arXiv subjects

Matthias Heinz

Publications and source records attributed to Matthias Heinz.

16 recordsLinked to original sources

arXiv2026

Accurate Charge Radius Measurement of $^{14}$C Confronts \textit{Ab Initio} Theory

Located at the neutron shell closure $N = 8$, the long-lived radioactive isotope $^{14}\mathrm{C} $ plays a critical role in geochronology and nuclear structure studies. Despite its widespread use, the nuclear charge radius of $^{14}$C has remained less precisely known compared to its stable counterpart $^{12}$C. Here, we report a high-precision determination of the $^{14}$C charge radius using collinear laser spectroscopy at the COALA setup at TU Darmstadt, improving upon the precision of previous muonic measurements by a factor $5$ and revealing a $1.9\sigma$ discrepancy of combined uncertainty, indicating a likely underestimated uncertainty in the muonic determination. This measurement challenges state-of-the-art \textit{ab initio} nuclear theory calculations, including auxiliary field diffusion Monte Carlo, the valence-space in-medium similarity renormalization group, and the no-core shell model, augmented by neural-network techniques. With $^{12}$C and $^{14}$C now forming one of the most precisely characterized even-even isotope pairs, these results also enable improved QED tests.

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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.

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arXiv2026

Ab initio calculations of parity-violating electron scattering off $^{48}$Ca and $^{208}$Pb

Parity-violating electron scattering off nuclei both serves as a low-energy precision probe to test electroweak interactions and allows one to access neutron distributions inside nuclei. It has implications for strong interactions in dense neutron-rich environments, also providing constraints for the properties of matter in neutron stars. Precision measurements are available for $^{48}$Ca and $^{208}$Pb by the CREX and PREX collaborations, respectively, and their interpretation requires advanced nuclear-structure calculations to draw firm conclusions. We perform the first ab initio calculations of the parity-violating asymmetry $A_\text{PV}$ based on nuclear forces from chiral effective field theory, fully including corrections due to Coulomb distortion effects. Based on these results, we critically reexamine correlation analyses employed to infer weak radii and quantify the resulting tensions between ab initio and experimental results. We find that ab initio calculations prefer values of $A_\text{PV}$ slightly smaller and larger than observed for $^{48}$Ca and $^{208}$Pb, respectively, with a global significance of $1.9\sigma$. Using theoretically consistent inputs for charge and weak densities, we infer from the experimental $A_\text{PV}$ a neutron skin of $^{208}$Pb of $R_n-R_p = 0.187(25)(18)$ fm, substantially smaller than that reported by PREX II.

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arXiv2026

Saturation of Nuclear Binding from Lattice Hamiltonians

There is a conundrum regarding the binding of $\alpha$ particles in nuclei. On one hand, auxiliary-field Monte Carlo simulations of Hamiltonians on discrete spatial lattices proposed that attractive two-nucleon potentials, alone or together with attractive three-nucleon potentials, yield accurate nuclear binding. On the other hand, such Hamiltonians typically overbind all but the lightest nuclei in continuum-space approaches. We address this puzzle by performing Hartree-Fock computations of the light nuclei $^4$He, $^8$Be, $^{12}$C, and $^{16}$O, and of nuclear and neutron matter using established lattice Hamiltonians. These variational upper bounds for the ground-state energies show that the Hamiltonians with only two-nucleon potentials do not yield accurate binding, in contrast to the results from auxiliary-field Monte Carlo simulations. The case is different for Hamiltonians with three-nucleon potentials although it is the dense packing on the lattice -- and not repulsive potentials -- that yield a constant binding energy per nucleon.

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arXiv2026

Taming nuclear size and shape effects in superallowed beta-decay

We present the first combined analysis of the statistical rate function f in superallowed beta decays with ab initio calculations and data. We focus on C10 to 10B, 14O to 14N and 26mAl to 26Mg, all of which are important channels for the precise determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vud. Nuclear charge form factors are obtained by combining experimental data on nuclear charge radii and theory calculations of ratios of moments with the in-medium similarity renormalization group, while the beta decay form factors are derived from exact isospin relations. This enables a rigorous study of the nuclear shape dependence in the statistical rate function f and the quantification of its uncertainties from both experiment and theory. The calculation leads to a more precise test for the first-row CKM unitarity with reduced theoretical uncertainties. This work demonstrates a reliable strategy for combining nuclear many-body calculations with high-precision nuclear data to describe beta decays at tree level for precision tests of the Standard Model.

