We perform a comprehensive Weinberg eigenvalue analysis of a representative set of modern nucleon-nucleon interactions derived within chiral effective field theory. Our set contains local, semilocal, and nonlocal potentials, developed by Gezerlis et al. [Phys. Rev. Lett. 111, 032501 (2013)], Epelbaum et al. [Phys. Rev. Lett. 115, 122301 (2015)] and Entem et al. [Phys. Rev. C 96, 024004 (2017)] as well as Carlsson et al. [Phys. Rev. X 6, 011019 (2016)], respectively. The attractive eigenvalues show a very similar behavior for all investigated interactions, whereas the magnitudes of the repulsive eigenvalues sensitively depend on the details of the regularization scheme of the short- and long-range parts of the interactions. We demonstrate that a direct comparison of numerical cutoff values of different interactions is in general misleading due to the different analytic form of regulators; for example, a cutoff value of $R=0.8$ fm for the semilocal interactions corresponds to about $R=1.2$ fm for the local interactions. Our detailed comparison of Weinberg eigenvalues provides various insights into idiosyncrasies of chiral potentials for different orders and partial waves. This shows that Weinberg eigenvalues could be used as a helpful monitoring scheme when constructing new interactions.

Background: Nuclear matter fourth-order symmetry energy $E_{\text{sym,4}}\left(\rho \right)$ may significantly influence the properties of neutron stars such as the core-crust transition density and pressure as well as the proton fraction at high densities. The magnitude of $E_{\text{sym,4}}\left(\rho \right)$ is, however, largely uncertain.

Purpose: Based on systematic analyses of several popular nonrelativistic energy density functionals with mean-field approximation, we estimate the value of the $E_{\text{sym,4}}\left(\rho \right)$ at nuclear normal density ${\rho }_0$ and its density dependence, and explore the correlation between $E_{\text{sym,4}}\left({\rho }_0\right)$ and other macroscopic quantities of nuclear matter properties.

Method: We use the empirical values of some nuclear macroscopic quantities to construct model parameter sets by the Monte Carlo method for four different energy density functionals with mean-field approximation, namely, the conventional Skyrme-Hartree-Fock (SHF) model, the extended Skyrme-Hartree-Fock (eSHF) model, the Gogny-Hartree-Fock (GHF) model, and the momentum-dependent interaction (MDI) model. With the constructed samples of parameter sets, we can estimate the density dependence of $E_{\text{sym,4}}\left(\rho \right)$ and analyze the correlation of $E_{\text{sym,4}}\left({\rho }_0\right)$ with other macroscopic quantities.

Results: The value of $E_{\text{sym,4}}\left({\rho }_0\right)$ is estimated to be $1.02\pm 0.49$ MeV for the SHF model, $1.02\pm 0.50$ MeV for the eSHF model, $0.70\pm 0.60$ MeV for the GHF model, and $0.74\pm 0.63$ MeV for the MDI model. Moreover, our results indicate that the density dependence of $E_{\text{sym,4}}\left(\rho \right)$ is model dependent, especially at higher densities. Furthermore, we find that the $E_{\text{sym},4}\left({\rho }_0\right)$ has strong positive (negative) correlation with isoscalar (isovector) nucleon effective mass $m_{s,0}^{*}$ ($m_{v,0}^{*}$) at ${\rho }_0$. In particular, for the SHF and eSHF models, the $E_{\text{sym,4}}\left(\rho \right)$ is completely determined by the isoscalar and isovector nucleon effective masses $m_s^{*}\left(\rho \right)$ and $m_v^{*}\left(\rho \right)$, and the analytical expression is given.

Conclusions: In the mean-field models, the magnitude of $E_{\text{sym,4}}\left({\rho }_0\right)$ is generally less than $2\mathrm{MeV}$, and its density dependence depends on models, especially at higher densities. $E_{\text{sym,4}}\left({\rho }_0\right)$ is strongly correlated with $m_{s,0}^{*}$ and $m_{v,0}^{*}$.

