Reaction cross sections of hypernuclei and the shrinkage effect

We calculate the reaction cross sections for $^6{\rm Li}$ and $^7_{\Lambda}{\rm Li}$ on a $^{12}{\rm C}$ target at $100\,{\rm MeV/nucleon}$ using the Glauber theory. To this end, we assume a two-body cluster structure for $^6$Li and $^7_{\Lambda}{\rm Li}$, and employ the few-body treatment of the Glauber theory, that is beyond the well known optical limit approximation. We show that the reaction cross section for $^7_{\Lambda}{\rm Li}$ is smaller than that for $^6$Li by about 4\%, reflecting the shrinkage effect of the $\Lambda$ particle.