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arXiv2026

Nuclear charge radii of aluminium isotopes at the proton drip line

Understanding the evolution of nuclear size away from stability remains a central challenge in nuclear physics. In neutron-deficient systems, charge radii can be highly sensitive to the interplay between strong and electromagnetic interactions, and the effects of weak binding, giving rise to exotic nuclear phenomena. However, experimental data on these systems has been limited by short lifetimes and low production rates. Here we report the first laser-spectroscopy measurements of nuclear charge radii along the neutron-deficient aluminium isotopic chain, from $^{25}$Al to the proton-drip-line nucleus $^{22}$Al, using the {Resonance Ionization Spectroscopy Experiment} (RISE) at the {Facility for Rare Isotope Beams} (FRIB). Our measurements reveal a step-like increase in charge radius toward the drip line, with similar radii for $^{22,\,23}$Al. A comparison of our results with those of their mirror partners reveals an almost identical correlation with the calculated proton skins and is consistent with the systematic trend of well-bound nuclei. These results offer insight for understanding the evolution of nuclear size at the proton dripline and place important constraints on modern nuclear theory. They also demonstrate the unique combined capabilities of RISE and FRIB to probe the structures of previously inaccessible nuclei at the limits of existence.

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arXiv2026

Similarity renormalization group for nuclear forces

Renormalization group methods generate low-resolution Hamiltonians that are more diagonal, with reduced coupling between low- and high-energy states, and thus easier to solve. This chapter reviews the similarity renormalization group for nuclear Hamiltonians, which is a popular method for generating low-resolution nuclear forces. It presents the similarity renormalization group flow equations, analyzes how the similarity renormalization group drives the Hamiltonian towards the diagonal, and studies the effect of induced many-body interactions. It concludes by highlighting the progress in first-principles calculations of nuclei driven by low-resolution nuclear Hamiltonians.

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arXiv2026

Computational schemes for the Magnus expansion of the in-medium similarity renormalization group

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schr\"odinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to $7\,\mathrm{MeV}$ for ground-state energies and $0.5\,\mathrm{MeV}$ for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.

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arXiv2025

Uncertainties with low-resolution nuclear forces

Low-resolution nuclear Hamiltonians, obtained from chiral effective field theory (EFT) and softened using renormalization group techniques, have been very successful in nuclear structure theory. The associated EFT truncation uncertainty for these potentials is difficult to quantify. We use singular value decompositions of low-resolution nuclear forces to obtain an operator basis to study Hamiltonian uncertainties for these potentials. We perform Bayesian inference for the singular values and three-body low-energy constants, the free parameters of nuclear Hamiltonians in our framework, using likelihoods based on nucleon-nucleon phase shifts and triton observables to account for the EFT truncation uncertainties in these quantities. Validating our inference, we find good reproduction of input uncertainties for low-energy phase shifts and three-nucleon observables. On the other hand, uncertainties for higher-energy phase shifts are systematically underestimated, which we attribute to limitations of the singular value decomposition and neglected correlations between phase shifts at different energies. We propagate the resulting distribution of Hamiltonians forward to predictions for ground-state properties of $^{24,28}$O and $^{48}$Ca, comparing against other state-of-the-art nuclear structure predictions. Our approach makes it possible to account for EFT uncertainties when using low-resolution potentials, which is important for many ongoing studies in exotic nuclei.

