Peripheral fragmentation of a 287 MeV/nucleon beam of the halo nucleus ${}^{11}\mathrm{Li}$ incident on a carbon target has been studied in a fragment-neutron coincidence experiment. The momentum distribution of the ${}^{10}\mathrm{Li}$ fragments gives access to the momentum distribution of the removed neutron in ${}^{11}\mathrm{Li}$. From the shape of the distribution, the $({1s}_{1/2}{)}^2$ contribution to the mixture of $({1s}_{1/2}{)}^2$ and $({0p}_{1/2}{)}^2$ components in the ground-state wave function was determined to be $(45\pm 10)\%$. The angular correlation between the knocked out neutron and the one from the decay of ${}^{10}\mathrm{Li}$ shows a skew distribution signaling interference of these two different parity states.

We have observed the two-proton radioactivity of the previously unknown ${}^{19}\mathrm{Mg}$ ground state by tracking the decay products in-flight. For the first time, the trajectories of the $2p$-decay products, ${}^{17}\mathrm{Ne}+p+p$, have been measured by using tracking microstrip detectors which allowed us to reconstruct the $2p$-decay vertices and fragment correlations. The half-life of ${}^{19}\mathrm{Mg}$ deduced from the measured vertex distribution is 4.0(15) ps in the system of ${}^{19}\mathrm{Mg}$. The $Q$ value of the $2p$ decay of the ${}^{19}\mathrm{Mg}$ ground state inferred from the measured $p-p-{}^{17}\mathrm{Ne}$ correlations is 0.75(5) MeV.

The first measurement of the elastic scattering of the halo nucleus ${}^{11}\mathrm{Li}$ and its core ${}^9\mathrm{Li}$ on ${}^{208}\mathrm{Pb}$ at energies near the Coulomb barrier is presented. The ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ elastic scattering shows a strong reduction with respect to the Rutherford cross section, even at energies well below the barrier and down to very small scattering angles. This drastic change of the elastic differential cross section observed in ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ is the consequence of the halo structure of ${}^{11}\mathrm{Li}$, as it is not observed in the elastic scattering of its core ${}^9\mathrm{Li}$ at the same energies. Four-body continuum-discretized coupled-channels calculations, based on a three-body model of the ${}^{11}\mathrm{Li}$ projectile, are found to explain the measured angular distributions and confirm that the observed reduction is mainly due to the strong Coulomb coupling to the dipole states in the low-lying continuum of ${}^{11}\mathrm{Li}$. These calculations suggest the presence of a low-lying dipole resonance in ${}^{11}\mathrm{Li}$ close to the breakup threshold.

We study the emission of two protons from nuclei where this is the only decay channel. A three-body model is developed. We compare the “diproton” model with the three-body calculations. We present exploratory studies of the ${}^{19}\mathrm{Mg}$ and ${}^{48}\mathrm{Ni}$ ground states, which are good candidates for two-proton radioactivity. The two-proton width for the ${}^{17}\mathrm{Ne}{3/2}^{-}$ state is also estimated. Our calculations give substantially lower values for the width than predicted by the diproton model, but larger than from direct decay to the continuum.