The entanglement between shape and rotation in the low-lying states is investigated for six even-even nuclei ${}^{112}\mathrm{Ru}, {}^{188}\mathrm{Os}, {}^{150}\mathrm{Nd}, {}^{150}\mathrm{Sm}, {}^{168}\mathrm{Er}$, and ${}^{238}\mathrm{U}$, using the five-dimensional collective Hamiltonian based on relativistic density functional theory. Analyses of potential energy surfaces, rotational frequencies, and staggering parameters reveal distinct deformation characteristics. The entanglement entropy exhibits divergent trends across the nuclei, with the triaxial nuclei ${}^{112}\mathrm{Ru}$ and ${}^{188}\mathrm{Os}$ showing an increasing entanglement entropy, the axial $\gamma$-soft nuclei ${}^{150}\mathrm{Nd}$ and ${}^{150}\mathrm{Sm}$ displaying a uniform staggering pattern, and the axial $\gamma$-rigid nuclei ${}^{168}\mathrm{Er}$ and ${}^{238}\mathrm{U}$ maintaining relatively low entanglement entropy values. The relationship between nuclear deformation and entanglement entropy is further elucidated by examining the corresponding probability distributions on the principal axes ($K$ distributions).

The lifetime of the $0_3^{+}$ state in ${}^{120}\mathrm{Sn}$ was measured for the first time by applying the fast-timing technique following thermal neutron capture. The mean lifetime of $\tau =50\left(7\right)$ ps leads to an $E0$ transition strength of ${10}^3\times {\rho }^2(E0;0_3^{+}\to 0_2^{+})=120\left(50\right)$, suggesting shape coexistence and a high degree of mixing between the $0_2^{+}$ and $0_3^{+}$ states. With the newly measured lifetime, the $B(E2;0_3^{+}\to 2_1^{+})$ value is 0.50(7) W.u., which reveals that the ${\rho }^2(E0;0_3^{+}\to 0_1^{+})$ increases by a factor of $\approx 3.4$ from ${}^{116}\mathrm{Sn}$ to ${}^{120}\mathrm{Sn}$.

The $\beta$-delayed $\gamma$-ray spectroscopy of ${}^{109}\mathrm{Nb}$ was performed to investigate the structure of ${}^{109}\mathrm{Mo}$ for the first time at the RIBF, Japan. Over one hundred transitions were assigned to ${}^{109}\mathrm{Mo}$, of these two were from the known isomeric state, and a new 33.1 keV excited state below the isomeric state was identified. The multipolarities of the transitions depopulating the isomeric state were restricted considering the internal conversion coefficients and empirically recommended upper limits of transition strengths. The intrinsic gyromagnetic ratio of the isomeric-state band was extracted, and the rotational band of the ground state was identified. The configurations of the ground and isomeric states in ${}^{109}\mathrm{Mo}$ were assigned to the $\nu 1/2^{+}\left[411\right]$ and $\nu 5/2^{+}\left[413\right]$ orbitals, respectively, with prolate shape. From the $logft$ analysis, the ground state in ${}^{109}\mathrm{Nb}$ and a new excited state in ${}^{109}\mathrm{Mo}$ with a small $logft$ value were assigned to the $\pi 5/2^{+}\left[422\right]$ and $\nu 5/2^{+}\left[402\right]$ orbitals, respectively. The assignments were supported by potential energy surface calculations using the configuration-constrained method with a triaxially deformed Woods-Saxon potential. Although the $\nu 1/2^{+}\left[411\right]$ orbital was successfully predicted as the ground state, the order of quasiparticle configurations for excited states was not reproduced. The neutron emission probability in ${}^{109}\mathrm{Nb}$ $\beta$-decay was evaluated to be $27\left(11\right)\%$ utilizing the $\beta$-delayed $\gamma$ rays of ${}^{109}\mathrm{Tc}$ and ${}^{108}\mathrm{Mo}$.

Background: Bayesian inference frameworks incorporating multimessenger astrophysical constraints have recently been applied to covariant density functional (CDF) models to constrain their parameters. Among these, frameworks utilizing CDFs with density-dependent meson-nucleon couplings furnishing the equation of state (EoS) of compact star (CS) matter have been explored. This class of CDF models has been extensively tested against various nuclear phenomena, providing a highly predictive description of CSs in terms of nuclear characteristics defined in the vicinity of nuclear saturation density and isopin symmetric limit.

