Paul-Gerhard Reinhard

Experimentally inaccessible regions of the nuclear chart remain a challenge for global models of atomic nuclei to predict. This includes exotic nuclei near particle drip lines, superheavy elements at the extremes of mass and charge, and the neutron-rich pathways of astrophysical processes in explosive stellar environments where heavy elements are created. Given that individual nuclear models are imperfect, deep extrapolations are best approached using model ensembles, which allow for the systematic combination of diverse theoretical predictions. In this study, we employ the recently introduced Bayesian model combination (BMC) method, based on statistical machine learning, that provides robust uncertainty quantification for forecasts using model ensembles. To account for the inherent degradation of predictive power as models extrapolate into the yet-unexplored domain, we introduce a heteroscedastic BMC framework in which the combined theoretical uncertainty is treated as a dynamic quantity. We apply this methodology to an ensemble of realistic energy density functionals with a specific focus on the Z = 46 – 52 isotopic chains. We rigorously validate the approach using both experimental data and synthetic data designed to assess performance in the deep extrapolation regime. Our results demonstrate that the proposed heteroscedastic approach yields superior calibration metrics and provides statistically principled assessments of the particle drip lines.

Isotonic (constant neutron number) systematics in the deformed rare-earth region have long suggested that nuclei with odd numbers of protons are more compact than their even-proton neighbors—except for Lu, whose recommended nuclear charge radius appeared anomalously large relative to Yb and Hf. We report a high-precision determination of the natural-abundance-averaged Lu-Yb charge-radius difference using extreme-ultraviolet spectroscopy of highly charged Na- and Mg-like ions, supported by high-accuracy relativistic atomic-structure calculations—a recently introduced method with the unique ability to measure inter-element charge-radius differences. Combined with muonic-atom and optical isotope-shift data, our results reestablish a pronounced odd-even staggering along the isotonic chain with neutron number N = 94 . Nuclear density functional theory calculations, including quantified uncertainties, fail to reproduce the large stagger, while successfully reproducing the charge-radii staggering along isotopic chains and in semi-magic nuclei. In this work, we resolve the Lu inversion anomaly and provide new constraints for experimental and theoretical studies of nuclear size.

In a recent series a papers, we have identified an unstable behavior in the electronic response of small molecules to some ultrafast XUV pulses. Calculations have been done using real-time Time-Dependent Density Functional Theory in the Local Density Approximation version complemented by a self-interaction correction. The aim of the present paper is to clarify the mechanism of dipole instability by associating it with a symmetry breaking. The line of arguments develops along two steps. We first discuss the spectral properties of the instability in dynamical scenarios, focusing on the simplified case of direct hole creation at initial time. We discuss in particular the potential relation of the instability to the plasmon. We show that, in some specific cases, the plasmon frequency characterizes the dipole instability. Still, in most cases, an oscillation between 2 single-particle levels pops up. As a second step, we analyze the energy surfaces associated with such single-particle transitions and see that these surfaces do indeed display a maximum in the case of direct drilling of a hole state. This characterizes a typical symmetry breaking in mean-field models.

This corrects the article DOI: 10.1103/PhysRevLett.133.232502.

The dependence of the E 2 matrix elements on isospin projection T z is linked to the conservation of the isospin symmetry. To study this conjecture, we calculated the B ( E 2 : 2 + → 0 + ) rates for the even-even T = 1 mirror nuclei with 42 ≤ A ≤ 98 within nuclear density functional theory, employing the generalized Bohr Hamiltonian, and carrying out angular momentum projection. We demonstrated that collective effects are crucial for describing experimental data near the N = Z line without invoking explicit beyond-Coulomb isospin symmetry-breaking corrections. We also determined the B ( E 2 ↓ ) values for odd-odd T z = 0 nuclei Br 70 and Y 78 in doubly blocked configurations. We discussed the requirements for accurately describing isobaric analog states and emphasized how current theoretical results should be interpreted within the study of isospin symmetry across isospin triplets.

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. We show that a folding radius of about 1\,fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.