The Excited 0 + State and Center-of-Mass Effects in Oxygen-16

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Abstract
The first excited state of O16 is investigated by the use of the harmonic-oscillator shell model with a nuclear interaction. A central potential with a Yukawa shape and Rosenfeld mixture is assumed as the residual interaction. The first excited state is assumed to be some admixture of possible configurations with an excitation energy of 2\hbarω above the shell model ground state which has a wave function corresponding to the double closed configuration (1s)4 (1p)12. In regard to this excited state, there are two pieces of data available, the excitation energy 6.06 Mev and the monopole transition probability to the ground state. The calculated matrix element for this transition (4.7 ×10-26 cm2) is in good agreement with the observed value (3.8 ×10-26 cm2), while the calculated excitation energy is twice as large as the experimental excitation energy. After considering the serious effects of the center-of-mass motion and removing the spurious states, the excitation energy is increased by 15% and the monopole matrix element has increased to twice the experimental value. It turns out that the lowest excited 0+ state obtained by the usual shell model calculation corresponds to the spurious state with the 2s center-of-mass motion.

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