Purpose: The aforementioned inference framework has not yet incorporated astrophysical objects with potentially extreme high masses or ultrasmall radii among its constraints, leaving its flexibility and predictive power under such extreme parameters still unknown. We aim at exploring the capabilities of this framework to account for these additional data.

Method: We apply the Bayesian inference framework based on CDFs with density dependent couplings. The astrophysical data are expanded to include not only the latest multimessenger constraints from the NICER (Neutron star Interior Composition Explorer) telescope and gravitational wave events but also the highest measured mass to date for the “black widow” pulsar PSR J0952-0607 and the mass-radius estimates for the ultracompact, low-mass object HESS J1731-347. The significance of the individual impact of these two sources, as well as the broader picture that emerges from their combined influence, is examined by analyzing the posterior distributions of key CS properties, nuclear characteristics at saturation density, and their correlations.

Results: Our systematic Bayesian analysis, which incorporates the PSR J0952–0607 and/or HESS J1731–347 data alongside typical astrophysical constraints, indicates that our CDF models can support higher maximum masses for CSs, reaching up to $2.4\text{–}2.5M_{\odot }$. However, achieving sufficient softening of the EoS in the low-density regime to accommodate the HESS J1731–347 data remains challenging. Nonetheless, we are able to impose tighter constraints on the parameter space of CDF models, ensuring consistency with current nuclear experimental and astrophysical data.

Conclusions: CDF models with density-dependent meson-nucleon couplings encompass a wide range of nuclear and astrophysical phenomena, providing a robust theoretical framework for interpreting compact objects. However, the predicted lower limit for the radii of low-mass stars is approximately 12 km, which stems from the restricted degrees of freedom in the isovector sector. These limitations can be addressed by extending CDF models to introduce more complex density dependence of the symmetry energy. Additionally, smaller radii may be achieved by allowing for a low-density deconfinement phase transition to quark matter.

The multiphoton excitation to the 8-eV nuclear isomeric state ${}^{229\text{m}}\mathrm{Th}$ in the direct laser-nucleus interaction is investigated theoretically. We solve the time-dependent Schrödinger equation with a method that allows us to study the $n$-photon absorption in the nuclear excitation in the direct laser-nucleus interaction. Based on the laser facilities available currently or in the near future, we analyze the impact of the laser parameters on the excitation probability of the multiphoton excitation. The possibilities of the two-, three-, and four-photon excitations to the isomeric state ${}^{229\text{m}}\mathrm{Th}$ from the ground state are discussed in detail. Our results show the strong impact of the laser intensity and pulse duration on the multiphoton excitation probability. The onset of high-order effects in the multiphoton excitation in the direct laser-nucleus interaction is also revealed. Our findings open new possibilities to study the multiphoton laser-nucleus interaction in high-power laser facilities.

The mechanism for generating directed and elliptic flow in heavy-ion collisions is investigated and quantified for the SIS18 and SIS100 energy regimes. The observed negative elliptic flow $v_2$ at midrapidity has been explained either via (in-plane) shadowing or via (out-of-plane) squeeze-out. To settle this question, we employ the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) to calculate $\mathrm{Au}+\mathrm{Au}$ collisions at $E_{\mathrm{lab}}=0.6A$ GeV, $E_{\mathrm{lab}}=1.23A$ GeV and $\sqrt{s_{NN}}=3.0$ GeV using a hard Skyrme-type equation of state to calculate the time evolution and generation of directed flow and elliptic flow. We quantitatively distinguish the impact of collisions and of the potential on $v_1$ and $v_2$ during the evolution of the system. These calculations reveal that, in this energy regime, the generation of $v_1$ and $v_2$ follows from a highly intricate interplay of different processes and the complex time-dependent geometry of the system. Initially, we find a strong out-of-plane pressure (squeeze-out), followed by a strong stopping and the buildup of an in-plane pressure (shadowing). The $v_2$, created subsequently by both processes, compensate to a large extent, therefore the net $v_2$ remains zero. We find that a finite net $v_2$ becomes visible late around $t\approx 1.5t_{\mathrm{overlap}}–2t_{\mathrm{overlap}}$, after the system has reached its highest density and has created a matter bridge between projectile and target remnant, which later breaks. The finally observed net $v_2$ is hence caused by the complex interplay of both early out-of-plane and subsequent in-plane pressure exerted by the potential, supplemented by local isotropization through collisions and the complex geometry of the dissolving matter bridge between projectile and target remnants, reflecting the freeze-out geometry. The results are highly relevant for experiments at GSI, RHIC-FXT, and the upcoming FAIR facility, but also for experiments at FRIB, and strengthen our understanding of the equation of state at large baryon densities.

