Nuclear core dynamics and rearrangement energy for hypernuclei

The effect of the nuclear core dynamics on the binding energies of Λ hypernuclei is studied in the framework of variational correlated wave functions. In addition to the core energy and to a Λ single-particle contribution ?_ν, we exhibit a rearrangement energy E_R which in particular depends on the ΛN correlations F and on the difference δφ_N between the core wave function and its exact ground-state value. E_R is nonzero only if there are both ΛN correlations (F ≠ 1) and if δφ_N ≠ 0. The latter can result from core polarization by the Λ or from errors in the ground-state variational wave function of the core. E_R varies linearly with δφ_N for small δφ_N. Detailed numerical results for central ΛN and NN potentials with repulsive cores confirm these general features. For a give core wave function ΛN correlations reduce the radius of the core nucleons relative to their c.m.; however E_R leads to an expansion of the core rather than to a contraction with only ?_ν. The core polarization eneegy is quite small ? 0.4 MeV. We study the effects of errors in the variational core wave function by detuning this as a function of one of the variational parameters.