Abstract
A three-body model of $^{14}\mathrm{C}$ $+n+n$ is applied to study the energy spectrum and the hindered E2 transition in $^{16}\mathrm{C}$. A realistic two-nucleon potential is used for the valence neutrons. Both spin-singlet and spin-triplet components for the neutrons are taken into account. The three-body problem with a Pauli constraint is solved in a stochastic variational method. For the $n\text{\ensuremath{-}}$$^{14}\mathrm{C}$ potential chosen to reproduce the properties of $^{15}\mathrm{C}$, the low-lying energy spectrum agrees reasonably well with experiment, but the ground state is predicted to be about 1 MeV high. The calculated $B(E2$; ${2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value is about twice the measured value if the polarization charge of the valence neutrons is taken to be the same as that required to fit the $^{15}\mathrm{C}$ data. The correlated motion of the valence neutrons is displayed through the two-neutron density distribution.
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