Papers

Against a background supported by the three pillars of emergent mass, this contribution challenges the fidelity of vector meson dominance as an instrument for relating the electromagnetic vector-meson (V) production reaction $e + p \to e^\prime + V + p$ to the hadronic process $V + p \to V + p$. It also describes a viable reaction model for exclusive photoproduction of light and heavy vector mesons from the proton, which exposes the $q\bar q$ content of the photon. That model's successes reveal that it is premature to link extant $V + p \to V + p$ data with, for instance, in-proton gluon distributions, the QCD trace anomaly, or pentaquark production. Improved reaction theory and more precise data are required before the validity of such links can objectively be assessed.

The paper reviews the theoretical and experimental progress achieved in the last 25 years in understanding the novel physics of artificial atoms and molecules as arising from the formation of Wigner molecules (WMs) of localized (to a stronger or lesser extent) fermionic or bosonic particles, which are finite quantum analogs of the more familiar bulk Wigner crystal. The term artificial atoms, as used here, encompasses a broad range of recently fabricated quantum nanodevices and experimental apparatuses consisting of a finite number of mutually repelling confined particles, including two-dimensional semiconductor and moiré transition metal dichalcogenide quantum dots, as well as trapped ultracold neutral atoms or ions. These nano-sized or micro-sized artificial devices and apparatuses (in single well or multi-well of variable-shape arrangements) hold a great promise for technological applications in the field of quantum information and quantum computers, as well as for advances in fundamental many-body physics. Prominent quantum effects of Wigner molecularization are the strong quenching of the spectral energy gaps, the appearance of rovibational spectra (in analogy with natural molecules), entanglement, and pinning due to an external perturbation. In high magnetic fields or at rapid rotation, WMs provide an alternative theory to the fractional quantum Hall effect. The physics of Wigner molecules is shown to derive from the solutions of the many-body Schrödinger equation (MBSE) in the regime of strong interparticle correlations arising from the dominance of the potential over the kinetic energy, or from a high magnetic field, as well as from a rapid rotation... (continues in the paper).

The cores of neutron stars have a combination of density, temperature, and neutron-proton asymmetry that cannot be replicated in laboratories or understood using first-principles quantum chromodynamics. Thus, observations of neutron stars are necessary to understand this regime. In particular, precise and accurate measurements of neutron star radii are highly informative about cold, catalyzed matter at a few times nuclear saturation density. X-ray observations with NASA's Neutron star Interior Composition Explorer (NICER) have yielded radius measurements for a few nonaccreting neutron stars, which have advanced substantially our understanding of dense matter. In this review we discuss the NICER radius measurements and their implications and demonstrate that the systematic errors thus far explored in NICER analyses have at most a minor effect on the inferred radii of neutron stars.

We make use of unique properties of scaling functions to estimate the chiral phase transition temperature and corresponding universal critical parameters of this phase transition directly from (2+1)-flavor QCD simulations with highly improved staggered fermions on lattices with temporal extent $N_\tau=8$. Working with an improved chiral order parameter for quantifying chiral symmetry breaking, we analyze the finite-volume dependence of this observable for a wide range of lattice volumes and light quark masses, and quantitatively estimate the deviations from the expected universal scaling behaviour as a function of the light-to-strange quark mass ratio.

We present AI-developed local infrared subtraction, building on projection to Born and EFT matching. The framework separates an integrable radiation term from a finite contribution at Born kinematics, referred to as the Born contact. The contact is determined using the EFT singular distribution in a resolution observable such as N-jettiness $\tau_N$. Under human physics guidance, an LLM develops two implementations. One uses a neural network for phase space projection and fits the contact by matching to EFT cumulants. The other uses an analytic construction that keeps the Born momenta fixed while integrating over radiation. It combines the EFT $\delta(\tau_N)$ coefficient with finite 4-dimensional radiation integrals to calculate the contact term directly. This gives a local subtraction formula without a slicing parameter, while reusing existing lower-order radiation calculations and EFT singular predictions. As a demonstration, we reconstruct the full NLO correction for massless 3- and 4-jet production in electron-positron annihilation. The attempt to the NNLO dijet production is also made by recursively using the NLO P2B construction with the LLM designing machine-learning controls to reduce the variance of the contact integral. The tested predictions are in good agreement with EERAD3. The numerical calculation and projection-network training use a 2020 Apple M1 MacBook, without GPU acceleration, illustrating the feasibility of the construction with modest computing resources. The appendices develop an extension of the local subtraction to 3-jet NNLO, giving explicit radiation maps and a proposed contact formula. We also show how to integrate over NNLO radiation while keeping the Born momenta fixed, for any number of massless final-state jets. Our results demonstrate how AI can help higher-order calculations by constructing infrared subtraction and improving its numerical integration.

