Binding energies of hypernuclei and three-bodyΛNNforces

Binding energies of hypernuclei are calculated with use of accurate variational methods for $A=3,5\mathrm{}$, with effective interaction calculations for $A=5,9,13,\infty$, and with Fermi hypernetted-chain variational calculations for $A=\infty$. Effective interactions and variational results agree within a few percent. For $\Lambda N$ forces consistent with $\Lambda \mathrm{p}$ scattering, agreement with the experimental energies is obtained with strongly repulsive Wigner type $\Lambda \mathrm{NN}$ forces, and for $A>\mathrm{}5\mathrm{}$ also with a weakened $p$-state $\Lambda \mathrm{N}$ strength about half that of the $s$-state strength.