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

TL;DR

This paper addresses the challenge of predicting masses near the proton drip line in the tin region, focusing on the doubly magic $^{100}$Sn vicinity. The authors perform the first high-precision Penning-trap mass measurement of $^{101}$Sn using phase-imaging cyclotron-resonance (PI-ICR) at LEBIT/FRIB, obtaining mass excess $ME(^{101}\mathrm{Sn}) = -59\,889.89(96)$ keV, a factor of $\sim$300 improvement over AME2020. They apply a Bayesian Model Combination (BMC) framework that fuses seven global EDF predictions to extrapolate tin masses down to $N=46$, showing results agree with data within $1\sigma$ and offering robust extrapolations toward the proton drip line. The measurement also helps resolve the $^{100}$Sn mass discrepancy and tightens uncertainties in the $\alpha$-decay chain $^{109}$Xe → $^{105}$Te → $^{101}$Sn, supporting the GSI/Hinke2012 value and demonstrating the value of combining precision mass measurements with Bayesian multi-model inference for nuclear mass predictions.

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 in nuclear binding at and around the doubly-magic \textsuperscript{100}Sn isotope. Precise mass measurements of neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies currently 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. This provides confidence in the extrapolation of tin masses down to $N=46$.

Figures (6)

• Figure 1: A filtered visual of $\approx$150 detected 101Sn2+ ions combined from three separate frequency measurements after ions accumulated phase while undergoing 163 ms of reduced-cyclotron motion is highlighted alongside unidentified background counts. The direction of motion along the gray elliptical path is shown with a black arrow and the fitted center for filtered counts is shown with a large black x. The filtered ions are fit to a two-dimensional Gaussian distribution in polar coordinates, where the center of the fit and $1\sigma$ error boundary are indicated by a small black x and a dashed black ellipse respectively.
• Figure 2: $\Delta_{3n}$ for the tin isotopic chain, displaying the discrepancy in the mass of $^{100}$Sn both before (dashed gray and green line) and after (solid black and red line) the mass measurement of $^{101}$Sn reported in this work via the odd-even staggering of the tin isotopic chain. For $N=51$, the mass of $^{100}$Sn is extracted using the mass of $^{100}$In from Ref. Mougeot2021 and either the $\beta$-decay $Q$-value from Ref. Hinke2012, or Ref. Lubos2019 (RIKEN). The ${}^{100}$Sn mass reported in AME2020AME2020 is based on the decay measurement from Ref. Hinke2012. All masses unspecified in the legend are taken from AME2020. The BMC predictions (solid blue) along with 1$\sigma$ uncertainty are also shown.
• Figure 3: BMC predictions of separation energies when including recent experimental (training) data from LEBIT. Panels a and b display one (solid gray) and two (dashed blue) neutron and proton separation energies, respectively. Red dots correspond to the experimental values obtained in this work, while black dots represent AME2020 data AME2020, with the exception of ${}^{103}$Sn which is derived from Ref. Ireland2025. Diamonds represent AME2020 extrapolations for $S_{1n(1p)}$ (magenta) and $S_{2n(2p)}$ (green). Squares label $S_{1n}$ (brown) and $S_{2n(2p)}$ values obtained using ${}^{100}$Sn mass from Ref. Lubos2019. The bands mark the $1\sigma$ uncertainty from the statistical mean of the BMC prediction. The insert shows the set of nuclei used in BMC for training (white) and validation (blue), together with the training data points for ${}^{101,103}$Sn from this work and Ref. Ireland2025 (red outline). The vertical dashed green line indicates the $N = 50$ shell closure.
• Figure 4: The difference of frequency ratios $R$ and their weighted average $\bar{R}$ for the 8 measurements of 101Sn using PI-ICR. From left to right, two initial measurements of $\nu_{+}$ with $t_{acc_{+}}=$5.5 and 13.8 ms, two measurements with 50 ms, one with 150 ms, and three measurements with 163 ms of $\nu_{+}$ accumulation time were performed. The $\pm 1 \sigma$ error in the weighted average $\bar{R}$ is displayed by the gray band.
• Figure 5: Tin separation energies of (a) one neutron, (b) one proton, (c) two neutrons, and (d) two protons calculated using the seven different EDFs utilized in this work, together with the BMC prediction and its $1\sigma$ uncertainty, compared to the experimental data taken from AME2020, this work, and Ref. Ireland2025.