Strong Evidence for Three-$α$ Clustering in the Ground State of $^{12}\mathrm{C}$

Abstract

The ground state of $^{12}\mathrm{C}$ has often been approximated by a mean-field picture. This conventional view has been challenged by recent nuclear theories suggesting non-negligible $α$-cluster formation, but experimental evidence remains inconclusive. Here, we show that existing $^{12}\mathrm{C}(p,pα)^{8}\mathrm{Be}$ data provide direct evidence for a pronounced $α$ cluster formation in the ground state of $^{12}\mathrm{C}$. We analyze the data with distorted-wave impulse approximation using $α$ preformation amplitudes from an unrestricted $3α$ cluster model and harmonic-oscillator-based models. The results show that the former reproduces the measured cross sections, whereas the latter underestimate them by more than an order of magnitude. Thus, contrary to conventional expectations, the data support a nearly fully developed three-$α$ cluster structure in the ground state of $^{12}\mathrm{C}$.