The 2p→1s transition energy in muonic ^9Be was measured using a metallic magnetic calorimeter, resulting in E_2p→ 1s=33 391.48(34)eV. The result is 30 times more precise than the previous best measurement and enables the extraction of the corresponding nuclear charge radius r_c(^9Be)=2.5506(51)fm. It is 2.4 times more precise than the commonly used value based on electron scattering and differs from it by 2.3 times the combined uncertainties. This measurement represents the first determination of a nuclear charge radius using muonic x-ray spectroscopy with microcalorimeters.

The matrix Numerov method provides an efficient framework for solving the time-independent Schrödinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order convergence deteriorates for low angular momenta due to the behavior of the potential near the origin. We show that this loss of accuracy originates from an implicit boundary assumption in the standard formulation. By incorporating analytic near-origin information into the discretized Hamiltonian, we derive simple boundary corrections that restore fourth-order convergence and can even produce higher convergence rates for s- and p-wave energies. The resulting scheme preserves the simplicity and computational efficiency of the original method while significantly improving its accuracy for singular potentials.

The Lorentz integral transform (LIT) method is a powerful tool for calculating quantum response functions; however, it requires an ill-posed inversion. Here we show that solutions of the LIT equation can also determine two additional integral transforms: a complex Stieltjes transform and a double-pole transform, at little additional computational cost. A Fourier analysis of the associated deconvolution problem shows that both alternative kernels are better conditioned than the Lorentzian kernel at the same width parameter Γ. We benchmark the resulting inversions for deuteron photodisintegration by adding controlled noise to the LIT solutions. Relative to the standard LIT, the alternative kernels yield response functions with reduced noise-induced scatter: by a factor of 2-3 for the complex Stieltjes kernel and 3-4 for the double-pole kernel.

Three-nucleon short-range correlations (3N-SRCs) represent one of the least understood manifestations of short-range nuclear dynamics. We investigate these correlations within the generalized contact formalism and compute three-body nuclear contacts using a mean-field description of the long-range component of the nuclear wave function. These contacts quantify the probability of finding correlated nucleon triplets at short distances and provide a natural extension of the contact formalism beyond nucleon pairs. We find that the ^3He and ^3H contacts exhibit significant isospin-symmetry breaking, analogous to that observed previously for two-body contacts. Motivated by the semi-empirical mass formula, we derive a simple scaling relation for three-body contacts and show that it accurately reproduces the calculated values across medium-mass and heavy nuclei. Our results reveal a systematic dependence of 3N-SRCs on nuclear mass and composition, suggesting that three-body contacts obey universal scaling patterns closely analogous to those governing short-range-correlated nucleon pairs.

We formulate a renormalizable pionless effective field theory (/pi EFT) with a nonperturbative treatment of the Coulomb interaction up to next-to-leading order (NLO) for few-nucleon systems. We extract scattering observables for charged clusters by employing two-, three-, and four-body contact interactions and using the stochastic variational method with a Coulomb-corrected harmonic oscillator trap. Our NLO results yield a pd spin-quartet scattering length and effective range of a3/2pd = 12.76(29) fm and r3/2 pd = 1.17(7) fm; for dd scattering in the spin-quintet channel we find a2dd = 6.26(3) fm and rd2d = 1.41(7) fm; and for p3He scattering the spin-singlet and spin-triplet channels are characterized by a0p3He = 11.26(4) fm, r0p3He = 1.65(26) fm and a1p3He = 9.06(4) fm, r1p3He = 1.36(25) fm, respectively. Our predictions exhibit mild cutoff dependence and agree well with existing experimental phase shift analyses and potential model calculations. This demonstrates the predictive power of /pi EFT for charged few-nucleon systems.

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. We demonstrate that a relatively simple nuclear Hamiltonian-based on a leading-order pionless EFT expansion and known to accurately reproduce ground-state energies of nuclei with A≤40-also provides a reliable description of the photoabsorption cross section.