We develop a new framework to perform a virtuality-resolved description of jet propagation in heavy-ion collisions using perturbative techniques. The role of virtuality is rigorously identified by first deriving a factorized jet cross section that defines an in-medium jet function. This new definition allows to extend the usual BDMPS-Z formalism to include the virtuality-differential transverse momentum broadening distribution and medium-induced soft gluon spectrum. We study both the cases of a medium which is created with some delay time $\tau_0$ after the hard collision as well as the case in which $\tau_0\to 0$. Integration over the complete virtuality range recovers the standard BDMPS-Z results, while finite virtuality reveals the interplay between vacuum-like evolution and medium-induced dynamics. We identify the ratio between the medium formation time and the jet formation time as the variable controlling which initial virtualities contribute appreciably to the jet function.

We study the spin-resolved spectral functions of $\phi$ and $K^{*0}$ in a thermal hadronic model with a constant magnetic field. We construct the rest-frame retarded propagators by combining real vacuum matching with exact Landau levels, connection contacts, and thermal scattering terms. The resulting stable-daughter calculation is checked against independent collision kernels and published expressions in common limits. We find that closed transverse thresholds give rise to narrow peaks with eV-scale detunings, whose areas must be resolved in the calculation of small spin spectral moments. We test the leading threshold estimate for the peak area by an independent integration of the full kernel. Using positive compact daughter spectra, we then investigate how a finite spectral spread changes the local threshold structure. The disappearance of zeros of the real part of the inverse propagator is controlled by the spread relative to the detuning, whereas the weight integrated over a finite patch can remain nearly unchanged. We relate this redistribution to smooth accepted moments through a weighted identity with a bounded Taylor remainder, and evaluate the complete-window response to three endpoint replacements, including the patch complement. For the stable-daughter $\phi$ spectra with a fixed smooth weight, the response at the two smallest sampled fields is negative and compatible with $b^2$ scaling. Hard-window results instead oscillate in sign, and pseudoscalar mixing substantially changes the smooth response coefficient. These results quantify the sensitivity to thresholds and spectral projection; microscopic daughter widths and source-matched experimental spin alignment require additional input.

We investigate the effective axial $U_A(1)$ symmetry restoration at finite temperature in an external magnetic field using meson screening masses, as well as meson susceptibilities, in a $(2+1)$-flavor Nambu-Jona-Lasinio (NJL) model. To incorporate inverse magnetic catalysis, we employ a magnetic-field-dependent four-quark coupling constrained by the lattice QCD chiral pseudo-critical temperature, with the 't Hooft coupling fixed. In the lattice-improved NJL model, the longitudinal screening mass difference between the $U_A(1)$ partners $\delta^0$ and $\pi^0$ and their normalized meson susceptibility difference exhibit axial magnetic catalysis at low temperatures and axial inverse magnetic catalysis near the chiral crossover, whereas the transverse screening mass difference increases with $eB$ at all temperatures. Despite these different responses, the axial pseudo-critical temperatures extracted from the thermal inflection points of these three alternative order parameters decrease with $eB$, implying that a decreasing pseudo-critical temperature can coexist with an increasing transverse screening mass difference at fixed temperature.

The relaxation-time Boltzmann equation governs relativistic matter far from equilibrium, but existing approaches rely on finite-order truncations that break down in this regime. We introduce ShARK (Stochastic Advection Relaxation Kinetics), the first fully 3D Monte Carlo kinetic framework to capture exact, far-from-equilibrium ultrarelativistic dynamics for arbitrary initial conditions while directly enforcing target transport coefficients, converging to the exact Anderson-Witting solution. Validated against the Bjorken and Gubser flows, the framework reproduces the exact kinetic result where truncated methods fail.

