We study the structure of the no-core shell model wave functions for ${}^6\mathrm{Li}$ and ${}^{12}\mathrm{C}$ by investigating the ground state and first excited state electron scattering charge form factors. In both nuclei, large particle-hole (ph) amplitudes in the wave functions appear with the opposite sign to that needed to reproduce the shape of the $(e,e^{\prime })$ form factors, the charge radii, and the B(E2) values for the lowest two states. The difference in sign appears to arise mainly from the monopole $\Delta \hslash \omega =2$ matrix elements of the kinetic and potential energy ($T+V$) that transform under the harmonic oscillator SU(3) symmetries as $(\lambda ,\mu )=(2,0)$. These are difficult to determine self-consistently, but they have a strong effect on the structure of the low-lying states and on the giant monopole and quadrupole resonances. The Lee-Suzuki transformation, used to account for the restricted nature of the space in terms of an effective interaction, introduces large higher-order $\Delta \hslash \omega =n,n>2$, ph amplitudes in the wave functions. The latter ph excitations aggravate the disagreement between the experimental and predicted $(e,e^{\prime })$ form factors with increasing model spaces, especially at high momentum transfers. For sufficiently large model spaces, the situation begins to resolve itself for ${}^6\mathrm{Li}$, but the convergence is slow. A prescription to constrain the ph excitations would likely accelerate convergence of the calculations.

• Received 6 August 2009

DOI:https://doi.org/10.1103/PhysRevC.81.054301