Quadrupole-quadrupole interaction calculations which include N=2 mixing

We carry out a study of the study of the $Q \cdot Q$ interaction in a model space which consists of several nucleons in an open shell and all $2 \hbar ω$ excitations. This interaction is $-t (X_o/2) Q \cdot Q$, where for t=1 we get the `accepted strength'. In the $0p$ space, the spectrum would scale with $t$. In this space, the $2^+_1$ and $2^+_2$ states of $^{10}$Be are degenerate, as are the [330] and [411] sets of $J=0^+, 1^+$ and $2^+$ triplets. When $2 \hbar ω$ admixtures are included, the degeneracies are removed. For $t \geq 1.8$ we have new ground state and a new $2_1^+$ state. These are states in which two particles are excited from the $0p$ to the $1s-0d$ shell. There is no mixing of these 2p-2h states with the other states. For these 2p-2h states the occupancy for 0s,0p,1s-0d and 1p-of are 4,4,2 and 0 respectively.

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