arXiv subjects

Paul-Gerhard Reinhard

Publications and source records attributed to Paul-Gerhard Reinhard.

At least 19 recordsLinked to original sources

arXiv2026

Laser spectroscopy illuminates the $N=32$ shell closure

Atomic nuclei are strongly correlated quantum many-body systems, and how their shell structure evolves with increasing neutron excess remains a central open question in nuclear physics. Calcium isotopes are an ideal testing ground: alongside the traditional magic numbers $N=20,28$, new shell closures have been proposed at $N=32,34$ ($^{52,54}\mathrm{Ca}$). While the charge radius rises rapidly towards $N=32$, further moments and radii in the isotopic chain have remained inaccessible due to the low production yield of a few ions per second. Here we apply a highly sensitive collinear laser spectroscopy technique, which reveals a strikingly simple behaviour: adding one neutron to $^{52}\mathrm{Ca}$ yields a pure single-particle magnetic dipole moment in $^{53}\mathrm{Ca}$, while the charge-radius slope towards $^{54}\mathrm{Ca}$ exceeds that towards $^{52}\mathrm{Ca}$. This provides strong evidence for a robust $N=32$ shell closure and stringently constrains nuclear structure models.

nucl-th↗

arXiv2026

Finite-range pairing in nuclear density functional theory

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.

nucl-th↗

arXiv2026

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

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.

nucl-ex↗

arXiv2025

Puzzling Isotonic Odd-Even Staggering of Charge Radii in Deformed Rare Earth Nuclei

The nuclear charge radius is a fundamental observable that encodes key aspects of nuclear structure, deformation, and pairing. Isotonic (constant neutron number) systematics in the deformed rare-earth region have long suggested that odd-$Z$ nuclei are more compact than their even-$Z$ neighbors - except for Lu, whose recommended 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-like 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 result resolves the longstanding Lu inversion anomaly and reestablishes a pronounced odd-even staggering along the $N=94$ isotonic chain. The magnitude of this staggering is unexpectedly large, far exceeding that observed in semi-magic nuclei and in deformed isotopic sequences. State-of-the-art nuclear density functional theory calculations, including quantified uncertainties, fail to reproduce this enhancement, possibly indicating missing structural effects in current models. Our work demonstrates the power of highly charged ions for precise, element-crossing charge-radius measurements and provides stringent new constraints for future theoretical and experimental studies of nuclear-size systematics.

physics.atom-ph↗

arXiv2025

Extreme Ultraviolet Spectroscopy of Highly Charged Lu and Yb Ions for Nuclear Charge Radius Determination

We report a high-precision determination of the natural-abundance-averaged nuclear charge-radius difference between Yb and Lu using extreme ultraviolet (EUV) spectroscopy of highly charged ions (HCIs). By measuring the $D_1$ transition energies in Na- and Mg-like charge states of Lu and Yb confined in the Tokyo electron-beam ion trap, we extract meV-level energy shifts that are directly sensitive to nuclear-size effects. Transition-energy differences obtained from these spectra are compared with state-of-the-art relativistic many-body perturbation theory, including a new treatment of Mg-like ions. We develop a generalized framework to propagate uncertainties arising from nuclear deformation and surface diffuseness and evaluate corresponding nuclear-sensitivity coefficients. Combining Na- and Mg-like results yields mutually consistent radius differences, demonstrating the robustness of both the experimental calibration and the theoretical predictions. To determine absolute isotopic radii, we perform a generalized least-squares optimization incorporating our HCI constraints together with optical-isotope-shift data and muonic-atom results. This analysis establishes that the $^{175}$Lu charge radius is smaller than that of $^{174}$Yb, restoring the expected odd-even staggering across the $N=94$ isotonic chain. Our recommended value, $R(^{175}\text{Lu}) = 5.291(11)$ fm, reduces the uncertainty of the Lu radius by a factor of three compared with the previous electron-scattering result and resolves a long-standing anomaly in rare-earth nuclear systematics. This work demonstrates that EUV spectroscopy of HCIs provides a powerful and broadly applicable method for precision nuclear-structure studies in heavy, deformed nuclei. The techniques developed here enable future investigations of isotonic and isoelectronic sequences, including radioactive nuclides and higher-$Z$ systems.

physics.atom-ph↗

arXiv2025

Toroidal dipole mode in nuclei

A short review on the toroidal dipole mode (TDM) in nuclei is done. The appearance of TDM in nuclei is justified. The experimental manifestation of TDM in (e,e') reaction in 58Ni is shortly reported. The relation of TDM and pygmy E1 resonance is discussed.

nucl-th↗

arXiv2024

Extended Fayans energy density functional: optimization and analysis

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even-even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity.

nucl-th↗

arXiv2023

Surprising charge-radius kink in the Sc isotopes at N=20

Charge radii of neutron deficient 40Sc and 41Sc nuclei were determined using collinear laser spectroscopy. With the new data, the chain of Sc charge radii extends below the neutron magic number N=20 and shows a pronounced kink, generally taken as a signature of a shell closure, but one notably absent in the neighboring Ca, K and Ar isotopic chains. Theoretical models that explain the trend at N=20 for the Ca isotopes cannot reproduce this puzzling behavior.

nucl-ex↗

arXiv2023

Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the Standard Model of particle physics. Such measurements impose higher precision requirements on a theoretical description. Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic corrections. Methods: The calculations are performed using Skyrme energy density functionals and density-dependent pairing force. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei. Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which impact high-precision predictions of isotopic shifts. Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements,precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends.

nucl-th↗

arXiv2023

Combined theoretical analysis of the parity-violating asymmetry for ${}^{48}$Ca and ${}^{208}Pb$