The charged-particle multiplicity distribution and the transverse-energy distribution measured in heavy-ion collisions at top RHIC and LHC energies are described using the two-component model approach based on a convolution of the Monte Carlo Glauber model with the Weibull model for particle production. The model successfully describes the multiplicity and transverse-energy distribution of minimum-bias collision data for a wide range of energies. The Weibull-Glauber model can be used to determine the centrality classes in heavy-ion collisions as an alternative to the conventional negative binomial distribution (NBD)-Glauber approach.

Background: Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective degrees of freedom.

Purpose: To predict the spectroscopic properties of odd-mass medium-heavy and heavy nuclei with a model that treats single-particle and collective degrees of freedom within the same microscopic framework.

Method: A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed that contains the collective excitations of even-mass cores and spherical single-particle states of the odd nucleon as calculated from a quadrupole collective Hamiltonian combined with a constrained triaxial relativistic Hartree-Bogoliubov model.

Results: Predictions of the new model for excitation energies, kinematic and dynamic moments of inertia, and transition rates are shown to be in good agreement with results of low-lying spectroscopy measurements of the axially deformed odd-proton nucleus ${}^{159}\mathrm{Tb}$ and the odd-neutron nucleus ${}^{157}\mathrm{Gd}$.

Conclusions: A microscopic CQC model based on covariant density functional theory is developed for odd-mass nuclei and shown to give predictions that agree with measurements of two medium-heavy nuclei. Future studies with additional nuclei are planned.

We use the generator-coordinate method (GCM) with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-$\beta$ decay of ${}^{48}\mathrm{Ca}$, ${}^{76}\mathrm{Ge}$, and ${}^{82}\mathrm{Se}$. We work in one major shell for the first isotope, in the $f_{5/2}p{g}_{9/2}$ space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter $\beta$, but also the triaxiality angle $\gamma$ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.

We argue that statistical data analysis of two-particle longitudinal correlations in ultrarelativistic heavy-ion collisions may be efficiently carried out with the technique of partial covariance. In this method, the spurious event-by-event fluctuations due to imprecise centrality determination are eliminated via projecting out the component of the covariance influenced by the centrality fluctuations. We bring up the relationship of the partial covariance to the conditional covariance. Importantly, in the superposition approach, where hadrons are produced independently from a collection of sources, the framework allows us to impose centrality constraints on the number of sources rather than hadrons, that way unfolding of the trivial fluctuations from statistical hadronization and focusing better on the initial-state physics. We show, using simulated data from hydrodynamics followed with statistical hadronization, that the technique is practical and very simple to use, giving insight into the correlations generated in the initial stage. We also discuss the issues related to separation of the short- and long-range components of the correlation functions and show that in our example the short-range component from the resonance decays is largely reduced by considering pions of the same sign. We demonstrate the method explicitly on the cases where centrality is determined with a single central control bin or with two peripheral control bins.

The STAR Collaboration reports on the photoproduction of ${\pi }^{+}{\pi }^{-}$ pairs in gold-gold collisions at a center-of-mass energy of 200 GeV/nucleon-pair. These pion pairs are produced when a nearly real photon emitted by one ion scatters from the other ion.

We fit the ${\pi }^{+}{\pi }^{-}$ invariant-mass spectrum with a combination of ${\rho }^0$ and $\omega$ resonances and a direct ${\pi }^{+}{\pi }^{-}$ continuum. This is the first observation of the $\omega$ in ultraperipheral collisions, and the first measurement of $\rho \text{−}\omega$ interference at energies where photoproduction is dominated by Pomeron exchange. The $\omega$ amplitude is consistent with the measured $\gamma p\to \omega p$ cross section, a classical Glauber calculation, and the $\omega \to {\pi }^{+}{\pi }^{-}$ branching ratio. The $\omega$ phase angle is similar to that observed at much lower energies, showing that the $\rho \text{−}\omega$ phase difference does not depend significantly on photon energy.

