Stroberg, Holt, Schwenk, and Simonis (Phys. Rev. Lett. 126, 022501 (2021)) performed a global ab initio survey of essentially all nuclei from helium to iron (Z = 2-26, close to 700 isotopes), computing ground-state and separation energies and predicting the proton and neutron drip lines with the valence-space in-medium similarity renormalization group (VS-IMSRG) and the chiral 1.8/2.0 (EM) Hamiltonian, but quantified the theoretical error by an empirical Bayesian linear calibration of residuals against measured separation energies. The paper itself listed what ab initio theory still owes for a credible boundary of the nuclear chart: rigorous propagation of chiral-EFT truncation and low-energy-constant uncertainties through the many-body approximation, many-body truncations systematically improvable beyond the two-body level, Hamiltonians that simultaneously reproduce radii and binding energies, explicit continuum and threshold physics near driplines, and computational scale-up to heavier nuclei. Every thread shows substantial progress - Bayesian truncation-error models, three-operator IMSRG(3) implementations, radii-consistent interactions, Gamow-shell-model continuum frameworks, and coupled-cluster reach toward 70Ca and beyond 132Sn - but no work integrates them: no ab initio global dripline or mass prediction exists whose uncertainties are propagated, rather than empirically calibrated, from the underlying chiral effective field theory and many-body method. The problem is open.

Background

Ab initio nuclear theory aims to compute atomic nuclei from nucleon-nucleon (NN) and three-nucleon (3N) forces derived from chiral effective field theory (EFT), the low-energy expansion of QCD in pions and nucleons organized as an order-by-order hierarchy (leading order LO, next-to-leading order NLO, N2LO, ...), with unknown low-energy constants (LECs) fit to few-body data. Two ingredients carry the calculations to medium-mass and heavy nuclei. First, the in-medium similarity renormalization group (IMSRG) decouples a small valence-space Hamiltonian from the full many-body Hilbert space by a continuous unitary transformation; in the valence-space implementation (VS-IMSRG) the resulting effective shell-model Hamiltonian is diagonalized in tractable valence spaces. In practice the IMSRG flow truncates operators at the normal-ordered two-body level - the IMSRG(2) approximation, where 'normal ordering' reorganizes operators relative to a reference Slater determinant (an independent-particle wave function built from occupied single-particle orbits) so that induced higher-body terms are partially resummed - and its residual error is a leading many-body uncertainty. Second, the drip lines, the particle boundaries of the nuclear chart where the neutron or proton separation energy (the energy to remove one nucleon) vanishes, define where nuclei cease to exist and are key input for the r-process (rapid neutron capture) of nucleosynthesis.

The 2021 survey of Stroberg, Holt, Schwenk, and Simonis computed ground-state, one- and two-nucleon separation energies and predicted proton and neutron drip-line locations for essentially all nuclei from helium to iron (Z = 2-26, close to 700 isotopes), using the chiral 1.8/2.0 (EM) NN+3N Hamiltonian: the Entem-Machleidt two-nucleon potential softened by a similarity-renormalization-group evolution (a continuous unitary transformation suppressing high-momentum components) to λ=1.8 fm−1\lambda = 1.8\,\mathrm{fm}^{-1}, combined with three-nucleon forces at a cutoff of 2.0 fm−12.0\,\mathrm{fm}^{-1} whose couplings are fit to the triton binding energy and the 4He^{4}\mathrm{He} charge radius (Hebeler et al., Phys. Rev. C 83, 031301(R) (2011); Simonis et al., Phys. Rev. C 93, 011302(R) (2016)). Because a rigorous error model was unavailable, they modeled residuals δS=Sth−Sexp\delta S = S^{\mathrm{th}} - S^{\mathrm{exp}} by a Bayesian linear regression δS=ASth+B+ϵ(σ2)\delta S = \mathcal{A}S^{\mathrm{th}} + \mathcal{B} + \epsilon(\sigma^2), whose slope A\mathcal{A} physically absorbs a known deficiency of the Hamiltonian: 1.8/2.0 (EM) underpredicts nuclear charge radii by roughly 4% (Simonis et al., Phys. Rev. C 96, 014303 (2017)), and a radius shift δR/R≈−0.04\delta R/R \approx -0.04 implies δS≈−2(δR/R)S\delta S \approx -2(\delta R/R)S. The empirical calibration is thus a stand-in for two unresolved sources of error: the order-by-order truncation error of chiral EFT together with LEC uncertainties, and the IMSRG(2) many-body truncation. The authors further note that the bound-state harmonic-oscillator-basis framework neglects threshold phenomena - halo nuclei (weakly bound systems with extended spatial profiles) and the 'island of inversion' near N=20N=20, where shell orderings invert as weak binding erodes shell gaps - which may shift near-threshold separation energies and dripline locations, and that computational limits (diagonalization in the largest valence spaces, storage of 3N matrix elements) cap the reachable mass region.

