Quadrupole-quadrupole interaction calculations which includeN=2mixing

We carry out a study of the study of the $\mathrm{Q}\mathrm{}\mathrm{\cdot }\mathrm{}\mathrm{Q}$ interaction in a model space which consists of several nucleons in an open shell and all 2ħω excitations. This interaction is $-t({\chi }_0/2)\mathrm{Q}\mathrm{\cdot }\mathrm{Q},$ where for $t=1\mathrm{}$ we get the “accepted strength.” In the $0p$ space, the spectrum would scale with $t.\mathrm{}$ In this space, the $2_1^{+}$ and $2_2^{+}$ states of ${}^{10}\mathrm{Be}$ are degenerate, as are the [330] and [411] sets of ${J=0\mathrm{}}^{+},$ $1^{+},$ and $2^{+}$ triplets. When 2ħω admixtures are included, the degeneracies are removed. For $t>~1.8$ 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 two-particle–two-hole (2p-2h) states with the other states. For these 2p-2h states the occupancy for $0s,$ $0p,$ $1s-0d,$ and $1p-0f$ are 4, 4, 2, and 0 respectively.