The ${\rho }^0$ differential cross section $d\sigma /dt$ exhibits a clear diffraction pattern, compatible with scattering from a gold nucleus, with two minima visible. The positions of the diffractive minima agree better with the predictions of a quantum Glauber calculation that does not include nuclear shadowing than with a calculation that does include shadowing.

The dependence of multiproton correlation functions and cumulants on the acceptance in rapidity and transverse momentum is studied. We find that the preliminary data of various cumulant ratios are consistent, within errors, with rapidity and transverse momentum-independent correlation functions. However, rapidity correlations which moderately increase with rapidity separation between protons are slightly favored. We propose to further explore the rapidity dependence of multiparticle correlation functions by measuring the dependence of the integrated reduced correlation functions as a function of the size of the rapidity window.

Continuing the study of suprathermal effects in the solar core [Phys. Rev. C 91, 028801 (2015); J. Phys. G 44, 045202 (2017)], we examine the roles of different $pp$ chain processes generating fast $\alpha$ particles as trigger for suprathermal $\mathrm{B}(\alpha ,p)\mathrm{A}$ reactions neglected in standard solar model simulations. The suprathermal impact on the balance of the $p{+}^{17}\mathrm{O}\rightleftarrows \alpha {+}^{14}\mathrm{N}$ reactions involved in the solar CNO cycle is determined. It is obtained that MeV $\alpha$ particles born in the ${}^7\mathrm{Li}(p,\alpha )\alpha$ and ${}^3\mathrm{He}{(}^3\mathrm{He},2p)\alpha$ reactions are the main agents that are able to crucially change the reaction balance through an appreciable enhancement of the reverse $(\alpha ,p)$ reaction. The comparative role of the $p{+}^7\mathrm{Li}$ and ${}^3\mathrm{He}{+}^3\mathrm{He}\alpha$ particles is clarified. It is found that the former particles control the reverse ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ reaction in the inner core, while the latter ones play a dominant role in the outer core, additionally increasing the $(\alpha ,p)$ reaction rate by several times and providing favorable conditions for synthesis of some elements. In particular, we show that the total suprathermal enhancement of ${}^{17}\mathrm{O}$ and ${}^{18}\mathrm{O}$ mass fractions in the outer core can reach $\sim 80$ or 50, depending on a model for $\alpha$-particle energy loss used in the simulation. In this context, we note that the $p{+}^7\mathrm{Li}\alpha$ particles alone provide the mass fraction enhancement by a factor of 20 or less.

Core collapse supernova simulations can be sensitive to neutrino interactions near the neutrinosphere. This is the surface of last scattering. We model the neutrinosphere region as a warm unitary gas of neutrons. A unitary gas is a low density system of particles with large scattering lengths. We calculate modifications to neutrino scattering cross sections because of the universal spin and density correlations of a unitary gas. These correlations can be studied in laboratory cold atom experiments. We find significant reductions in cross sections, compared to free space interactions, even at relatively low densities. These reductions could reduce the delay time from core bounce to successful explosion in multidimensional supernova simulations.

The shape evolutions of the pear-shaped nuclei ${}^{224}\mathrm{Ra}$ and even-even ${}^{144–154}\mathrm{Ba}$ with temperature are investigated by the finite-temperature relativistic mean field theory with the treatment of pairing correlations by the BCS approach. The free energy surfaces as well as the bulk properties including deformations, pairing gaps, excitation energy, and specific heat for the global minimum are studied. For ${}^{224}\mathrm{Ra}$, three discontinuities found in the specific heat curve indicate the pairing transition at temperature 0.4 MeV and two shape transitions at temperatures 0.9 and 1.0 MeV, namely one from quadrupole-octupole deformed to quadrupole deformed, and the other from quadrupole deformed to spherical. Furthermore, the gaps at $N=136$ and $Z=88$ are responsible for stabilizing the octupole-deformed global minimum at low temperatures. Similar pairing transition at $T\sim 0.5\mathrm{MeV}$ and shape transitions at $T=0.5–2.2\mathrm{MeV}$ are found for even-even ${}^{144–154}\mathrm{Ba}$. The transition temperatures are roughly proportional to the corresponding deformations at the ground states.