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arXiv2025

Exactness of the normal-ordered two-body truncation of three-nucleon forces

Reference-state-based many-body methods start from Hamiltonians that are normal ordered with respect to the reference state. In low-energy nuclear physics applications normal-ordered Hamiltonians consisting of two- and three-nucleon forces are usually truncated at the two-body rank with residual three-nucleon operators being discarded. Benchmark computations have shown that this truncation is accurate, but we lack an understanding about why it works. We show that the normal-ordered two-body truncation is exact for zero-range three-body forces when nuclei are computed using the coupled cluster with singles and doubles method. As the nuclear three-nucleon force is short ranged and a three-body contact is a leading term in effective field theories of quantum chromodynamics, our result provides an analytical basis for the popular normal-ordered two-body approximation.

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arXiv2025

Toward scalable quantum computations of atomic nuclei

We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and $^3$He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for $^2$H and $^3$He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.

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arXiv2025

The nuclear charge radius of $^{13}\mathrm{C}$

The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of $^{13}\mathrm{C}$ and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the $2\,^3\mathrm{S} \rightarrow 2\,^3\mathrm{P}$ fine-structure triplet in $^{13}\mathrm{C}^{4+}$ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than $2\,\mathrm{MHz}$ although second-order hyperfine-structure effects shift individual lines by several $\mathrm{GHz}$. We improved the uncertainty of $R_\mathrm{c}(^{13}\mathrm{C})$ determined with electrons by a factor of $6$ and found a $3σ$ discrepancy with the muonic atom result of similar accuracy.

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arXiv2025

Connecting Relativistic Density Functional Theory to Microscopic Calculations

The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For global nuclear calculations, density functional theories (DFTs) have been developed to reduce the complexity and computational cost required in describing nuclear systems. However, DFT often makes approximations and assumptions about terms included in the functional, which may introduce systematic uncertainties compared to microscopic calculations using EFTs. In this work, we investigate possible avenues of improving nuclear DFT using nonlinear relativistic mean-field (RMF) theory. We explore the impact of RMF model extensions by fitting the nonlinear RMF model to predictions of nuclear matter and selected closed-shell nuclei using four successful chiral EFT Hamiltonians. We find that these model extensions are impactful and important in capturing the physics present within chiral Hamiltonians, particularly for charge radii and neutron skins of closed-shell nuclei. However, there are additional effects that are not captured within the RMF model, particularly within the isoscalar sector of RMF theory. Additional model extensions and the reliability of the nonlinear RMF model are discussed.

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arXiv2025

Probing new bosons and nuclear structure with ytterbium isotope shifts

In this Letter, we present mass-ratio measurements on highly charged Yb$^{42+}$ ions with a precision of $4\times 10^{-12}$ and isotope-shift measurements on Yb$^{+}$ on the $^{2}$S$_{1/2}$ $\to$ $^{2}$D$_{5/2}$ and $^{2}$S$_{1/2}$ $\to$ $^{2}$F$_{7/2}$ transitions with a precision of $4\times 10^{-9}$ for the isotopes $^{168,170,172,174,176}$Yb. We present a new method that allows us to extract higher-order changes in the nuclear charge distribution along the Yb isotope chain, benchmarking ab-initio nuclear structure calculations. Additionally, we perform a King plot analysis to set bounds on a fifth force in the keV$/c^2$ to MeV$/c^2$ range coupling to electrons and neutrons.

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arXiv2024

Ab initio calculations of overlap integrals for $\mu\to e$ conversion in nuclei

The rate for $\mu\to e$ conversion in nuclei is set to provide the most stringent test of lepton-flavor symmetry and a window into physics beyond the Standard Model. However, to disentangle new lepton-flavor-violating interactions, in combination with information from $\mu\to e\gamma$ and $\mu\to 3e$, it is critical that uncertainties at each step of the analysis be controlled and fully quantified. In this regard, nuclear response functions related to the coupling to neutrons are notoriously problematic, since they are not directly constrained by experiment. We address these shortcomings by combining ab initio calculations with a recently improved determination of charge distributions from electron scattering by exploiting strong correlations among charge, point-proton, and point-neutron radii and densities. We present overlap integrals for $^{27}$Al, $^{48}$Ca, and $^{48}$Ti including full covariance matrices, allowing, for the first time, for a comprehensive consideration of nuclear structure uncertainties in the interpretation of $\mu\to e$ experiments.

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arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

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