Search for the alpha-cluster 2$^{+}_{2}$ state in $^{12}$C

Alpha particle clustering is an important concept in nuclear physics. Many works were devoted to examine the alpha-cluster structure in atomic nuclei. The $^{12}$C nucleus is one of the well-investigated nuclei, and its energy level is successfully explained by the alpha-cluster-model (ACM) calculations except for the 2$^{+}_{2}$ state. The ACM calculation strongly suggests the 2$^{+}$ state should be observed at E$_{x}\sim $ 10 MeV. Recently, Itoh et al suggested both the 0$^{+}$ and 2$^{+}$ states exist in a broad bump at E$_{x }\sim $ 10 MeV in $^{12}$C, but Fynbo et al claimed they observed no 2$^{+}$ states in the bump. Thus the existence of the 2$^{+}_{2}$ state is still controversial. We propose to measure the cross sections for the $^{16}$O(d,$^{6}$Li) reaction at E$_{d}$ = 45 MeV to search for the 2$^{+}_{2}$ state in $^{12}$C. We will perform the multipole-decomposition analysis on the basis of the DWBA calculation and pin down the 2$^{+}$ strengths in the broad bump at E$_{x }\sim $ 10 MeV. We will use a $\Delta $E-E Si counter to detect reaction products. This counter consists of two Si strip detectors with the thicknesses of 65 $\mu $m and 500 $\mu $m. We performed a test experiment and confirmed the performance of the $\Delta $E-E Si counter is good enough to carry out the proposed measurement.