As part of a continuing effort to test the unitarity of the Cabbibo-Kobayashi-Maskawa matrix, we have measured the branching ratio for the superallowed $0^{+}\to 0^{+}{\beta }^{+}$-decay transition from ${}^{26}\mathrm{Si}$ to be 0.7569(14), a result with 0.18% relative precision. With this result, the $ft$ value for the transition is now established with comparable precision to the well-known superallowed transitions currently used in the determination of $V_{ud}$. It also completes a second pair of mirror superallowed transitions, ${}^{26}\mathrm{Si}$ $\to$ ${}^{26m}\mathrm{Al}$ and ${}^{26m}\mathrm{Al}$ $\to$ ${}^{26}\mathrm{Mg}$, the ratio of whose measured $ft$ values provides a sensitive test of the method used to calculate the isospin-symmetry-breaking correction ${\delta }_C$ needed to determine $V_{ud}$. Like the previously measured ratio for the mass-38 mirror pair, the new result agrees well with the calculation based on Woods-Saxon radial wave functions and strengthens the case for rejecting the calculation that uses Hartree-Fock radial functions.

We develop a novel approach to fusion reactions for synthesis of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugged into the dynamical diffusion model as an initial condition. We apply this approach to hot fusion reactions leading to formation of the element $Z=120$, that is, the ${}^{48}\mathrm{Ca}+{}^{254,257}\mathrm{Fm}$, ${}^{51}\mathrm{V}+{}^{249}\mathrm{Bk}$, and ${}^{54}\mathrm{Cr}+{}^{248}\mathrm{Cm}$ reactions. Our calculations indicate that the distances of the closest approach for these systems are similar to each other and thus the difference in the probabilities of evaporation residue formation among those reaction systems originates mainly from the evaporation process, which is sensitive to the fission barrier height and the excitation energy of a compound nucleus.

Background: The Nijmegen extended-soft-core (ESC) models describe the nucleon-nucleon (NN), hyperon-nucleon (YN), and the $S=-2$ hyperon-hyperon/nucleon ($YY/\mathrm{\Xi }N$) interactions in a unified way using broken SU(3) symmetry. The potentials consist of local and nonlocal potentials due to (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial-vector mesons, (ii) two pseudoscalar exchange (TPS), (iii) meson-pair exchange (MPE), and (iv) diffractive exchanges. Both the OBE and pair vertices are regulated by Gaussian form factors producing potentials with a soft behavior near the origin. Broken SU(3) symmetry serves to connect the NN, YN, and YY channels. In particular, the meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the NN analysis as input. The assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices is dependent on the SU(3) classification of the exchanged mesons for OBE and a similar scheme for MPE.

Purpose: The $S=-1$ YN results are presented from a new version ESC16 of the ESC potential model for baryon-baryon (BB) scattering. The obtained two-body BB potentials are applied to the hyperonic many-body systems as well. Next to the standard ingredients of the ESC models, a contribution of the possible short-range repulsion due to the quark Pauli principle in the BB channels is described in a systematic way for the first time.

Methods: Major novel ingredients with respect to the former versions ESC04–ESC08 are the inclusion of (i) short-range Gaussian Odderon potentials corresponding to the odd numbers of gluon exchanges next to the Pomeron potentials due to even gluon exchanges and (ii) short-range repulsion in all NN, YN, and YY channels due to Pauli-forbidden six-quark cluster ${\left(0s\right)}^6$ configurations. Further new elements are (i) the extension of the $J^{PC}=1^{++}$ axial-vector meson coupling, (ii) the inclusion of the $J^{PC}=1^{+-}$ axial-vector mesons, (iii) a completion of the $1/M$ corrections for the meson-pair-exchange (MPE) potentials, and (iv) the treatment of the scalar $\kappa \left(861\right)$ meson within the Gell-Mann-Okubo (GMO) meson-mixing scheme and as a broad meson, like the $\rho \left(760\right)$ and $\epsilon \left(620\right)$. In contrast to ESC04, we do not consider medium strong flavor-symmetry breaking (FSB) of the coupling constants. The charge-symmetry breaking (CSB) in the $\mathrm{\Lambda }p$ and $\mathrm{\Lambda }n$ channels, which is an SU(2) isospin breaking, is included in the OBE, TPS, and MPE potentials. In addition to the usual set of 35 YN data and 3 ${\mathrm{\Sigma }}^{+}p$ cross sections from the recent KEK-E289 experiment, we added 11 elastic and inelastic $\mathrm{\Lambda }p$ and three elastic ${\mathrm{\Sigma }}^{-}p$ cross sections at higher energy. For the ESC16 model, we performed a simultaneous fit to the combined NN and YN scattering data, supplied with constraints on the YN and YY interaction originating from the $G$-matrix information on hypernuclei.

