The mass of $^{101}$Sn and Bayesian extrapolations to the proton drip line

Abstract

The favorable energy configurations of nuclei at magic numbers of ${N}$ neutrons and ${Z}$ protons are fundamental for understanding the evolution of nuclear structure. The ${Z=50}$ (tin) isotopic chain is a frontier for such studies, with particular interest at and around the doubly-magic \textsuperscript{100}Sn isotope, for which the mass is a topic of debate. Precise mass values for neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies remain out of reach. In this work, we report the first Penning trap mass measurement of \textsuperscript{101}Sn. The determined mass excess of $-59\,889.89(96)$~keV for \textsuperscript{101}Sn represents a factor of 300 improvement over the current precision and indicates that \textsuperscript{101}Sn is less bound than previously thought. Mass predictions from a recently developed Bayesian model combination (BMC) framework employing statistical machine learning and nuclear masses computed within seven global models based on nuclear Density Functional Theory (DFT) agree within 1$σ$ with experimental masses from the $48 \le Z \le 52$ isotopic chains. The framework's resilience to new mass data gave confidence in the extrapolation of tin masses down to $N=46$. Our calculations suggest that \textsuperscript{96}Sn is a two-proton drip line nucleus and predict a mass excess of $-58\,090(800)$~keV for $^{100}$Sn, showing a preference within 1$σ$ for the mass of \textsuperscript{100}Sn derived from the $β$-delayed $Q$-value measured at GSI.