We investigate the properties of electromagnetic fields in isobaric ${}_{44}^{96}\mathrm{Ru}+{}_{44}^{96}\mathrm{Ru}$ and ${}_{40}^{96}\mathrm{Zr}+{}_{40}^{96}\mathrm{Zr}$ collisions at $\sqrt{s}=200\mathrm{GeV}$ by using a multiphase transport model with special emphasis on the correlation between magnetic-field direction and participant plane angle ${\mathrm{\Psi }}_2$ (or spectator plane angle ${\mathrm{\Psi }}_2^{\mathrm{SP}}$), i.e., $\langle cos2({\mathrm{\Psi }}_B-{\mathrm{\Psi }}_2)\rangle$ [or $\langle cos2({\mathrm{\Psi }}_B-{\mathrm{\Psi }}_2^{\mathrm{SP}})\rangle$]. We confirm that the magnetic fields of ${}_{44}^{96}\mathrm{Ru}+{}_{44}^{96}\mathrm{Ru}$ collisions are stronger than those of ${}_{40}^{96}\mathrm{Zr}+{}_{40}^{96}\mathrm{Zr}$ collisions due to their larger proton fraction. We find that the deformation of nuclei has a non-negligible effect on $\langle cos2({\mathrm{\Psi }}_B-{\mathrm{\Psi }}_2)\rangle$ especially in peripheral events. Because the magnetic-field direction is more strongly correlated with ${\mathrm{\Psi }}_2^{\mathrm{SP}}$ than with ${\mathrm{\Psi }}_2$, the relative difference of the chiral magnetic effect observable with respect to ${\mathrm{\Psi }}_2^{\mathrm{SP}}$ is expected to be able to reflect much cleaner information about the chiral magnetic effect with less influences of deformation.

Linearly polarized monocromatic beams of $\gamma$ rays, that will be available at the ELI-NP facility, will open up the way to nuclear fluorescence experiments aimed at measuring the depolarization ratio of the outcoming photons. This is the ideal tool to clearly discriminate among the various proposed geometric configurations for $\alpha$-cluster nuclei, such as ${}^{12}\mathrm{C}$ in a model-independent way. For this nucleus, all possible outcomes have been enumerated in this Rapid Communication, and the predicted theoretical patterns of intensities will serve as a guide for the conclusive experimental identification of its nuclear molecular structure.

Background: There is significant current interest in knowing the value of the proton radius and also its proper definition.

Purpose: Combine the disparate literatures of hydrogen spectroscopy and diverse modern parton distributions to understand the meaning of the proton radius in a manner consistent with the separate bodies of work.

Methods: Use perturbation theory, light-front dynamics, and elementary techniques to find relativistically correct definitions of the proton radius and charge density.

Results: It is found that the very same proton radius is accessed by measurements of hydrogen spectroscopy and elastic lepton scattering. The derivation of the mean-square radius as a moment of a spherically symmetric three-dimensional density is shown to be incorrect. A relativistically correct, two-dimensional charge density is related to the diverse modern literature of various parton distributions. Relativistically invariant moments thereof are derived in a new relativistic moment expansion, the RME.

Conclusion: The equation $r_p^2\equiv -6G_E^{\prime }\left(0\right)$ is the definition of the proton radius.

Elliptic flow ($v_2$) in ultrarelativistic nucleus-nucleus collisions fluctuates event to event, both in magnitude and in orientation with respect to the reaction plane. Even though the reaction plane is not known event to event in experiment, we show that the statistical properties of $v_2$ fluctuations in the reaction plane can be precisely extracted from experimental data. Previous studies have shown how to measure the mean, variance and skewness using the first three cumulants $v_2\left\{2\right\}$, $v_2\left\{4\right\}$, and $v_2\left\{6\right\}$. We complement these studies by providing a formula for the kurtosis, which requires an accurate determination of the next cumulant $v_2\left\{8\right\}$. Using existing data, we show that the kurtosis is positive for most centralities, in contrast with the kurtosis of triangular flow fluctuations, which is negative. We argue that these features are robust predictions of fluid-dynamical models.

