Double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>hypernuclei in the Skyrme-Hartree-Fock approach and nuclear core polarization

Abstract

Extension of the Skyrme-Hartree-Fock approach to double-$\ensuremath{\Lambda}$ hypernuclei is presented. Several Skyrme-like $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potentials are fitted to the binding energy of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{13}\mathrm{B}.$ So-called $\ensuremath{\Lambda}\ensuremath{\Lambda}$ bond energy $\ensuremath{\Delta}{B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ appears generally from a complicated interplay between the $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potential, the nuclear core polarization, and $\ensuremath{\Lambda}$ spatial distributions. The core polarization gives a positive contribution to the bond energy even in the absence of $\ensuremath{\Lambda}\ensuremath{\Lambda}$ interaction. This contribution can be substantial even in heavy double-$\ensuremath{\Lambda}$ hypernuclei. The greatest uncertainties in extraction of the $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potential from empirical data arise if hyperons contract the core, a $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potential is of a short range, and the nuclear incompressibility is small.