The synthesis of superheavy elements provides crucial insights into the stability and structure of nuclei at the limits of the periodic table. This study investigates the ${}^{50}\mathrm{Ti}+{}^{244}\mathrm{Pu}$ and ${}^{50}\mathrm{Ti}+{}^{251}\mathrm{Cf}$ reactions as pathways to form superheavy elements (SHEs) 116 (livermorium) and 120, respectively. Using the dinuclear system model, key parameters such as fusion probability and fusion cross section were calculated. These findings were used to examine neutron emission and survival probability through a statistical approach. The reaction ${}^{50}\mathrm{Ti}+{}^{244}\mathrm{Pu}$ is explored as a continuation of experimental efforts to extend the known isotopic range of element 116, while the ${}^{50}\mathrm{Ti}+{}^{251}\mathrm{Cf}$ reaction represents a frontier for the synthesis of element 120. The role of shell effects, excitation energy, and angular momentum on the production and stability of these nuclei is discussed. The results provide theoretical predictions to guide future experimental efforts aimed at advancing our understanding of the island of stability and the limits of nuclear existence.

We present a novel Monte Carlo implementation of the EKRT model, MC-EKRT, for computing partonic initial states in high-energy nuclear collisions. Our new MC-EKRT event generator is based on collinearly factorized, dynamically fluctuating perturbative QCD (pQCD) minijet production, supplemented with a saturation conjecture that controls the low-$p_T$ particle production. Previously, the EKRT model has been very successful in describing low-$p_T$ observables at midrapidity in heavy-ion collisions at energies available at the CERN Large Hadron Collider (LHC) and the BNL Relativistic Heavy Ion Collider (RHIC). As novel features, our new MC implementation gives a full three-dimensional initial state event by event, includes dynamical minijet-multiplicity fluctuations in the saturation and particle production, introduces a new type of spatially dependent nuclear parton distribution functions, and accounts for the conservation of energy/momentum and valence-quark number. In this proof-of-principle study, we average a large set of event-by-event MC-EKRT initial conditions and compute the rapidity and centrality dependence of the charged hadron multiplicities and elliptic flow for LHC $\mathrm{Pb}+\mathrm{Pb}$ and RHIC $\mathrm{Au}+\mathrm{Au}$ collisions using $(3+1)\mathrm{D}$ viscous fluid-dynamical evolution. Also event-by-event fluctuations and decorrelations of initial eccentricities are studied. The good agreement with the rapidity-dependent data suggests that the same saturation mechanism that has been very successful in explaining the midrapidity observables works well also at larger rapidities.

The nuclear modification factor ($R_{\mathrm{AA}}$) of $B_c$ mesons in high-energy nuclear collisions provides a novel probe of heavy quark interactions with the quark-gluon plasma (QGP). Based on a linear Boltzmann transport model that incorporates both Yukawa and string types of interactions between heavy quarks and the QGP, we study the production and evolution of heavy quarks and $B_c$ mesons within the same framework. A $B_c$ bound state dissociates while one of its constituent heavy quarks scatters with the QGP with momentum transfer greater than its binding energy. The medium-modified charm and bottom quarks can recombine into $B_c$ mesons, and the medium-modified bottom quarks can also fragment to $B_c$ mesons. We find that most primordial $B_c$ mesons generated from the initial hard collisions dissociate inside the QGP. The production of $B_c$ mesons is primarily driven by the recombination mechanism at low transverse momentum and fragmentation at high transverse momentum. The string interaction dominates over the Yukawa interaction in the nuclear modification of $B_c$ mesons. The participant number dependence of the $B_c$ meson $R_{\mathrm{AA}}$ is determined by the complicated interplay between the heavy quark yield, energy loss, and the QGP volume. We obtain a reasonable description of the $R_{\mathrm{AA}}$ of $B_c$ mesons in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, and provide predictions for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Superheavy nuclei represent the extreme atoms and nuclides known at the limit of mass and charge. The observed superheavy nuclei are all proton-rich; they decay primarily by emitting $\alpha$ particles and by fission with a possible small electron capture (EC) branch. Due to the huge atomic numbers and associated relativistic effects, EC decays of superheavy systems are expected to differ from what is known in lighter nuclei. In this letter, using the quantified relativistic nuclear density functional theory and the quasiparticle random-phase approximation with the interaction optimized to experimental $\mathrm{EC}/{\beta }^{\pm }$-decay half-lives, and Gamow-Teller resonance energies, we study the $\mathrm{EC}/{\beta }^{\pm }$ decays in $Z=101–118$ nuclei. Both allowed ($1^{+}$) and first-forbidden ($0^{-},1^{-}$ and $2^{-}$) transitions are considered. We show that the first-forbidden $1^{-}$ transitions dominate the decay rates in almost all studied nuclei. For proton-rich nuclei, EC dominates over ${\beta }^{+}$ decay. Based on calculations with two relativistic energy density functionals, we identify 45 candidate nuclei in which a competition between weak decays and $\alpha$ decay and spontaneous fission is expected.