Results: The fitting of NN dominates the determination of the couplings and the cutoff masses. Only a few parameters are strongly influenced by the YN data and by the constraints for the YY interactions following from $G$-matrix analyses of hypernuclei and hyperonic matter. Like in the ESC04 model, the obtained octet and singlet coupling constants and $F/(F+D)$ ratios of the model confirm the predictions of the quark-antiquark pair-creation (QPC) model with dominance of the ${}^{3}P_0$ mechanism. This not only for the OBE couplings but also for the MPE couplings and $F/(F+D)$ ratios. We obtained within this simultaneous fit ${\chi }^2/N{N}_{\mathrm{data}}=1.10$ and ${\chi }^2/Y{N}_{\mathrm{data}}=1.04$. In particular, we were able to fit the precise experimental datum $r_R=0.468\pm 0.010$ for the inelastic ${\mathrm{\Sigma }}^{-}p$ capture ratio at rest very well.

Conclusions: Besides the good results for the fit to the $S=-1$ scattering data, which to a large extent defines the model, also the information of hypernuclear systems, using the $G$-matrix method, is rather important in establishing the complete ESC model. Different versions of the model give somewhat different results for hypernuclei. The reported $G$-matrix calculations are performed for YN ($\mathrm{\Lambda }N$ and $\mathrm{\Sigma }N$) in nuclear matter and also for some hypernuclei. The obtained well depths ($U_{\mathrm{\Lambda }}$, $U_{\mathrm{\Sigma }}$, $U_{\mathrm{\Xi }}$) reveal distinct features of the ESC model. The inclusion of a quark core Pauli repulsion can make the $\mathrm{\Sigma }$-nucleus interaction less attractive, as seems to be required by the available experimental evidence. Furthermore, the ESC16 model gives small spin-orbit splittings in $\mathrm{\Lambda }$ hypernuclei, which is also indicated by experiment.

Background: Correlations from charge correlation, known as charge balance functions, provide critical tests of the chemical evolution of matter in a heavy-ion collision. Comparisons of experimental balance functions with calculations from parametric descriptions of the final state suggest that the charge production in the earliest stages of a heavy-ion collision are consistent with having generated an amount of light up, down, and strange quarks that are largely consistent with expectations for creating a chemically equilibrate quark-gluon plasma.

Purpose: This work describes a full simulation of the evolving correlations superimposed on a state-of-the-art microscopic description of the collision.

Methods: The creation and diffusion of balancing charges is modeled on the background of a hybrid description of the evolution based on hydrodynamics, for when the matter's temperature is above 155 MeV, and a microscopic hadronic simulation, for the breakup stage. The translation of the charge-charge correlation function, indexed by the flavors up, down, and strange, into correlations between specific hadron species is built on the assumption that differential charges enhance differential yields according to statistical equilibrium. Monte Carlo methods are implemented when applicable.

Results: The charge balance functions are predicted for pairs indexed by charge alone or by whether the particle pairs are any combination of pions, kaons, or protons. Comparisons with experiment are remarkably successful except for the proton-kaon balance functions.

Conclusions: This demonstrates first that two-particle correlations from charge conservation can be calculated for a state-of-the-art model of the evolution with moderate amounts of computation. Aside from the magnitude of the proton-kaon correlations, the calculations well describe preliminary experimental results from the STAR Collaboration at the Relativistic Heavy Ion Collider. Ignoring the one disagreement, this suggests that the matter in a heavy-ion collision comes close to maintaining chemical equilibrium during the superhadronic stage of a heavy-ion collision.

Neutron-deficient ${}^{177-185}\mathrm{Hg}$ isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility in an experiment combining different detection methods tailored to the studied isotopes. These include either α-decay tagging or multireflection time-of-flight gating for isotope identification. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of ${}^{177-180}\mathrm{Hg}$. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole, and electric quadrupole moments of the odd-$A$ isotopes and arguments in favor of $I=7/2$ spin assignment for ${}^{177,179}\mathrm{Hg}$ were deduced. Experimental results are compared with density functional theory (DFT) and Monte Carlo shell model (MCSM) calculations. DFT calculations using Skyrme parametrizations predict a jump in the charge radius around the neutron $N=104$ midshell, with an odd-even staggering pattern related to the coexistence of nearly degenerate oblate and prolate minima. This near-degeneracy is highly sensitive to many aspects of the effective interaction, a fact that renders perfect agreement with experiments out of reach for current functionals. Despite this inherent difficulty, the SLy5s1 and a modified $\mathrm{UNEDF}{1}^{\mathrm{SO}}$ parametrization predict a qualitatively correct staggering that is off by two neutron numbers. MCSM calculations of states with the experimental spins and parities show good agreement for both electromagnetic moments and the observed charge radii. A clear mechanism for the origin of shape staggering within this context is identified: a substantial change in occupancy of the proton $\pi h_{9/2}$ and neutron $\nu i_{13/2}$ orbitals.

