Abstract
The response of the core nucleus to the Λ in a hypernucleus is studied with a local density approximation. This reproduces the energies and radii of the core nuclei as well as the Λ-single particle (s.p.) energies quite well. The polarizing effect of the Λ depends on the core response through an “effective” compression modulus of the nucleus. For a certain class of energy functional, is found to be almost independent of the compression modulus of the infinite nuclear matter. This indeed is a surprising result, and varies with the Hartree-Fock calculations with effective interactions. Reasons for this discrepancy are carefully examined. We consider values of in the range MeV. Furthermore, the polarizing effects also depend critically on , the Λ binding in nuclear matter at density . For only a direct force: and the core nucleus contracts giving rise to relatively larger core polarization. However, for a “saturating” (with a maximum at , where is the nuclear matter equilibrium density), which is required to fit the s.p. data, the -shell hypernuclei binding energies and the low energy scattering data, which results from a force (including exchange) and forces, there may be an expansion of the nucleus with nucleons flowing from the interior to the surface. This is shown to reduce the core polarization effects substantially (for in the neighborhood of ). The resulting changes in root mean square radius and core energy depend on , but are mostly very small, justifying their general neglect.
11 More- Received 14 March 2007
DOI:https://doi.org/10.1103/PhysRevC.77.034312
©2008 American Physical Society