Large-angleα-particle scattering onC12and search for signatures ofα-particle Bose condensation

Abstract

Evidence of the $3\ensuremath{\alpha}$-particle condensate character of the Hoyle state (the ${0}_{2}^{+}$ state at $7.65$ MeV in $^{12}\mathrm{C}$) implies not only an enhanced radius of $^{12}\mathrm{C}$ in this state, which was established by many theoretical calculations and confirmed by the recent diffraction model analysis, but also zero relative angular momenta between clusters. We performed coupled-channels model calculations of the angular distributions of $\ensuremath{\alpha}+{}^{12}$C elastic and inelastic (to the $4.44$-MeV $2$${}^{+}$, $7.65$-MeV $0$${}_{2}^{+}$, and $9.65$-MeV ${3}_{1}^{\ensuremath{-}}$ states) scattering at $110$ MeV and found the ratio of the empirical spectroscopic factors $S(L)$. As the differential cross sections of these reactions are characterized by pronounced enhancement and strong oscillations at large angles, we assumed a potential scattering in the forward hemisphere and the direct transfer of a $^{8}\mathrm{Be}$ cluster at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}>{90}^{\ifmmode^\circ\else\textdegree\fi{}}$ and took into account the direct transfer of $^{8}\mathrm{Be}$ in the ground state and in the first excited ${2}^{+}$ and ${4}^{+}$ states. We found that the cluster configuration with $L=0$ dominates in the ${0}_{2}^{+}$ state, being more than three times larger than that in the ground state. This result provides additional evidence of the condensed structure of the Hoyle state in $^{12}\mathrm{C}$ with a dominance of zero relative angular momentum. The negative-parity ${3}_{1}^{\ensuremath{-}}$ excited state in $^{12}\mathrm{C}$ observed above the $3\ensuremath{\alpha}$ threshold is also considered to have the $3\ensuremath{\alpha}$-cluster structure. The present calculations described well the structure of the large-angle cross section on this state. We found a positive interference for all allowed $\ensuremath{\alpha}+{}^{8}$Be configurations with a dominance of the $p$-orbital $(69%)\ensuremath{\alpha}+{}^{8}$Be motion and confirmed the exotic, but hardly a condensed, structure of this state.