Reaction cross sections of hypernuclei and the shrinkage effect

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

Figure 1

(a) The intercluster radial wave functions $u\left(R\right)$, defined as ${\psi }_{\mathrm{rel}}\left(\mathbf{R}\right)=\frac{u\left(R\right)}{R}{Y}_{00}\left(\widehat{\mathbf{R}}\right)$, for the ground state of ${}^6\mathrm{Li}$ (the dashed line) and ${}_{\Lambda }^7\mathrm{Li}$ (the solid line) nuclei obtained with the semimicroscopic cluster model. The $\alpha +\text{deuteron}$ and ${}_{\Lambda }^5\text{He}+\text{deuteron}$ structures are assumed for ${}^6\mathrm{Li}$ and ${}_{\Lambda }^7\mathrm{Li}$, respectively. (b) The same as (a), but for the one-body densities $\rho \left(r\right)$ calculated with ${\psi }_{\mathrm{rel}}$.