Binding Energy of aΛParticle in Nuclear Matter

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