Lambda) for which the Lambda N spin-orbit (LS) and antisymmetric spin-orbit (ALS) forces are relevant. In the microscopic 2 alpha + Lambda (3 alpha + Lambda) model for Be-9(Lambda) (C-13(Lambda)). all the available Nijmegen one-boson-exchange (OBE) model Lambda N interactions lead to a wide range of splittings of 0.08-0.20 MeV in Be-9(Lambda) and 0.39-0.96 MeV in C-13(Lambda). On the other hand, if we use information from quark-model Lambda N interactions which have generally large ALS force, the splittings become about half of the smallest OBE model prediction.