The occurrence of low-lying charge-exchange non-spin-flip dipole modes below the giant resonance in neutron-rich nuclei is predicted on the basis of nuclear density functional theory. The ground and excited states are described within the framework of the self-consistent Hartree–Fock–Bogoliubov theory and the proton-neutron quasiparticle-random-phase approximation employing a Skyrme-type energy density functional. The model calculations are performed for the spherical neutron-rich Ca, Ni, and Sn isotopes. It is found that the low-lying states appear sensitive to the shell structure associated with the $-1\hslash {\omega }_0$ excitation below the Gamow–Teller states. Furthermore, the pygmy resonance emerges below the giant resonance when the neutrons occupy the low-$\ell (\ell \le 2–3)$ orbitals analogous to the pygmy resonance seen in the electric-dipole response.

Based on the preformed cluster model, we have carried out a comprehensive theoretical study on the decay paths of ground state actinide and transactinide nuclei, specifically from ${}^{232}\mathrm{U}$ to ${}^{264}\mathrm{Hs}$ exhibiting the phenomenon of spontaneous fission (SF). This is an extension of our earlier studies on $\alpha$ decay, exotic cluster emission, and heavy particle radioactivity, where an effort is made to identify the most probable fragments in the SF process. These observations in turn, could provide a testing ground for future SF half-life measurements. To obtain a clear picture of the dynamics involved, the variations of fragmentation potential, preformation factor, and decay barrier height have been examined. The calculated potential energy surfaces show a change from a predominantly asymmetric fission to a symmetric fragmentation with the increase in the N/Z ratio of parent nuclei. In addition, an exclusive analysis of SF with $\alpha$ and other possible cluster emissions for the ${}^{232,234,236,238}\mathrm{U}$ parents was made to have better insight of nuclear structure information. In other words, the comparative nature of $\alpha$, cluster, heavy fragment, and SF decay paths is analyzed in view of shell closure property of the decay fragments. Interestingly, the calculated decay half-lives for the ${}^{82}\mathrm{Ge}$ heavy cluster are in fact shown to lie within the limits of experiments, thereby presenting themselves as exciting new possibilities which may be validated via future experiments.

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The ${}^{26}\mathrm{F}$ nucleus, composed of a deeply bound $\pi 0d_{5/2}$ proton and an unbound $\nu 0d_{3/2}$ neutron on top of an ${}^{24}\mathrm{O}$ core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^{\pi }=1_1{}^{+}-4_1{}^{+}$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^{\pi }=1_1{}^{+},2_1{}^{+},4_1{}^{+}$ bound states have been determined, and only a clear identification of the $J^{\pi }=3_1{}^{+}$ is missing.

Purpose: We wish to complete the study of the $J^{\pi }=1_1{}^{+}-4_1{}^{+}$ multiplet in ${}^{26}\mathrm{F}$, by studying the energy and width of the $J^{\pi }=3_1{}^{+}$ unbound state. The method was first validated by the study of unbound states in ${}^{25}\mathrm{F}$, for which resonances were already observed in a previous experiment.

Method: Radioactive beams of ${}^{26}\mathrm{Ne}$ and ${}^{27}\mathrm{Ne}$, produced at about $440A\mathrm{MeV}$ by the fragment separator at the GSI facility were used to populate unbound states in ${}^{25}\mathrm{F}$ and ${}^{26}\mathrm{F}$ via one-proton knockout reactions on a ${\mathrm{CH}}_2$ target, located at the object focal point of the ${\mathrm{R}}^3\mathrm{B}$/LAND setup. The detection of emitted $\gamma$ rays and neutrons, added to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the determination of the energy of three unbound states in ${}^{25}\mathrm{F}$ and two in ${}^{26}\mathrm{F}$.