The search for a possible critical point in the QCD phase diagram is ongoing in heavy-ion collision experiments at the BNL Relativistic Heavy Ion Collider (RHIC) which scan the phase diagram by scanning the beam energy; a coming upgrade will increase the luminosity and extend the rapidity acceptance of the solenoidal tracker at RHIC (STAR) detector. In fireballs produced in RHIC collisions, the baryon density depends on rapidity. By employing Ising universality together with a phenomenologically motivated freeze-out prescription, we show that the resulting rapidity dependence of cumulant observables sensitive to critical fluctuations is distinctive. The dependence of the kurtosis (of the event-by-event distribution of the number of protons) on rapidity near midrapidity will change qualitatively if a critical point is passed in the scan. Hence, measuring the rapidity dependence of cumulant observables can enhance the prospect of discovering a critical point, in particular if it lies between two energies in the beam energy scan.

We study the impact of the Landau-Pomeranchuk-Midgal (LPM) effect on the dynamics of parton interactions in proton-proton collisions at energies available at the CERN Large Hadron Collider. For our investigation we utilize a microscopic kinetic theory based on the Boltzmann equation. The calculation traces the space-time evolution of the cascading partons interacting via semihard pQCD scatterings and fragmentations. We focus on the impact of the LPM effect on the production of charm quarks, since their production is exclusively governed by processes well described in our kinetic theory. The LPM effect is found to become more prominent as the collision energy rises and at central rapidities, and may significantly affect the model's predicted charm distributions at low momenta.

We study the manifestation of the ${\mathrm{\Delta }}^{++}-{\mathrm{\Delta }}^{-}$ component of the deuteron wave function in the exclusive reaction $\overline{p}d\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$. Due to the large binding energy the internal motion in the $\mathrm{\Delta }-\mathrm{\Delta }$ system is relativistic. We take this into account within the light-cone (LC) wave function formalism and, indeed, found large differences between calculations based on the LC and nonrelativistic (NR) wave functions. We demonstrate that the consistent LC treatment of the $\mathrm{\Delta }-\mathrm{\Delta }$ system plays the key role in the separation of the signal and background. Within the LC approach, the characteristic shape of the momentum distribution of the $\mathrm{\Delta }-\mathrm{\Delta }$ bound system predicted by the meson-exchange model is well visible on the background of usual annihilations at beam momenta between 10 and 15 GeV/$c$.

We carry out simulations using a multiphase transport (AMPT) model to describe the observed flow signatures in $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb collisions. Especially, we calculate the flow fluctuations of $v_2$ in terms of cumulant ratios and the standardized skewness. Based on event-by-event AMPT simulations, we study the linear and cubic response relation between $v_2$ and ${\varepsilon }_2$. We found that the observed response relation is compatible to what has been noticed in hydrodynamic modelings, with similar dependence on shear viscosity. Besides, this response relation is not sensitive to nonflow effects.

The correlation of the tidal polarizabilities ${\mathrm{\Lambda }}_1-{\mathrm{\Lambda }}_2$ for GW170817 is predicted by combining dense-matter equations of state (EOSs) that satisfy nuclear physics constraints with the chirp mass and mass asymmetry for this event. Our models are constrained by calculations of the neutron-matter EOS using chiral effective field theory Hamiltonians with reliable error estimates up to once or twice the nuclear saturation density. In the latter case, we find that GW170817 does not improve our understanding of the EOS. We contrast two distinct extrapolations to higher density: a minimal model (MM) which assumes that the EOS is a smooth function of density described by a Taylor expansion and a more general model parametrized by the speed of sound that admits phase transitions. This allows us to identify regions in the ${\mathrm{\Lambda }}_1-{\mathrm{\Lambda }}_2$ plots that could favor the existence of new phases of matter in neutron stars. We predict the combined tidal polarizability of the two neutron stars in GW170817 to be $80\le \tilde{\mathrm{\Lambda }}\le 580$ ($280\le \tilde{\mathrm{\Lambda }}\le 480$ for the MM), which is smaller than the range suggested by the LIGO-Virgo data analysis. Our analysis also shows that GW170817 requires a NS with $M=1.4M_{\odot }$ to have a radius $9.0\text{km}<R_{1.4}<13.6\text{km}$ ($11.3\text{km}<R_{1.4}<13.6\text{km}$ for the MM).