We show that the Anderson-Witting relaxation-time approximation (relativistic Bhatnagar-Gross-Krook (BGK) equation) emerges as the $N\rightarrow \infty$ limit of a stochastic $N$-body particle gas, in which collisions perform a full microcanonical momentum redraw that enforces local energy-momentum conservation at every event. Using the RAMBO algorithm to sample the Lorentz-invariant phase space, we derive the finite-$N$ single-particle momentum spectrum and show that it converges to the Jüttner-Boltzmann equilibrium distribution as the local particle number grows. We couple this relaxation kernel to an advection-relaxation splitting scheme to construct ShARK (Stochastic Advection Relaxation Kinetics), a 3D Monte Carlo relativistic solver for the relaxation time approximation Boltzmann equation. The framework is conceptually related to lattice Boltzmann methods, but formulated in continuous momentum space to avoid the accuracy loss caused by finite-order momentum discretizations far from local equilibrium. We validate the numerical results against analytical solutions for two highly symmetric conformal expansions, the Bjorken and Gubser flows. The framework provides a first-principles route to far-from-equilibrium relativistic transport, with applications ranging from heavy-ion collisions to expanding astrophysical plasmas.

To calculate transmission coefficients, current Hauser-Feshbach reaction codes assume a one-dimensional fission path that is both independent of excitation energy and universal across different fission channels. In contrast, microscopic fission studies typically explore multiple collective variables. Predicting observable fission quantities such as cross sections based on microscopic input thus requires a way to reduce the dimensionality of the latter. For spontaneous fission, the least action path (LAP) – which minimizes the semiclassical action and maximizes the transmission coefficient – is the solution. We demonstrate that the LAP does not generalize to other fission modes such as neutron-induced or $\beta$-delayed fission: at finite excitation energy, the LAP generally does not maximize the transmission. A microscopic PES can have multiple coexisting stationary-action paths. We show that these (i) can switch their action ordering as a function of excitation energy and (ii) yield different neutron-induced fission cross sections predictions, yet match known spontaneous fission lifetimes equally well. For the BSkG3 Skyrme-type energy density functional model, the transition from the axially symmetric LAP at zero excitation energy to a path exploiting the triaxial degree of freedom occurs at an excitation energy that is smaller than the neutron separation energy for essentially all actinides and the majority of unknown exotic nuclei.

In the present study, we investigate the phase diagram of strongly-interacting fermions under imaginary rotation. We employ the linear sigma model coupled to quarks in the mean field approximation. The fermion expectation values are computed in the local density approximation (LDA), using the well-known expressions derived using cylindrical modes for states under rigid rotation, at finite temperature $T$ and chemical potential $\mu$. We study the impact of the fractalization of thermodynamics on the phase diagram in the far-field limit (far from the rotation axis). We also reveal non-trivial features such as a complete inhibition of the chiral symmetry restoration on the rotation axis above a critical imaginary angular velocity. We demonstrate explicitly how the transition line interpolates between its shape on the rotation axis and in the far-field limit by studying the chiral phase transition at finite distances from the rotation axis. We also address the moment of inertia of the system and discuss differences and similarities to lattice studies of QCD matter under imaginary rotation.

We investigate the Seebeck coefficient as a probe of collective transport behavior in graphene and quark-gluon plasma using a kinetic-theory approach in the hydrodynamic regime. The Seebeck coefficient is obtained by solving the Boltzmann transport equation in the relaxation-time approximation. At high-charge-carrier density, corresponding to the Fermi-liquid domain, our result approaches the behavior expected from the conventional Mott relation. In contrast, significant deviations from the Mott relation are observed in the low-carrier-density regime, corresponding to the Dirac fluid domain. These facts are in good agreement with experimental Seebeck coefficient data for graphene. This behavior indicates the emergence of collective hydrodynamic transport in graphene. The enthalpy per particle plays a key role for the Seebeck coefficient in the Dirac fluid regime. We extend our formalism to the ultra-relativistic quark-gluon plasma. A similar deviation from the Mott relation is observed, supporting a similar fluid response in the Seebeck coefficient across two markedly different strongly correlated quantum systems - graphene and quark matter.

