Binding Energy of aΛParticle in Nuclear Matter

Abstract

The binding energy of a $\ensuremath{\Lambda}$ particle in nuclear matter, ${B}_{\ensuremath{\Lambda}}(\ensuremath{\infty})$, is calculated self-consistently with the help of the Brueckner theory. In the $K$-matrix equations for the $\ensuremath{\Lambda}\ensuremath{-}N$ interaction, pure kinetic energies in the intermediate states are used. The $K$-matrix equations are solved numerically. The rearrangement energy is taken into account. The values of ${B}_{\ensuremath{\Lambda}}(\ensuremath{\infty})$ calculated with several central $\ensuremath{\Lambda}\ensuremath{-}N$ potentials ${v}_{\ensuremath{\Lambda}N}$- though smaller than the values obtained by other authors - are, in general, larger than the empirical value of ${B}_{\ensuremath{\Lambda}}(\ensuremath{\infty})$. An agreement with this value is obtained only if ${v}_{\ensuremath{\Lambda}N}$, adjusted to the binding energy of $_{\ensuremath{\Lambda}}\mathrm{He}^{5}$, has a sufficiently large hard core and is sufficiently suppressed in odd states. Possible ways of reducing the calculated value of ${B}_{\ensuremath{\Lambda}}(\ensuremath{\infty})$ are discussed. A critical discussion of the independent-pair approximation applied by other authors in calculating ${B}_{\ensuremath{\Lambda}}(\ensuremath{\infty})$ is presented.