Mass Probe of Tetrahedral Symmetry in Atomic Nuclei
Tetrahedral symmetry has long been predicted as an exotic shape degree of freedom in atomic nuclei, yet clear experimental manifestations remain elusive. We show that the triple binding energy difference $\delta V_{pn}^{(3)}$ can isolate a structural effect of tetrahedral symmetry in $^{80}$Zr. Using relativistic density functional theory solved on a three-dimensional lattice without symmetry restrictions, the experimental $\delta V_{pn}^{(3)}$ values for even-even $^{80\text{-}90}$Zr isotopes are well reproduced without adjustable parameters. While an enhancement of $\delta V_{pn}^{(3)}$ near $N\simeq Z$ is commonly attributed to proton-neutron correlations beyond the mean field, the pronounced nonmonotonic peak at $N=40$ emerges at the mean-field level only when the tetrahedral degree of freedom is included. Constraining the tetrahedral deformation to zero removes the peak and leads to clear deviations from experiment. The anomaly is traced to a well-localized tetrahedral minimum in $^{80}$Zr, supported by potential energy surfaces and characteristic single-particle level splittings. Calculations restricted to quadrupole and triaxial shapes fail to reproduce the localized enhancement, indicating that the effect is not a generic proton-neutron correlation but a symmetry-selective increase of proton-neutron binding associated with tetrahedral geometry. We therefore identify the $\delta V_{pn}^{(3)}$ anomaly in $^{80}$Zr as a structural mechanism distinct from the conventional Wigner-type enhancement and show that nuclear masses constitute a sensitive probe of tetrahedral symmetry.