We study the effects of in-medium modification of the elementary cooling processes on observable properties of isolated neutron stars. We then deduce the neutron star mass distributions compatible with the cooling analysis and compare with current theoretical models. We conclude that current cooling data require fast direct Urca (DU) cooling, moderated by proton superfluidity, to be active in most neutron stars, and that the DU onset threshold must lie below canonical masses. In that case medium modifications of modified Urca (MU) rates are practically insignificant, but the $nn$ Bremsstrahlung rate plays a dominant role.

We reconstruct elastic $s$-wave neutron-proton ($np$) phase shifts from trapped spectra measured on IBM Aachen using a compressed RODEO circuit. For a schematic square-well interaction represented by classically constructed four-dimensional effective Hamiltonians, four positive-energy levels at five trap strengths supply twenty inputs to classical modified effective range expansion (MERE) extrapolation to free space. The six-cycle factorized geometric-time RODEO implementation (FG-R6) combines ancilla reuse, exact query-phase separation, post-compilation binding, and six numerically optimized geometric evolution times. Numerical cycle-count tests support this choice within the adopted local spectral tolerances. At the same three-qubit width and equal shot budgets, FG-R6 reduces median compiled depth and two-qubit-gate count by 33.1% and 37.2% relative to ten-cycle dynamic direct RODEO (direct R10), increases the median fitted amplitude, and lowers median finite-shot energy uncertainty from 0.610 to 0.534 keV. For this dataset's primary fit on the 0.1-30.0 MeV grid, the maximum central phase-shift deviation from exact-energy MERE decreases from $0.842^\circ$ to $0.163^\circ$, despite a larger root-mean-square (RMS) trapped-energy deviation. The full-grid gain arises mainly in the low-energy extrapolation region; direct R10 has slightly smaller residuals relative to the same reference on the 10.0-30.0 MeV common energy-interpolation subset. The FG-R6 central curve differs from the analytical square-well solution by at most $0.156^\circ$. Fit-form sensitivity remains appreciable and is assessed separately from finite-shot uncertainty. This reduced-space benchmark connects RODEO circuit compression to nuclear continuum observables and shows why circuit performance must be assessed through the scattering reconstruction and its energy range, not spectral RMS errors alone.

The sign of the D-term is negative for a variety of hadrons, including the proton and pion. Speculation that this is the result of a mechanical stability condition has persisted despite counterexamples, including the positive D-term of the hydrogen atom. In this work, I explore how the sign of the D-term is influenced by the stress carried by static abelian force fields, finding the contributions from spin-even fields to be negative and the contributions from spin-odd fields (such as the electromagnetic field) to be positive. These contributions correlate with the signs of the D-terms of the fields' respective quanta. Since fields with different spin can produce identical potentials—thus resulting in equally-stable composite systems with identical wave functions—the sign of the D-term has nothing to do with stability. Since hadrons are bound by spin-one gluons, their negative D-terms appear atypical and require explanation. I briefly speculate on how color flux confinement could produce a negative hadronic D-term.

We study the $\bar{K}^0d$ system using a new formulation of the fixed-center approximation that preserves elastic unitarity. The resulting scattering amplitude predicts a bound state below threshold, which can be interpreted as a $\Lambda(1380)N$ configuration complementary to the $K^-pp$ state associated with the higher $\Lambda(1405)$ pole. The interaction is attractive, with scattering parameters of the same order as recent $K^-d$ determinations. We further calculate the $\bar{K}^0d$ correlation function, which exhibits a characteristic structure associated with the bound state and provides a Coulomb-free observable that can be tested in future ALICE measurements. Results obtained with two different $\bar{K}N$ models are very similar, indicating the robustness of the predictions against the choice of the underlying interaction.

We consider the nuclear recoil spectrum following allowed $\beta$ decay as a laboratory for Beyond Standard Model searches, and perform an exhaustive treatment of the Standard Model prediction. We consider final state interactions, nuclear structure corrections, kinematic corrections and radiative corrections, derive new results and show that the nuclear recoil spectrum is theoretically exceptionally clean. We construct a clean statistical framework and analyze the Fisher information for extracting exotic current constraints and testing Cabibbo-Kobayashi-Maskawa top-row unitarity, and consider a number of sterile neutrino scenarios. In addition, we find that for select isotopes separate measurement of the $\beta$-asymmetry and recoil spectrum can achieve an increase in the statistical power of up to a factor 40.

