Lowest4+Level inC12: An Example of Nuclear Spectroscopy with Nucleon-Cluster Transfer Reaction

The intermediate-coupling shell model predicts a level with spin $4^{+}$ in ${\mathrm{C}}^{12}$ at excitation energy of about 12 MeV, its main configuration being $p^8\mathrm{}\left[44\right]\mathrm{}{}_{}{}^{11}{}_{}{}^{}G$. Experimental evidence for this level is limited at present to observation only in ${\mathrm{C}}^{12}$-${\mathrm{C}}^{12}$ inelastic scattering. In order to investigate further possibilities for observing this level, nuclear direct interactions with various nucleon-cluster transfers are examined in detail. In particular, the spectroscopic-factor amplitudes in the deuteron reduced width for the ground state of ${\mathrm{N}}^{14}$ leading to all the available $p^8$ configurations of ${\mathrm{C}}^{12}$ are calculated by making use of the harmonic-oscillator shell model; it is found that the spectroscopic factor leading to $\mathrm{}\left[44\right]\mathrm{}{}_{}{}^{11}{}_{}{}^{}G_4^{}{}_{}{}^{}$ is quite large. Direct-interaction mechanisms are discussed in some detail, mainly from the kinematical standpoint (i.e., polology), and partly from the standpoint of nuclear-cluster structure. As a result, it is conjectured that the ${\mathrm{N}}^{14}(d, \alpha ){\mathrm{C}}^{12}$ reaction will proceed predominantly through the transfer process. It is then concluded that the lowest $4^{+}$ level of ${\mathrm{C}}^{12}$ could be most easily observed in the ${\mathrm{N}}^{14}(d, \alpha ){\mathrm{C}}^{12}$ reaction at higher energy (∼15-20-MeV deuterons).