Two-nucleon excitation from $p$ to $sd$ shell in $^{12,14}$C

The effect of the two-nucleon excitation from $p$ to $sd$ shell is discussed in $^{12}$C and $^{14}$C in the frame work of shell model. The recently suggested shell-model Hamiltonian YSOX provides an suitable tool to investigate the $2~\hbar\omega$ excitation in $psd$ region. Because the strength of the $<pp|V|sdsd>$ interaction, which represents the interaction between the $0~\hbar\omega$ and $2~\hbar\omega$ configurations, is considered in the construction of the YSOX. The level of $^{12}$C is almost independent on the $<pp|V|sdsd>$ interaction, but excitation energies of certain states in $^{14}$C are strongly affected by it. Further investigation shows that the percentage of $2~\hbar\omega$ configuration in these states is quite different from that of the ground state.