The statistical machinery for a more rigorous treatment exists in embryo: Melendez, Wesolowski, and Furnstahl (Phys. Rev. C 96, 024003 (2017)) and Melendez et al. (Phys. Rev. C 100, 044001 (2019)) built Bayesian models for correlated EFT truncation errors, applied so far to NN observables and few-body systems; Carlsson et al. (Phys. Rev. X 6, 011019 (2016)) and Ekström and Hagen (Phys. Rev. Lett. 123, 252501 (2019)) quantified LEC sensitivities and order-by-order behavior, the latter for bulk properties of a single nucleus (16^{16}O) using fast emulators (surrogate models interpolating expensive calculations). On the many-body side, IMSRG implementations with explicit three-body operators (Heinz et al., Phys. Rev. C 103, 044318 (2021); Stroberg, Morris, and He, Phys. Rev. C 110, 044316 (2024); He and Stroberg, Phys. Rev. C 110, 044317 (2024)) and a Bayesian error model for many-body perturbation theory (Svensson et al., Phys. Rev. C 113, 024303 (2026)) have been developed, and continuum-coupled ab initio frameworks such as the Gamow shell model - a shell model built on a Berggren basis, in which bound, resonant, and continuum single-particle states are treated on the same footing (Michel, Li, and Xu, Commun. Theor. Phys. 74, 097303 (2022)) - exist for light dripline systems. What has not been achieved is the synthesis of these ingredients at global scale.

Problem Statement

Place ab initio predictions of the limits of nuclear existence on a rigorous footing, replacing the empirical Bayesian calibration of residuals used in the 2021 global VS-IMSRG dripline survey with first-principles error propagation. Concretely: construct calculations of nuclear separation energies, radii, and drip-line locations over a target region of the nuclear chart that extends beyond the 2021 survey's Z = 2-26 coverage (essentially all nuclei from helium to iron) into the calcium-to-tin region (Z = 20-50) and at least part of the heavier, neutron-rich region beyond N = 82 relevant to the r-process, comprising at least several hundred isotopes across more than one element, in which (i) the order-by-order truncation errors of the chiral effective field theory Hamiltonian and the covariance of its low-energy constants are propagated through the many-body method, rather than absorbed into a regression against measured data; (ii) the many-body truncation is systematically improvable, going beyond the normal-ordered two-body IMSRG(2) approximation so that its residual error is quantified and reduced; (iii) the underlying Hamiltonian simultaneously reproduces charge radii and binding energies across the region, removing the linear-slope empirical correction associated with the ~4% radius underprediction of 1.8/2.0 (EM); and (iv) continuum, halo, and island-of-inversion physics near thresholds is treated explicitly where it can shift near-threshold separation energies and drip-line locations. These four conditions (i)-(iv) characterize the single integrated objective rather than four separately certifiable achievements: the deliverable is an uncertainty-quantified ab initio boundary of the nuclear chart over the target region above, whose propagated uncertainties are consistent with measured separation energies and drip-line constraints in that region at the confidence level it reports, extending to masses and drip lines that still lack ab initio predictions. A construction that delivers this boundary over the target region resolves the problem; work covering a smaller region, or realizing only part of the integrated first-principles treatment described in (i)-(iv), is a partial contribution rather than a resolution.

References

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