Structure of the particle-hole amplitudes in no-core shell model wave functions

We study the structure of the no-core shell model wave functions for 6Li and 12C 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') 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 Δ(ℎ/2π)ω=2 matrix elements of the kinetic and potential energy (T+V) that transform under the harmonic oscillator SU(3) symmetries as (λ,μ)=(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 Δ(ℎ/2π)ω=n,n>2, ph amplitudes in the wave functions. The latter ph excitations aggravate the disagreement between the experimental and predicted (e,e') form factors with increasing model spaces, especially at high momentum transfers. For sufficiently large model spaces, the situation begins to resolve itself for 6Li, but the convergence is slow. A prescription to constrain the ph excitations would likely accelerate convergence of the calculations.