We initiate the study of quantum state tomography—the experimental reconstruction of the complete spin density matrix—of massless and massive quark-antiquark pairs produced at the future Electron-Ion Collider (EIC). We show that all components of the spin density matrix can be accessed through azimuthal angular correlations between hadron and dihadron pairs generated by the Collins and dihadron fragmentation functions. This enables the experimental investigation of a variety of quantum information properties at the EIC, such as entanglement and Bell-nonlocality. We predict that the recently discovered maximal entanglement in the heavy-quark sector is signaled by a strong modification of the usual Collins angular dependence $\cos(\phi+\phi')$

The structure of the neutron-rich nucleus $^{21}$B is investigated within a three-body model consisting of a $^{19}$B core and two neutrons. The three-body wave functions are computed using the hyperspherical adiabatic expansion method combined with the complex-scaling technique. Four potential parametrizations compatible with the available experimental information on $^{20}$B are considered. The calculations predict a low-lying $\frac{3}{2}^-$ state below the experimentally observed resonance at 2.47~MeV. An analysis of the dependence on the three-body interaction shows that this state cannot be shifted to the experimental resonance energy; instead, it remains either bound or becomes a near-threshold resonance with a rapidly increasing width. These results indicate that the observed resonance is more naturally interpreted as the second $\frac{3}{2}^-$ state, whereas a lower-lying $\frac{3}{2}^-$ state, dominated by an $s_{1/2}$ configuration, has so far eluded experimental observation. Momentum correlations are obtained for the experimentally observed resonance. In addition, the existence of other resonances is investigated.

We present a systematic study of the ground states of pentaquark systems using the neural network variational Monte Carlo method within the constituent quark potential model. We investigate all manifestly exotic pentaquark systems with negative parity, which cannot mix with the conventional baryons through the creation and annihilation of light or strange quark pair. We exhaust 387 color, spin, and isospin configurations and identify 21 pentaquark bound state candidates with binding energies ranging from $2$ to $15$ MeV. A striking observation is that all of the bound states are shallowly bound molecular states, and a deeply bound pentaquark state does not exist. The $QQqq\bar{Q}$, $ssqq\bar{Q}$, $Qsqq\bar{Q}$ and $Qqqq\bar{Q}$ bound states are composed of a heavy vector meson and a baryon, while the $QQqq\bar{s}$ and $Qqqq\bar{s}$ bound states are composed of a $K$ meson and a heavy baryon. As a cross-validation, the ground-state energies of the unbound systems converge to the baryon–meson thresholds from above, which are consistent with the S-wave scattering states and provide a reliable baseline for the bound-state criterion. Especially, we reproduce the lowest scattering states $\eta_c N$ and $\eta_c \Lambda$ in the $qqqc\bar{c}$ and $qqsc\bar{c}$ channels respectively, where the hidden-charm pentaquark resonances were observed experimentally. We also find that all fully heavy pentaquark states are unbound. Our results provide valuable guidance for future pentaquark searches at LHCb, Belle II, and other experiments.

We study the effects of the moat regime on meson and quark correlation functions and the quark-antiquark potential in low-energy QCD, building on the two-flavor quark meson model in a random-phase approximation. We investigate the relation between the moat regime and Friedel oscillations in the quark-antiquark potential at large density and zero temperature. As it turns out, oscillations from the moat regime are a distinct phenomenon, arising from poles on unphysical Riemann sheets in this region. Furthermore, we find that in addition to pions and the sigma meson, also other mesons, including vector mesons and the eta, are sensitive to the moat regime. This leads in particular to an enhancement of the meson spectral function in the spacelike region. The quarks, on the other hand, appear to be essentially insensitive. This can have far-reaching consequences for the phase diagram, as for example the chiral phase boundary, including the location of the critical endpoint, can be affected in the moat regime even in absence of inhomogeneous instabilities.

We report the first quantum-hardware implementation of Real-time Estimators for Scattering Observables (RESOs). The physical model is a one-dimensional lattice theory of non-relativistic spin-1/2 fermions with a single contact interaction. The lattice sizes studied are up to $N_x=54$ lattice sites and up to $20$ time steps. Spacetime correlation functions were computed on IBM's quantum computers, using $109$ qubits with $10,806$ CZ gates applied, reaching a two-qubit gate depth of $246$. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.