We present a self-consistent theory for the description of the spectroscopic properties of odd nuclei, which includes exact blocking, particle-number and angular-momentum projection, and configuration mixing. In our theory the pairing correlations are treated in a variation-after-projection approach and the triaxial deformation parameters are explicitly considered as generator coordinates. The angular-momentum and particle-number symmetries are exactly recovered. The use of the effective finite-range density-dependent Gogny force in the calculations provides an added value to the theoretical results. We apply the theory to the textbook example of ${}^{25}\mathrm{Mg}$ and, although this nucleus has been thoroughly studied in the past, we still provide a novel view of nuclear phenomena taking place in this nucleus. We obtain an overall good agreement with the known experimental energies and transition probabilities without any additional parameter such as effective charges. In particular, we clearly identify six bands, two of which we interpret as collective $\gamma$ bands.

In the rapid shape change from spherical to deformed nuclei in the $Z=40$ Zr isotopic chain, recent work has identified shape coexistence in ${}^{96}\mathrm{Zr}$. Between ${}^{96}\mathrm{Zr}$ and the strongly deformed ${}^{100}\mathrm{Zr}, {}^{98}\mathrm{Zr}$ is expected to also exhibit coexistence of nuclear shapes. The degree of mixing between different configurations is mainly determined by the nucleon-nucleon interactions. For nuclear model predictions, experimental constraints are needed, but they are barely available for ${}^{98}\mathrm{Zr}$. To study low-lying transitions in ${}^{98}\mathrm{Zr}$, a Coulomb excitation experiment was conducted at the Argonne Tandem-Linac Accelerator System (ATLAS) facility using a ${}^{98}\mathrm{Zr}$ beam extracted from the Californium Rare Ion Breeder Upgrade (CARIBU) ion source and Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA) for $\gamma$-ray spectroscopy coupled to the compact heavy ion counter (CHICO2) for ion detection. This paper reports on the first decisive deduction of the $B(E2;2_1^{+}\to 0_1^{+})$ transition strength in ${}^{98}\mathrm{Zr}$ and on its interpretation.

A key question concerning the spherical-vibrator attributes of states in cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular nonyrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states as observed in ${}^{110}\mathrm{Cd}$.

We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. We use and briefly review a plane-wave-based discrete variable representation, which allows a convenient implementation of periodic boundary conditions. With these calculations we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multibody resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist.

Background: The mass, or binding energy, is the basis property of the atomic nucleus. It determines its stability and reaction and decay rates. Quantifying the nuclear binding is important for understanding the origin of elements in the universe. The astrophysical processes responsible for the nucleosynthesis in stars often take place far from the valley of stability, where experimental masses are not known. In such cases, missing nuclear information must be provided by theoretical predictions using extreme extrapolations. To take full advantage of the information contained in mass model residuals, i.e., deviations between experimental and calculated masses, one can utilize Bayesian machine-learning techniques to improve predictions.

Purpose: To improve the quality of model-based predictions of nuclear properties of rare isotopes far from stability, we consider the information contained in the residuals in the regions where the experimental information exist. As a case in point, we discuss two-neutron separation energies $S_{2n}$ of even-even nuclei. Through this observable, we assess the predictive power of global mass models towards more unstable neutron-rich nuclei and provide uncertainty quantification of predictions.

Methods: We consider 10 global models based on nuclear density functional theory with realistic energy density functionals as well as two more phenomenological mass models. The emulators of $S_{2n}$ residuals and credibility intervals (Bayesian confidence intervals) defining theoretical error bars are constructed using Bayesian Gaussian processes and Bayesian neural networks. We consider a large training dataset pertaining to nuclei whose masses were measured before 2003. For the testing datasets, we considered those exotic nuclei whose masses have been determined after 2003. By establishing statistical methodology and parameters, we carried out extrapolations toward the $2n$ dripline.