The deuteron yield in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ is consistent with thermal production at a freeze out temperature of $T=155\mathrm{MeV}$. The existence of deuterons with binding energy of 2.2 MeV at this temperature was described as “snowballs in hell” [P. Braun-Münzinger, B. Dönigus, and N. Löher, CERN Courier, August 2015]. We provide a microscopic explanation of this phenomenon, utilizing relativistic hydrodynamics and switching to a hadronic afterburner at the above-mentioned temperature of $T=155\mathrm{MeV}$. The measured deuteron $p_T$ spectra and coalescence parameter $B_2\left(p_T\right)$ are reproduced without free parameters, only by implementing experimentally known cross sections of deuteron reactions with hadrons, most importantly $\pi d\leftrightarrow \pi np$.

Background: While coupled-cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ameliorated by permitting the mean-field reference to break physical symmetries. Symmetry-broken coupled-cluster, e.g., Bogoliubov-coupled-cluster, theory can indeed provide reasonably accurate energetic predictions, but the broken symmetry can compromise the quality of the resulting wave function and predictions of observables other than the energy.

Purpose: Merging symmetry projection and coupled-cluster theory is therefore an appealing way to describe strongly correlated systems. One indeed expects to inherit and further improve the energetic accuracy of broken-symmetry coupled cluster while retaining proper symmetries.

Methods: Independently, two different but related formalisms have been recently proposed to achieve this goal. The two formalisms are contrasted in this manuscript, with results tested on the Richardson pairing Hamiltonian. While the present paper focuses on the breaking and restoration of $U\left(1\right)$ global-gauge symmetry associated with particle-number conservation, the symmetry-projected coupled-cluster formalism is applicable to other symmetries such as rotational (i.e., spin) symmetry.

Results: Both formalisms are based on the disentangled cluster representation of the symmetry-rotated coupled-cluster wave function. However, they differ in the way that the disentangled clusters are solved. One approach sets up angle-dependent coupled-cluster equations, while the other involves first-order ordinary differential equations. The latter approach yields energies and occupation probabilities significantly better than those of number-projected Bardeen-Cooper-Schrieffer (BCS) and BCS coupled cluster and, when the disentangled clusters are truncated at low excitation levels, has a computational cost not too much larger than that of BCS coupled cluster.

Conclusions: The high quality of results presented in this manuscript indicates that symmetry-projected coupled cluster is a promising method that can accurately describe both weakly and strongly correlated finite many-fermion systems.

We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations of nuclei. Our focus is on novel basis sets defined by the natural orbitals of a correlated one-body density matrix that is obtained in second-order many-body perturbation theory. Using a perturbatively improved density matrix as the starting point informs the single-particle basis about the dominant correlation effects on the global structure of the many-body state, while keeping the computational cost for the basis optimization at a minimum. Already the comparison of the radial single-particle wave functions reveals the superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We compare the model-space convergence of energies, root-mean-square radii, and selected electromagnetic observables for all three basis sets for selected $p$-shell nuclei using chiral interactions with explicit three-nucleon terms. In all cases the natural-orbital basis provides the fastest and most robust convergence, making it the most efficient basis for no-core shell model calculations. As an application we present no-core shell model calculations for the ground-state energies of all oxygen isotopes and assess the accuracy of the normal-ordered two-body approximation of the three-nucleon interaction in the natural-orbital basis.

The longitudinal proton-proton femtoscopy (Hanbury Brown–Twiss) correlation function, based on the idea that in a heavy-ion collision at $\sqrt{s}\lesssim 20\mathrm{GeV}$ stopped protons are likely to be separated in configuration space, is evaluated. It shows a characteristic oscillation which appears sufficiently pronounced to be accessible in experiment. The proposed measurement is essential for estimating the baryon density in the central rapidity region and can be also viewed as an (almost) direct verification of the Lorentz contraction of the fast-moving nucleus.

We calculate the electromagnetic (charge, magnetic, and quadrupole) form factors and the associated static moments of heavy quarkonia (charmonia and bottomonia) using the basis light front quantization (BLFQ) approach. For this work, we adopt light front wave functions (LFWFs) generated by a holographic QCD confining potential and a one-gluon exchange interaction with fixed coupling. We compare our BLFQ results with the limiting case of a single BLFQ basis state description of heavy quarkonia and with other available results. These comparisons provide insights into relativistic effects. Using the same LFWFs generated in the BLFQ approach, we also present the generalized parton distributions (GPDs) for selected mesons including those for radially excited mesons such as ${\psi }^{\prime }$ and ${\mathrm{{\rm Y}}}^{\prime }$. Our GPD results establish the foundation within BLFQ for further investigating hadronic structure such as probing the spin structure of spin-one hadrons in the off-forward limit.

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.