$A$--Dependence of $\Lambda \Lambda$ Bond Energies in Double---$\Lambda$ Hypernuclei

Abstract

The $A$-dependence of the bond energy $\Delta B_{\Lambda \Lambda }$ of the $\Lambda \Lambda$ hypernuclear ground states is calculated in a three-body $\Lambda +\Lambda +{}^{A}Z$ model and in the Skyrme-Hartree-Fock approach. Various $\Lambda \Lambda$ and $\Lambda$-nucleus or $\Lambda N$ potentials are used and the sensitivity of $\Delta B_{\Lambda \Lambda }$ to the interactions is discussed. It is shown that in medium and heavy $\Lambda \Lambda$ hypernuclei, $\Delta B_{\Lambda \Lambda }$ is a linear function of $r_{\Lambda }^{-3}$, where $r_{\Lambda }$ is rms radius of the hyperon orbital. It looks unlikely that it will be possible to extract $\Lambda \Lambda$ interaction from the double-$\Lambda$ hypernuclear energies only, the additional information about the $\Lambda$-core interaction, in particular, on $r_{\Lambda }$ is needed.

Comments: 11 pages, LaTex, 3 figures