Results: While both Gaussian processes and Bayesian neural networks reduce the root-mean-square (rms) deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power of microscopic models aided by the statistical treatment is quite astonishing: The resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. We found that Bayesian neural networks results are prone to instabilities caused by the large number of parameters in this method. Moreover, since the classical sigmoid activation function used in this approach has linear tails that do not vanish, it is poorly suited for a bounded extrapolation. The empirical coverage probability curves we obtain match very well the reference values, in a slightly conservative way in most cases, which is highly desirable to ensure honesty of uncertainty quantification. The estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models and also make quantified predictions using groups of models.

Conclusions: The proposed robust statistical approach to extrapolation of nuclear model results can be useful for assessing the impact of current and future experiments in the context of model developments. The new Bayesian capability to evaluate residuals is also expected to impact research in the domains where experiments are currently impossible, for instance, in simulations of the astrophysical $r$ process.

A hybrid (hydrodynamics + hadronic transport) theoretical framework is assembled to model the bulk dynamics of relativistic heavy-ion collisions at energies accessible in the beam energy scan program at the Relativistic Heavy-Ion Collider and the NA61/SHINE experiment at CERN. The system's energy-momentum tensor and net-baryon current are evolved according to relativistic hydrodynamics with finite shear viscosity and nonzero net-baryon diffusion. Our hydrodynamic description is matched to a hadronic transport model in the dilute region. With this fully integrated theoretical framework, we present a pilot study of the hadronic chemistry, particle spectra, and anisotropic flow. Phenomenological effects of a nonzero net-baryon current and its diffusion on hadronic observables are presented for the first time. The importance of the hadronic transport phase is also investigated.

The dependence of the nuclear level density on intrinsic deformation is an important input to dynamical nuclear processes such as fission. The auxiliary-field Monte Carlo (AFMC) method is a powerful method for computing state densities. However, the statistical distribution of intrinsic shapes is not readily accessible due to the formulation of the AFMC method in a spherical configuration-interaction shell-model approach. Instead, the theory of deformation has largely relied on a mean-field approximation which breaks rotational symmetry. We show here how the distributions of the intrinsic quadrupole deformation parameters can be calculated within the AFMC method and present results for a chain of even-mass samarium nuclei (${}^{148}\mathrm{Sm}, {}^{150}\mathrm{Sm}, {}^{152}\mathrm{Sm}, {}^{154}\mathrm{Sm}$) which includes spherical, transitional, and strongly deformed isotopes. The method relies on a Landau-like expansion of the Helmholtz free energy in invariant polynomials of the quadrupole tensor. We find that an expansion to fourth order provides an excellent description of the AFMC results.

The precision of the current generation of cosmic-ray (CR) experiments, such as AMS-02, PAMELA, CALET, and ISS-CREAM, is now reaching $\approx 1–3\%$ in a wide range in energy per nucleon from GeV/nucleon to multi-TeV/nucleon. Their correct interpretation could potentially lead to discoveries of new physics and subtle effects that were unthinkable just a decade ago. However, a major obstacle in doing so is the current uncertainty in the isotopic production cross sections that can be as high as 20–50% or even larger in some cases. While there is a recently reached consensus in the astrophysics community that new measurements of cross sections are desirable, no attempt to evaluate the importance of particular reaction channels and their required precision has been made yet. It is, however, clear that it is a huge work that requires an incremental approach. The goal of this study is to provide the ranking of the isotopic cross sections contributing to the production of the most astrophysically important CR Li, Be, B, C, and N species. In this paper, we (i) rank the reaction channels by their importance for a production of a particular isotope, (ii) provide comparisons plots between the models and data used, and (iii) evaluate a generic beam time necessary to reach a 3% precision in the production cross sections pertinent to the AMS-02 experiment. This first road map may become a starting point in the planning of new measurement campaigns that could be carried out in several nuclear and/or particle physics facilities around the world. A comprehensive evaluation of other isotopes $Z\le 30$ will be a subject of follow-up studies.