Neutron scattering on exotic nuclides is a class of processes that cannot be studied directly now and in any foreseeable future. Resonance proton scattering of exotic nuclide on a thick target in inverse kinematics can be used to infer the properties of the low-energy neutron scattering of this nuclide, assuming the isobaric symmetry. However, the results of such resonance proton scattering reactions have so far been analyzed in theoretical approaches (optical, R-matrix models), which are missing important aspects of isospin dynamics, isospin violation in continuum, and threshold dynamics. The isospin-conserving coupled-channel model (ICM) is proposed, providing a more reliable basis for understanding such experimental studies. Qualitatively different phase shifts for the ${}^8\mathrm{He}+pT=5/2$ and $T=3/2$ resonances are predicted by ICM with a quite unusual profile for the $T=5/2$ states. An alternative interpretation of the existing ${}^8\mathrm{He}+p$ data is proposed. The observable properties of the $T=5/2$ resonances may be strongly affected by the isobaric-partner $T=3/2$ states. The crucial importance of studies of the neutron-emission channel for disentangling this possible influence is demonstrated.

The zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of-the-art nuclear structure approach, we provide a detailed analysis of the properties of ${}^{90,96,98}\mathrm{Zr}$. This region includes a benchmarking case and offers insights into nuclear deformation phenomena. To investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the quasiparticle random phase approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed ${}^{98}\mathrm{Zr}$ nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the $K^{\pi }=0^{+}$ QRPA components and demonstrate an analogous dipole-octupole coupling through the $K^{\pi }=0^{-}$ and $K^{\pi }=1^{-}$ components. Intrinsic transition densities and associated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e., we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.

The zero-sound modes at finite temperature are investigated with the relativistic random phase approximation to signal the uncertainty of the equation of state (EOS) of asymmetrical nuclear matter. It is observed that in typically selected stiff and soft relativistic mean-field (RMF) models, zero-sound modes arise at low temperature, whereas increasing the temperature gradually breaks the zero sound in soft models, with a smaller density range compared to stiff models. At high density, the presence or absence of zero sound turns out to be correspondingly the character of the stiff or soft RMF EOS. More strikingly, we find by analyzing the dispersion relation and sound velocity that at finite temperature the zero-sound modes in RMF models with the stiff EOS undergo a thermal bifurcation, resulting in the transform of zero sound into the first sound at some momentum $Q>T$. The thermally bifurcated sound branch in the stiff models and the zero-sound branch in the soft models are both highly sensitive to the slope of the symmetry energy, providing promising signals for the pending high-density symmetry energies. In addition, it is found that there exists a nonlinear dispersion relation for both the stiff and soft models that supports the zero sound in the relatively lower-density region.

Background: Halo effective field theory (Halo-EFT) provides a very efficient description of loosely bound nuclei in models of reaction. It offers a very systematical ranking of the significance of nuclear-structure observables in reaction calculations. This greatly helps to infer reliable structure information from reaction cross sections. However, for a meaningful analysis, the Halo-EFT scheme needs to have converged.

Purpose: In a previous study P. Capel et al. [Phys. Rev. C 98, 034610 (2018)], next-to-leading-order (NLO) descriptions of ${}^{11}\mathrm{Be}$ have been developed and lead to excellent agreement with existing breakup data. However, the convergence of the scheme at NLO was not fully demonstrated. Moreover, a significant dependence on the regulator of the effective ${}^{10}\mathrm{Be}\text{−}n$ interaction has been observed.