We formulate two methods to facilitate the calculation of perturbative corrections to quantum few-body observables. Both techniques are designed for a numerical realization in combination with any tool that obtains either the entire spectrum or solely the eigenvalues of an operator corresponding to the observable of interest. We exemplify these methods in the context of the nuclear contact theory without pions (Pionless EFT) and benchmark them in the deuteron channel with available analytical, field-theoretical calculations, as well as in the triton and 3-helium channels through earlier extractions within the dibaryon formalism, where in all three systems the point-proton root-mean-square charge radius (rms) was the perturbed observable of choice. Beyond these A≤3 consistency and accuracy checks, we employ the numerical methods to predict the rms of the 4-helium nuclear ground state to assess three different ways of integrating the Coulomb interaction into Pionless EFT. By comparing the respective results at leading and next-to-leading order for 3- and 4-helium, we find that the uncertainty due to the strong, short-range interaction is significantly larger compared with that due to the long-range Coulomb interaction for both bound states with their different binding momenta. Thereby, we provide strong support for simplifying extractions of bound-state observables by shutting off any Coulomb interaction if the strong part of the potential is considered only up to first order in the effective range expansion.

Considering the elastic scattering of two charged particles, we present two methods for numerically solving the generalized Coulomb-corrected BERW formula with high accuracy across the entire energy spectrum. We illustrate these methods using p−α scattering, employing a phenomenological p−α short-range interaction. Our results reproduce the phase shifts computed with the Numerov method for all l=0 and l=1 channels. We also provide full access to the Python script used to obtain these results, which can be readily applied to a wide range of core-fragment scattering problems in nuclear and atomic physics.

We utilize the generalized contact formalism in conjunction with the Woods-Saxon mean-field description of the long-range part of the nuclear wave function to assess the relative prevalence of short-range correlation pairs within atomic nuclei. We validate our approach for proton-proton and neutron-proton pairs by fitting ab initio calculations, experimental charge density results, and electron scattering experiments to a very good agreement. Applying our model, we calculate the spin-zero short-range correlations contact ratios. Interestingly, for nuclei with A > 50, we observe a notable dependence on the neutron-to-proton ratio N/Z. Specifically, the probability per nucleon to find neutron-neutron pairs increases, while that of proton-proton pairs decreases, whereas the probability of finding neutron-proton pairs remains relatively constant. To interpret this isospin symmetry-breaking effect, we employ a simple model based on generalized Levinger constants, linking it to differences in nuclear proton and neutron radii.

This White Paper presents an overview of the current status and future perspective of QCD research, based on the community inputs and scientific conclusions from the 2022 Hot and Cold QCD Town Meeting. We present the progress made in the last decade toward a deep understanding of both the fundamental structure of the sub-atomic matter of nucleon and nucleus in cold QCD, and the hot QCD matter in heavy ion collisions. We identify key questions of QCD research and plausible paths to obtaining answers to those questions in the near future, hence defining priorities of our research over the coming decades.

We study the relation between measured high-$x_B$, high-$Q^2$, Helium-3 to Tritium, $(e,e')$ inclusive-scattering cross-section ratios and the relative abundance of high-momentum neutron-proton ($np$) and proton-proton ($pp$) short-range correlated (SRC) nucleon pairs in three-body ($A=3$) nuclei. Analysis of this data using a simple pair-counting cross-section model suggested a much smaller $np/pp$ ratio than previously measured in heavier nuclei, questioning our understanding of $A=3$ nuclei and, by extension, all other nuclei. Here we examine this finding using spectral-function-based cross-section calculations, with both an \textit{ab initio} $A=3$ spectral function and effective Generalized Contact Formalism (GCF) spectral functions using different nucleon-nucleon interaction models. The \textit{ab initio} calculation agrees with the data, showing good understanding of the structure of $A=3$ nuclei. An 8\% uncertainty on the simple pair-counting model, as implied by the difference between it and the \textit{ab initio} calculation, gives a factor of 5 uncertainty in the extracted $np/pp$ ratio. Thus we see no evidence for the claimed ``unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3''.

We analyze the asymptotic behaviour of the coupled cluster many-body wave-function in the limit of highly excited two- and three-particles states. We find that in this limit the different coupled cluster amplitudes exhibit a recurring behaviour, factorizing into a common asymptotic two- or three-body term. These asymptotic terms depend on the potential and in general are system specific. We also suggest that the knowledge of the asymptotic behaviour can potentially help solving the coupled cluster equations in a more efficient way.