In proton-nucleus and nucleus-nucleus collision experiments, one determines the centrality of a collision according to the multiplicity or energy deposited in a detector. This serves as a proxy for the true collision centrality, as defined by the impact parameter. We show that the probability distribution of impact parameter in a given bin of experiment-defined centrality can be reconstructed without assuming any specific model for the collision dynamics, in both proton-nucleus and nucleus-nucleus systems. The reconstruction is reliable up to about 10% centrality, and is more accurate for nucleus-nucleus collisions. We perform an application of our procedure to experimental data from all the CERN Large Hadron Collider collaborations, from which we extract, in Pb+Pb and $p$+Pb collisions, the corresponding distributions of impact parameter.

The structure of even-even ${}^{108–116}\mathrm{Cd}$ isotopes is investigated based on the self-consistent mean-field approach. By mapping the quadrupole-$(\beta ,\gamma )$ deformation energy surface, obtained from the constrained self-consistent mean-field calculations with a choice of the Skyrme force and pairing property, onto the Hamiltonian of the interacting boson model with configuration mixing, the strength parameters of the Hamiltonian are determined. The low-lying excitation spectra and electric quadrupole and monopole transition rates for the considered Cd nuclei are computed by the resultant Hamiltonian, and are compared in detail with the experimental data. Our semimicroscopic prediction identifies several intruder states as suggested empirically, and overall, provides a reasonable qualitative description of the experimental energy levels and transition rates.

Background: Many nuclear-structure features have been observed in actinides in recent decades. In particular, the octupole degree of freedom has been discussed lately after the successful measurement of the $B\left(E3;0_1^{+}\to 3_1^{-}\right)$ reduced transition strength in ${}^{224}\mathrm{Ra}$. Recent results stemming from $\gamma$-spectroscopy experiments and high-resolution $(p,t)$ experiments suggested that strong octupole correlations might be observed for some positive-parity states of actinide nuclei.

Purpose: This work completes a series of $(p,t)$ experiments on actinide nuclei by adding the data on ${}^{240}\mathrm{Pu}$. The $(p,t)$ experiments allow us to study low-spin states up to $J^{\pi }=6^{+}$. Besides two-nucleon transfer cross sections, spin and parity can be assigned to excited states by measuring angular distributions, and several rotational bands are recognized based on these assignments.

Methods: A high-resolution (p,t) experiment at $E_p=24$ MeV was performed to populate low-spin states in the actinide nucleus ${}^{240}\mathrm{Pu}$. The Q3D magnetic spectrograph of the Maier-Leibnitz Laboratory (MLL) in Munich (Germany) was used to identify the ejected tritons via $dE/E$ particle identification with its focal-plane detection system. Angular distributions were measured at nine different Q3D angles to assign spin and parity to the excited states based on a comparison with coupled-channel distorted-wave Born approximation calculations.

Results: In total, 209 states have been excited in ${}^{240}\mathrm{Pu}$ up to an excitation energy of 3 MeV. Many previously known states have also been observed and their spin-parity assignments were confirmed. However, many of the populated states have been seen for the first time, e.g., 15 new and firmly assigned $J^{\pi }=0^{+}$ states. In addition, all low-spin one-octupole phonon excitations, i.e., $K^{\pi }=0^{-},1^{-},2^{-},3^{-}$, could be observed and a new candidate for the $K=3$ projection is proposed. Furthermore, the double-octupole or $\alpha$-cluster structure of the $0_2^{+}$ state in ${}^{240}\mathrm{Pu}$ has been studied in more detail. It is shown that the $0_2^{+}$ state in ${}^{230}\mathrm{Th}$ has a distinctly different structure. In addition, strongly excited $1^{-}$ states have been observed at 1.5 and 1.8 MeV in ${}^{240}\mathrm{Pu}$. The present study suggests that similar states might be observed in ${}^{230}\mathrm{Th}$.

Conclusions: At least two different and distinct structures for $J^{\pi }=0^{+}$ states are present in the actinides. These are pairing states and states with enhanced octupole correlations. We have shown that it is crucial to consider negative-parity single-particle states being admixed to some $K^{\pi }=0_2^{+}$ rotational bands to understand the $\alpha$-decay hindrance factors and enhanced $E1$-decay rates. Based on our analysis, we have identified the double-octupole or $\alpha$-cluster $K^{\pi }=0^{+}$ candidates from ${}^{224}\mathrm{Ra}$ to ${}^{240}\mathrm{Pu}$.