Microscopic calculations in theA=6system

The A=6 structure problem is solved within the framework of the nuclear shell model. Model states are expanded upon a basis of properly symmetrized, translationally invariant harmonic oscillator eigenstates including states of up to 6ħω of excitation. The model interaction is based upon a modification of the two-body Sussex interaction. Eigenvalues and ($J^{\pi }$,T) values are predicted for the ground states of the following systems: ${}_{}{}^6{}_{}{}^{}\mathrm{n}$, ${}_{}{}^6{}_{}{}^{}\mathrm{H}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^6{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{C}$. The ground state binding energies are within 4 percent of experiment for ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$. Excited states for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ systems are determined and compared to experiment and other calculations. The model spectra for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ system is similar to that proposed by Ajzenberg-Selove. However, the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ spectra contain levels in addition to those suggested by existing compilations. In particular, the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ level spectra have the following level ordering: ($0^{+}$,1), ($2^{+}$, 1), ($1^{+}$,0), ($0^{+}$,1), ($0^{+}$,1), ($3^{+}$,0) ($2^{+}$,1), ($4^{\mathrm{-}}$,1), ($2^{\mathrm{-}}$,1), ($3^{\mathrm{-}}$,1), and ($4^{+}$,1).