We study massive spin-$1/2$ Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order $\mathcal{O}(\hbar^2)$. For such a system, the fluid velocity becomes an independent thermodynamic variable and fundamental thermodynamic relations have to be extended. Employing the Wigner-function formalism, we show that the standard mass-shell condition $k^2 = m^2$ is modified at order $\mathcal{O}(\hbar^2)$ by contributions quadratic in the thermal vorticity. Incorporating this modified mass-shell constraint, we derive the (net) particle-number current, energy-momentum tensor, spin-current tensor, and associated thermodynamic quantities in the kinetic, canonical, and de Groot–van Leeuwen–van Weert (GLW) pseudo-gauges. We explicitly demonstrate that, while global quantities, like the total particle number or total energy, are independent of the choice of pseudo-gauge, local quantities, like the particle-number density or the energy density, are pseudo-gauge dependent. We then examine the thermodynamic relations in each pseudo-gauge and demonstrate that thermodynamic consistency requires that the thermodynamic Maxwell relations are satisfied. We find that these relations hold in the kinetic-theory pseudo-gauge, whereas they are in general violated in the canonical and GLW pseudo-gauges. These findings suggest a preference for using the kinetic-theory pseudo-gauge in applications such as spin hydrodynamics.

In Mueller's dipole cascade without transverse dimensions, with one counted particle for each dipole produced in a window, the multiplicities in three consecutive rapidity windows are Poisson counts of one Gamma-distributed source. We show that at fixed middle multiplicity the outer two share less information than the Gaussian value $-\tfrac12\ln(1-\rho^2)$ of their partial correlation, a value that second moments alone determine. For windows of one common width at a constant splitting rate this value never exceeds $\tfrac12\ln(4/3)$. The Gaussian value is not a bound on mutual information in general, and for a source of the same mean and variance with another law the information can exceed it. The law of the counts keeps its form under migration of particles across window edges and detection losses when both act on each particle independently of the others and of the source, and its factorial cumulants of second and third order test necessary conditions for it. In Monte Carlo simulations of the cascade with transverse dimensions at leading logarithmic accuracy and fixed coupling, the counts are not Poisson counts of one source, so the bound is a result of the model without them. In the model without transverse dimensions the law also fixes the normalized second factorial cumulant of one window at $1/k$, with $k$ the number of initial dipoles. The values of this cumulant formed from the mean and variance that H1 publishes for deep inelastic scattering lie far below the value one of a cascade from a single initial dipole with one counted particle for each dipole produced in a window. The quantity bounded is a classical conditional mutual information between counted multiplicities.

Standard r-process models often treat the freeze-out phase as a passive, uniform smoothing of the global abundance pattern. We demonstrate, however, that the final pattern is instead actively sculpted by a dynamic “neutron economy” that operates well after the free neutron source is exhausted. By analyzing cold neutron star merger outflows, we identify a distinct neutron exporter-importer relationship: the second-peak region ($A \sim 130$) transitions early into a $\beta$-decay dominated regime, acting as a net exporter, while the third-peak ($A \sim 195$) and Rare Earth ($A \sim 164$) regions remain capture-dominated neutron importers. Targeted simulations reveal that the final peak structures emerge from a competition between two opposing forces: a global “push” driven by neutron capture shifting mass toward heavier nuclei, and a local “pull” from beta delayed neutron emission returning material back toward lighter masses. We identify $^{136}\text{Pd}$, $^{135}\text{Ag}$, and $^{130}\text{Ru}$ as the primary exporters driving this economy, while third-peak fine structure is governed by $N=126$ isotones (Sm to Tb). Physically, this transport reflects a fundamental drive toward shell closure, where nuclei that overshoot the $N=82$ closed shell shed mass to migrate back toward this stable configuration, while nuclei in the third peak capture these redistributed neutrons to anchor themselves at the $N=126$ shell. Crucially, our models overproduce the odd-even staggering in the third peak compared to solar data. This discrepancy suggests current models likely overestimate the $\beta$-delayed neutron emission probabilities ($P_n$) for these $N=126$ nuclei, highlighting them as high-priority targets for theoretical refinement and future FRIB experiments.

