Abstract
The ground state and the first excited state of $^{4}\mathrm{He}$ are investigated in harmonic oscillator shell-model bases including all the configurations up to 10\ensuremath{\Elzxh}\ensuremath{\omega} excitation energy. The Gogny et al. potential and versions I/III and V of the Malfliet-Tjon potential are used in the calculation. The difficulties in describing these states in a consistent manner are not overcome by substantially enlarging the shell-model bases. The lowest eigenvalue with a 1\ensuremath{\Elzxh}\ensuremath{\omega} center-of-mass wave function is also extracted from the energy matrices, providing the absolute energy of the first ${J}^{\ensuremath{\Pi}}$${=1}^{\mathrm{\ensuremath{-}}}$, T=0 level. It is found that the agreement with experiment for this level is significantly improved when the model space is enlarged.
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