Structure ofC15,16and phenomenology of the hinderedE2transition inC16

Abstract

The three-body model of ${}^{14}\mathrm{C}+n+n$ is applied to study the $E2$ transition in ${}^{16}\mathrm{C}$. The $n\text{‐}{}^{14}\mathrm{C}$ potential is chosen to reproduce the single-particle energies of ${}^{15}\mathrm{C}$. The wave functions of ${}^{16}\mathrm{C}$ are obtained as a combination of correlated Gaussians by including the Pauli requirement. It is found that the hindered $E2$ transition can be accounted for by a polarization charge of about $0.10e$ while the $E2$ transition in ${}^{15}\mathrm{C}$ requires a little larger charge of $0.16e$. The soundness of this result is contrasted to the $E2$ transitions in $({}^{17}\mathrm{O},{}^{18}\mathrm{O})$ and $({}^{17}\mathrm{F},{}^{18}\mathrm{Ne})$ nuclei. The longitudinal momentum distribution of ${}^{15}\mathrm{C}$ fragments from ${}^{16}\mathrm{C}$ breakup can be well reproduced.