We develop a permutation-invariant Set Transformer to reconstruct the equation of state (EoS) of dense matter from variable-size, unordered sets of neutron star (NS) observations. The model takes stellar masses together with radii, tidal deformabilities, or both, and predicts either the pressure $P(n)$ or the sound speed $c_s^2(n)$ on a fixed density grid, along with density-dependent uncertainties. Nothing in the architecture prescribes which star informs which density: self-attention couples all observations nonlinearly, and each density point reads the full set through its own learnable query, so the star-to-density mapping is learned from the data. Trained on independent piecewise-polytropic and Gaussian-process EoS ensembles, the model provides well-calibrated predictions whose uncertainty increases in density regions that stable stars cannot probe. Reconstruction errors decrease with the number of observations, while tidal deformability generally improves accuracy at a fixed observation count, even when it carries its own measurement noise. Sensitivity analysis reveals a density-local mapping: in the pressure models, predictions at density $n$ depend most strongly on stars whose central densities are near $n$. We also show that the sensitivity of the model to the inferred stellar compactness provides information on the minimum central density. These results demonstrate that set-based neural inference, in which the star-to-density mapping is learned rather than assumed, can extract physically interpretable EoS information with calibrated uncertainties.

We propose a Quantization-Constrained Parameter Method (QCPM) for determining the Woods-Saxon (WS) potential depth $V_0$ and diffuseness $a$ in studies of $\alpha$ and cluster decay half-lives. In this approach, the parameters are derived analytically by imposing the Bohr–Sommerfeld (BS) quantization condition, thereby eliminating the need for parameter fitting. The calculated diffuseness values exhibit a strong dependence on nuclear shell structure. The reliability of the QCPM-derived WS potential is validated through optical model analyses of elastic $\alpha$ scattering data. The resulting $\alpha$ and cluster decay half-lives show good agreement with experimental values. Our results highlight the significant role of daughter-nucleus deformation in improving the consistency between theoretical predictions and experimental data. In addition, we introduce a modified Woods–Saxon (mWS) potential that effectively approximates the surface behavior of folding potentials incorporating the nuclear medium effect. This modification leads to closer agreement with the measured half-lives. Free of adjustable parameters such as $V_0$ and $a$, the QCPM enhances the predictive power of phenomenological potentials for $\alpha$ and cluster decay studies.

We explore experimental probes for constraining the equation of state (EOS) of spin-polarized nuclear matter, where spins of nucleons are aligned along a particular direction. For this purpose, we calculate the $12^+$ isomeric state of the \ce{^{52}Fe} nucleus with the relativistic point-coupling model. We argue that the spin skin thickness of this high-spin state, that is, the difference between the radius of the spin-up density and that of the spin-down density, strongly correlates with the spin slope parameter of the EOS. This is in analogy to the well known linear correlation between the slope parameter of the symmetry energy and the neutron skin thickness of finite nuclei. We show that this correlation is retained even when one considers the difference of the radii between the $12^+$ and the ground states, even though the correlation is much weaker than in the case of the difference between the spin-up and the spin-down radii. We also discuss the mean-square charge radii of the $12^+$ state. We find that by taking the square of the radii the dependence on the spin slope parameter becomes much stronger, and thus it can serve as a good probe of the spin slope parameter given a high resolution of laser-spectroscopy experiments.

Accurately modeling $\beta$-decay half-lives of highly neutron-rich nuclei is a critical challenge for understanding $r$-process nucleosynthesis and the resulting kilonova light curves. We introduce a data-driven approach to model $\beta$ decay that uses Mixture Density Networks (MDNs) trained on the latest experimental measurements to extrapolate the half-lives of neutron rich nuclei. Unlike standard deterministic regression, the MDN directly parameterizes the probability distribution of the half-lives, providing intrinsic (aleatoric) uncertainty. We contrast the intrinsic uncertainty of a single model with the range of models produced by using random variations of the input training data samples. While all models show excellent agreement with experimental data, we find that varying the training data sets produces a wide range of extrapolations, particularly along data-poor regions such as the $N=126$ isotonic chain. We then propagate a selection of model results into $r$-process network calculations to evaluate their impact on isotopic abundances. Finally, by coupling the resulting isotopic abundances with thermalization efficiencies, we translate the effective nuclear heating rates into bolometric light curves. We compare the ranges of outcomes produced from the intrinsic uncertainty of a single model to those produced by multiple independent models trained on different training data sets.