Method: We develop effective-potential descriptions of ${}^{11}\mathrm{Be}$ at ${\mathrm{N}}^2\mathrm{LO}$ and use them in an accurate breakup-reaction code. We compare our theoretical cross sections with experiment on Pb and C targets at about 70 MeV per nucleon.

Results: On Pb, the ${\mathrm{N}}^2\mathrm{LO}$ descriptions of ${}^{11}\mathrm{Be}$ lead to little change to the NLO results of the previous study, supporting the convergence of that scheme. On C, the reaction is significantly affected by the presence of $d$ resonances in the low-energy spectrum of ${}^{11}\mathrm{Be}$. In effective-theory power counting these resonances appear only at ${\mathrm{N}}^2\mathrm{LO}$; our new descriptions include them naturally. Going to ${\mathrm{N}}^2\mathrm{LO}$ removes also the cutoff dependence observed in the previous study.

Conclusions: We demonstrate the convergence of the effective description of ${}^{11}\mathrm{Be}$ at NLO for Coulomb breakup and at ${\mathrm{N}}^2\mathrm{LO}$ for nuclear-dominated dissociation. The reliability of the nuclear-structure information inferred in the previous study is thus confirmed.

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.

New experimental data for the elastic scattering of deuterons from ${}^6\mathrm{He}$ at 26 MeV/nucleon were measured in inverse kinematics at the ACCULINNA-2 isotope on-line separator at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna. In the same experiment, proton scattering from ${}^6\mathrm{He}$ was also measured. Effective potentials for both systems were derived from optical model analyses of the data. A microscopic analysis of the deuteron data using the continuum discretized coupled channel method revealed that the weakly bound structure of the deuteron has only a modest influence on the $d+{}^6\mathrm{He}$ elastic scattering, compared with that of the structure of ${}^6\mathrm{He}$. It was found that the deuteron elastic breakup cross section is dominated by quadrupole couplings to the continuum $D$ states. However, the main effect of the breakup coupling on the elastic scattering comes from monopole couplings to the deuteron continuum $S$ states. The results of the analysis suggest a significant influence on the elastic scattering from the nucleon-transfer reactions.

The production of Λ hyperons and light hypernuclei in heavy-ion collisions provides critical insights into the nuclear equation of state (EoS) and hyperon interactions in dense matter, addressing the longstanding “hyperon puzzle” in neutron star physics. Using the $\mathrm{INCL}+\mathrm{ABLA}$ and AMPT-HC models, we systematically investigate $\mathrm{C}+\mathrm{C}$ collisions at beam energies of 1.1 and 1.9 GeV/nucleon to explore the sensitivity of hyperon and hypernuclei yields to the EoS and hyperon potential. Our results reveal that Λ hyperon production is predominantly influenced by the nuclear EoS, while light hypernuclei formation (e.g., ${}^3\mathrm{\Lambda }\mathrm{H}$) exhibits stronger sensitivity to the hyperon potential at high/low densities with the incident beam energies of 1.1/1.9 GeV. The study provides a framework for future experiments at facilities like HIAF and FAIR/GSI to resolve the hyperon puzzle, thus advancing our understanding of quantum chromodynamics in high-density regimes.

The JETSCAPE Collaboration reports a new determination of the jet transport parameter $\widehat{q}$ in the quark-gluon plasma (QGP) using Bayesian inference, incorporating all available inclusive hadron and jet yield suppression data measured in heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). This multi-observable analysis extends the previously published JETSCAPE Bayesian inference determination of $\widehat{q}$, which was based solely on a selection of inclusive hadron suppression data. jetscape is a modular framework incorporating detailed dynamical models of QGP formation and evolution, and jet propagation and interaction in the QGP. Virtuality-dependent partonic energy loss in the QGP is modeled as a thermalized weakly coupled plasma, with parameters determined from Bayesian calibration using soft-sector observables. This Bayesian calibration of $\widehat{q}$ utilizes active learning, a machine-learning approach, for efficient exploitation of computing resources. The experimental data included in this analysis span a broad range in collision energy and centrality, and in transverse momentum. In order to explore the systematic dependence of the extracted parameter posterior distributions, several different calibrations are reported, based on combined jet and hadron data; on jet or hadron data separately; and on restricted kinematic or centrality ranges of the jet and hadron data. Tension is observed in comparison of these variations, providing new insights into the physics of jet transport in the QGP and its theoretical formulation.