Search for the 6$\alpha$ condensed state in ${}^{24}$Mg using the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering

Abstract

We searched for the 6$\alpha$-condensed state in ${}^{24}$Mg by measuring the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering with the SAKRA Si detector array at E_\rm{cm} = 17.5-25.0 MeV. By using the invariant-mass method for the detected 3$\alpha$ particles, the inclusive cross sections for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}\to {}^{12}\mathrm{C}(0_2^{+})+\mathrm{X}$ and ${}^{12}\mathrm{C}(3_1^{-})+\mathrm{X}$ reactions were determined. In addition, the missing-mass spectroscopy was successfully utilized to determine the excitation energy of the residual ${}^{12}\mathrm{C}$ nucleus and the exclusive cross sections for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}\to {}^{12}\mathrm{C}(0_2^{+})+{}^{12}\mathrm{C}(0_1^{+})$, ${}^{12}\mathrm{C}(0_2^{+})+{}^{12}\mathrm{C}(2_1^{+})$, and ${}^{12}\mathrm{C}(0_2^{+})+{}^{12}\mathrm{C}(0_2^{+})$ reactions. In both the inclusive ${}^{12}\mathrm{C}(0_2^{+})+\mathrm{X}$ channel and the exclusive ${}^{12}\mathrm{C}(0_2^{+})+{}^{12}\mathrm{C}(0_1^{+})$ channel, the cross section peaked at $E_{r}mcm$ = 19.4 MeV, which correspond to the excitation energy of $E_x$ = 33.3 MeV in ${}^{24}\mathrm{Mg}$. This 19.4-MeV state is a candidate for the 6$\alpha$-condensed state because of the agreement of the excitation energy with the theoretical value and its decay property. In the exclusive ${}^{12}\mathrm{C}(0_2^{+})+{}^{12}\mathrm{C}(0_2^{+})$ channel, a broad state was observed at E_\rm{cm} = 22.5 MeV, which correspond to the excitation energy of $E_x$ = 36.4 MeV in ${}^{24}\mathrm{Mg}$. From the angular distribution of the differential cross section, the spin and parity of this 22.5-MeV state was assigned to be $4^{+}$. In addition, a $2^{+}$ state was suggested at the low-energy side of the 22.5-MeV state. Because their excitation energies are higher than the theoretical value of the 6$\alpha$-condensed state, these states might be excited states of the 6$\alpha$-condensed state such as the $2_2^{+}$ and $4_1^{+}$ states in ${}^{12}\mathrm{C}$.

Comments: 8 pages, 6 figures