First $0^{+}$ Level in ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$

A model is proposed to explain the electric monopole ($0^{+}$ ${\to 0}^{+}$) matrix element for the transition between the ground and 7.68-Mev state in ${\mathrm{C}}^{12}$ and between the ground and 6.06-Mev state in ${\mathrm{O}}^{16}$. In this model the first excited $0^{+}$ state in ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$ is described by an independent-particle wave function which is identical to the ground-state wave function except for the fact that one of the $1s$ nucleons in the "alpha-particle core" is replaced by a $2s$ nucleon. The calculation is performed using harmonic-oscillator wave functions and the results are found to be in excellent agreement with the present experimental information.