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

Y. Fujikawa, T. Kawabata, S. Adachi, S. Enyo, T. Furuno, Y. Hijikata, K. Himi, K. Hirose, Y. Honda, K. Inaba, H. Makii, K. Miyamoto, M. Murata, K. Nishio, S. Okamoto, R. Orlandi, K. Sakanashi, F. Suzaki, S. Tsuji, K. Yahiro, J. Zenihiro
Nuclear Experiment, Nuclear Experiment (nucl-ex), Nuclear Theory (nucl-th)
Physics Letters B 848 (2024) 138384
2023-12-28 00:00:00
We searched for the 6$\alpha$-condensed state in $^{24}$Mg by measuring the $^{12}\rm{C}+{}^{12}\rm{C}$ 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 $^{12}\rm{C}+{}^{12}\rm{C}\to{}^{12}\rm{C}(0^+_2)+X$ and $^{12}\rm{C}(3^-_1)+X$ reactions were determined. In addition, the missing-mass spectroscopy was successfully utilized to determine the excitation energy of the residual $^{12}\rm{C}$ nucleus and the exclusive cross sections for the $^{12}\rm{C}+{}^{12}\rm{C}\to{}^{12}\rm{C}(0^+_2)+{}^{12}\rm{C}(0^+_1)$, $^{12}\rm{C}(0^+_2)+{}^{12}\rm{C}(2^+_1)$, and $^{12}\rm{C}(0^+_2)+{}^{12}\rm{C}(0^+_2)$ reactions. In both the inclusive $^{12}\rm{C}(0^+_2)+X$ channel and the exclusive $^{12}\rm{C}(0^+_2)+{}^{12}\rm{C}(0^+_1)$ channel, the cross section peaked at $E_rm{cm}$ = 19.4 MeV, which correspond to the excitation energy of $E_x$ = 33.3 MeV in $^{24}\rm{Mg}$. 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 $^{12}\rm{C}(0^+_2)+{}^{12}\rm{C}(0^+_2)$ 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 $^{24}\rm{Mg}$. 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 $^{12}\rm{C}$.
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