We present a systematic analysis of the nuclear 2 and 3-body short range correlations, and their relations to the zero-energy eigenstates of the Schrodinger equation. To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these Coupled-Cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear 2-body short range correlations, and it might also be helpful for general Coupled-Cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

and GRETINA a 1{pi} detector is under construction. However, the momentum in developing this technology to its full potential must continue towards GRETA, a full 4{pi} calorimeter. GRETA will carry {gamma}-ray spectroscopy into the next generation where it will be needed to fully exploit the science opportunities at radioactive beam facilities and increase the reach of stable beam facilities. In addition, {gamma}-ray tracking technology will have important applications for science, medicine, and homeland security.

We perform a systematic study of the α-particle excitation from its ground state 0_{1}^{+} to the 0_{2}^{+} resonance. The so-called monopole transition form factor is investigated via an electron scattering experiment in a broad Q^{2} range (from 0.5 to 5.0  fm^{-2}). The precision of the new data dramatically supersedes that of older sets of data, each covering only a portion of the Q^{2} range. The new data allow the determination of two coefficients in a low-momentum expansion, leading to a new puzzle. By confronting experiment to state-of-the-art theoretical calculations, we observe that modern nuclear forces, including those derived within chiral effective field theory that are well tested on a variety of observables, fail to reproduce the excitation of the α particle.

We present the first five-body calculations of s-wave n-4He scattering within leading order and next-to-leading order (NLO) pionless effective field theory (π̸EFT). Using an harmonic oscillator trap technique and π̸EFT fitted to just six well-established experimental parameters, we predict the s-wave n-4He phase shifts, scattering length an4He1/2(NLO)=2.47(4num.)(17theor.)fm, and effective range rn4He1/2(NLO)=1.384(3num.)(211theor.)fm in agreement with experiment. The apparent cutoff independence of our results is used to estimate the theoretical errors coming as an integral part of our final results.

In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant S-state. It is worth noting that the considered states include the well-known states of the electron–nucleus and electron–electron coalescences as a particular case. The simplicity and compactness imply that the considered wave functions represent linear combinations of a few single exponentials. We have calculated such model wave functions for the ground state of helium and the two-electron ions with nucleus charge 1≤Z≤5. The parameters and the accompanying characteristics of these functions are presented in tables for number of exponential from 3 to 6. The accuracy of the resulting wave functions are confirmed graphically. The specific properties of the relevant codes by Wolfram Mathematica are discussed. An example of application of the compact wave functions under consideration is reported.

Light hypernuclei containing one or two Λ baryons are the subject of an ongoing experimental campaign aiming to study the spectrum of these systems, as well as the 2 and 3-body interaction between Λ hyperons and nucleons. Here we shortly review the theoretical study of these systems within the framework of baryonic effective field theory.

Response functions are at the heart of any comparison of theory with experiment in studies of the nuclear dynamics with electroweak probes. Calculations performed in the laboratory frame often suffer from center of mass contaminations that need to be removed. By confining the system in a harmonic oscillator, we derive a set of analytical formulas to subtract the center of mass effects from calculations of response functions and associated sum rules. After a general analytical derivation, we first deal specifically with the longitudinal response function appearing in electron scattering and provide expressions for the center of mass correcting functions. Next, we present a proof of principle study for the case of the electric dipole sum rules in a two-body problem with a numerical implementation of our formalism. These steps pave the way to applying the proposed method to heavier nuclei in the future.

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses could bridge the gap between nuclear physics and its fundamental theory. Such calculations are performed on a finite grid, and thus extrapolation of finite-volume numerical results to the physical-relevant free-space quantities is needed. A common approach for the extrapolation utilizes the two-body Lüscher formula and its generalization to larger systems. To understand better the accuracy of this approach we study here two model systems, bosonic and fermionic. The few-body systems are solved with the stochastic variational method in a periodic box, and the extrapolated values are compared to those calculated directly in free space.