The recent experimental determination of the parity violating asymmetry $A_{\rm pv}$ in ${}^{48}$Ca and ${}^{208}$Pb at Jefferson Lab is important for our understanding on how neutrons and protons arrange themselves inside the atomic nucleus. To better understand the impact of these measurements, we present a rigorous theoretical investigation of $A_{\rm pv}$ in ${}^{48}$Ca and ${}^{208}$Pb and assess the associated uncertainties. We complement our study by inspecting the static electric dipole polarizability in these nuclei. The analysis is carried out within nuclear energy density functional theory with quantified input. We conclude that the simultaneous accurate description of $A_{\rm pv}$ in ${}^{48}$Ca and ${}^{208}$Pb cannot be achieved by our models that accommodate a pool of global nuclear properties, such as masses and charge radii, throughout the nuclear chart, and describe -- within one standard deviation -- the experimental dipole polarizabilities $α_{\rm D}$ in these nuclei.

nucl-th↗

arXiv2022

Unexpected dipole instabilities in small molecules after ultrafast XUV irradiation

We investigate the depletion of single-electron states in small molecules under the influence of very short XUV pulses. In N$_2$, for a certain window of XUV energies around 50 eV, we observe a marked occupation inversion, i.e. a situation where depletion of the deepest bound valence electron state is much larger than for any other state. This represents a realistic mechanism which is able to cut, almost instantaneously, a hole into a deep lying state, a situation which is often assumed ad hoc in numerous theoretical studies of energetic ultrafast processes. This occupation inversion furthermore drives a dipole instability, i.e. a spontaneous reappearance of the dipole signal long after the laser pulse is over and the dipole signal has died out. The dipole signal that emerges from this instability can be identified as a particular low-energy structure in photo-electron spectra.

physics.atm-clus↗

arXiv2022

Statistical correlations of nuclear quadrupole deformations and charge radii

Shape deformations and charge radii, basic properties of atomic nuclei, are influenced by both the global features of the nuclear force and the nucleonic shell structure. As functions of proton and neutron number, both quantities show regular patterns and, for nuclei away from magic numbers, they change very smoothly from nucleus to nucleus. In this paper, we explain how the local shell effects are impacting the statistical correlations between quadrupole deformations and charge radii in well-deformed even-even Er, Yb, and Hf isotopes. This implies, in turn, that sudden changes in correlations can be useful indicators of underlying shell effects. Our theoretical analysis is performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. The statistical analysis is carried out by means of the linear least-square regression. The local variations of nuclear quadrupole deformations and charge radii, explained in terms of occupations individual deformed Hartree-Fock orbits, make and imprint on statistical correlations of computed observables. While the calculated deformations or charge radii are, in some cases, correlated with those of their even-even neighbors, the correlations seem to deteriorate rapidly with particle number. The statistical correlations between nuclear deformations and charge radii of different nuclei are affected by the underlying shell structure. Even for well deformed and superfluid nuclei for which these observables change smoothly, the correlation range usually does not exceed $ΔN=4$ and $ΔZ=4$, i.e., it is rather short. This result suggests that the frequently made assumption of reduced statistical errors for the differences between smoothly-varying observables cannot be generally justified.

nucl-th↗

arXiv2022

Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. The accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.

nucl-th↗

arXiv2022

Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the Standard Model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2} \rightarrow {}^2F_{7/2}$ octupole transition of trapped $^{168,170,172,174,176}$Yb ions. When combined with previous measurements in Yb$^+$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240$σ$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with 4.3$σ$ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

physics.atom-ph↗

arXiv2022

Information content of the differences in the charge radii of mirror nuclei

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, R_mir, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability. In particular, this quantity correlates poorly with both the neutron skin and L. We demonstrate that R_mir is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on R_mir, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.

nucl-th↗

arXiv2021

Universal trend of charge radii of even-even Ca-Zn nuclei

Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $δ\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from calcium to zinc using two state-of-the-art theories based on quantified nuclear interactions: the ab-initio coupled cluster theory and nuclear density functional theory. Both theories reproduce the smooth rise of differential charge radii and their weak dependence on the atomic number. By considering a large set of isotopic chains, we show that this trend can be captured by just two parameters: the slope and curvature of ${δ\langle r^2_c\rangle(n)}$. We demonstrate that these parameters show appreciable model dependence, and the statistical analysis indicates that they are not correlated with any single model property, i.e., they are impacted by both bulk nuclear properties as well as shell structure.

nucl-th↗

arXiv2021

Information content of the parity-violating asymmetry in $^{208}$Pb

The parity violating asymmetry $A_{PV}$ in $^{208}$Pb, recently measured by the PREX-2 collaboration, is studied using modern relativistic (covariant) and non-relativistic energy density functionals. We first assess the theoretical uncertainty on $A_{PV}$ which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability $α_D$ of $^{208}$Pb. We then add the quantified value of $A_{PV}$ together with $α_D$ to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in $^{208}$Pb $r_\mathrm{skin} =0.19\pm 0.02$\,fm and the symmetry-energy slope $L=54\pm 8$\,MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the $A_{PV}$ value in $^{48}$Ca that will be soon available from the CREX measurement.

nucl-th↗

arXiv2020

Optimization and Supervised Machine Learning Methods for Fitting Numerical Physics Models without Derivatives

We address the calibration of a computationally expensive nuclear physics model for which derivative information with respect to the fit parameters is not readily available. Of particular interest is the performance of optimization-based training algorithms when dozens, rather than millions or more, of training data are available and when the expense of the model places limitations on the number of concurrent model evaluations that can be performed. As a case study, we consider the Fayans energy density functional model, which has characteristics similar to many model fitting and calibration problems in nuclear physics. We analyze hyperparameter tuning considerations and variability associated with stochastic optimization algorithms and illustrate considerations for tuning in different computational settings.

nucl-th↗