Mesonic decay of neutron-rich $\Lambda$ hypernuclei

Although the pionic decay of $\Lambda$ particle is suppressed in finite nuclei due to the Pauli principle, it still competes with the more dominant non-mesonic decay mode in light hypernuclei. In this contribution, we discuss the pionic decay of light neutron-rich $\Lambda$ hypernuclei. To this end, we describe the structure of hypernuclei with the Skyrme-Hartree-Fock method, and compute the decay rate with the single-particle wave function so obtained. We apply this method to carbon isotopes, from $^{13}_{\Lambda}$C to $^{23}_{\Lambda}$C. Our calculation indicates that the decay rate for the $\pi^{-}$ mode, $\Lambda \rightarrow$ p $+ \pi^{-}$, increases as a function of mass number, while that for the $\pi^{0}$ mode, $\Lambda \rightarrow$ n $+ \pi^{0}$, is largely suppressed as expected. This is due to the fact that the proton single-particle potential is deepened for neutron-rich nuclei because of a strong proton-neutron interaction. We will also discuss the effect of the final state interaction between $\pi$ meson and nuclei.