Structure of low-lying positive-parity states ofO18

Data on single-nucleon transfer, ($t,p$) cross sections, and static and dynamic electromagnetic properties place severe limitations on the structure of the low-lying positive-parity states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. We deduce wave functions that best reproduce these data by use of a model space that includes one collective state each of spin $0^{+}$, $2^{+}$, and $4^{+}$ together with all basis states formed from a closed ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core plus two $d_{\frac{5}{2}}$, $s_{\frac{1}{2}}$ neutrons and up to one $d_{\frac{3}{2}}$ neutron. There is need for only a small $d_{\frac{3}{2}}$ admixture. The $0^{+}$ collective configuration is the dominant constituent of the $0_2^{+}$ state at 3.63 MeV, and the $2^{+}$ collective configuration dominates the $2_3^{+}$ state at 5.25 MeV. Overall, the data favor a small negative value ($\frac{Q}{e}\simeq -5\mathrm{}$ ${\mathrm{fm}}^2$) for the quadrupole moment of the first $2^{+}$ level. The matrix elements of the Hamiltonian that reproduce both the observed energies and transition rates are constructed. Several experiments are suggested to further probe the structure of this nucleus.