Quantifying alpha clustering in light nuclei from binding energies

What is the origin of nuclear clustering and how does it emerge from the nuclear interaction? While there is ample experimental evidence for this phenomenon, its theoretical characterization directly from nucleons as degrees of freedom remains a challenge. In this work, it is shown that the degree of one- and two-alpha (${ {}^{4}\text{He} }$) clustering in a given nucleus can be quantified empirically using only the binding energies of its partition subsystems. The proposed clustering measures are parameter-free and correctly identify alpha clustering features in light nuclei and long-lived excited states such as the Hoyle state in $^{12}$C and the ${ {0}_{2}^{+} }$ state of $^{14}$C at 6.59 MeV. It is revealed that in light nuclei ranging from ${ {}^{6}\text{Li} }$ to ${ {}^{14}\text{C} }$, state-of-the-art density functional theory and \textit{ab initio} approaches fail to adequately capture alpha clustering. Stringent constraints on binding energies are then provided by back-propagating 10\% relative uncertainties on the experimental one-alpha clustering measure using a parallel Markov chain Monte Carlo algorithm. It is demonstrated that the nuclei $^{6,7}$Li, $^7$Be, $^{10,11}$B, and $^{11}$C are particularly sensitive to alpha clustering despite not being the most clustered systems identified. Using results on $^{10}$B, a strong case is made for a link between three-body forces and alpha clustering. This study provides the first quantification of alpha clustering based on binding energies only, as well as new and practical constraints for future optimizations of nuclear forces, potentially helping with the current issues in medium-mass nuclei.