Results: Based on its width and decay properties, the first unbound state in ${}^{25}\mathrm{F}$, at the relative energy of 49(9) keV, is proposed to be a $J^{\pi }=1/2^{-}$ arising from a $p_{1/2}$ proton-hole state. In ${}^{26}\mathrm{F}$, the first resonance at 323(33) keV is proposed to be the $J^{\pi }=3_1{}^{+}$ member of the $J^{\pi }=1_1{}^{+}-4_1{}^{+}$ multiplet. Energies of observed states in ${}^{25,26}\mathrm{F}$ have been compared to calculations using the independent-particle shell model, a phenomenological shell model, and the ab initio valence-space in-medium similarity renormalization group method.

Conclusions: The deduced effective proton-neutron interaction is weakened by about 30–40% in comparison to the models, pointing to the need for implementing the role of the continuum in theoretical descriptions or to a wrong determination of the atomic mass of ${}^{26}\mathrm{F}$.

We present finite-temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean-field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using relativistic mean field theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.

Background: The ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ reaction is one of the neutron sources for the $s$ process in massive stars. The properties of levels in ${}^{26}\mathrm{Mg}$ above the $\alpha$-particle threshold control the strengths of the ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}$($\alpha ,\gamma$)${}^{26}\mathrm{Mg}$ reactions. The strengths of these reactions as functions of temperature are one of the major uncertainties in the $s$ process.

Purpose: Information on the existence, spin, and parity of levels in ${}^{26}\mathrm{Mg}$ can assist in constraining the strengths of the ${}^{22}\mathrm{Ne}$($\alpha ,\gamma$)${}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ reactions, and therefore in constraining $s$-process abundances.

Methods: Inelastically scattered $\alpha$ particles from a ${}^{26}\mathrm{Mg}$ target were momentum-analyzed in the K600 magnetic spectrometer at iThemba LABS, South Africa. The differential cross sections of states were deduced from the focal-plane trajectory of the scattered $\alpha$ particles. Based on the differential cross sections, spin and parity assignments to states are made.

Results: A newly assigned $0^{+}$ state was observed in addition to a number of other states, some of which can be associated with states observed in other experiments. Some of the deduced $J^{\pi }$ values of the states observed in the present study show discrepancies with those assigned in a similar experiment performed at RCNP Osaka. The reassignments and additions of the various states can strongly affect the reaction rate at low temperatures.

Conclusion: The number, location, and assignment of levels in ${}^{26}\mathrm{Mg}$ that may contribute to the ${}^{22}\mathrm{Ne}+\alpha$ reactions are not clear. Future experimental investigations of ${}^{26}\mathrm{Mg}$ must have an extremely good energy resolution to separate the contributions from different levels. Coincidence experiments of ${}^{26}\mathrm{Mg}$ provide a possible route for future investigations.

We propose the use of a pure spin-3/2 propagator in the $(3/2,0)\oplus (0,3/2)$ representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the $\mathrm{\Delta }$ resonance contribution to the elastic $\pi N$ scattering as an example. We find that the use of a conventional gauge-invariant interaction Lagrangian leads to a problem: the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of the Rarita-Schwinger formalism, we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.

The single-${\mathrm{\Xi }}^{-}$ hypernuclei are studied using a quark mean-field model. At the quark level, the ${\mathrm{\Xi }}^{-}$ hyperon is composed of one $d$ quark and two $s$ quarks, which are confined by the harmonic oscillator potentials. In the case of hadrons, the baryons interact with each other by exchanging $\sigma ,\omega$, and $\rho$ mesons between quarks in different baryons. The single-${\mathrm{\Xi }}^{-}$ binding energies of $\mathrm{\Xi }$ hypernuclei are investigated from $\mathrm{Be}$ to $\mathrm{Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$\mathrm{\Lambda }$ and single-$\mathrm{\Xi }$ potentials at the nuclear saturation density. For the bound states of ${\mathrm{\Xi }}^{-}+{}^{14}\mathrm{N}$ (i.e., $\mathrm{C}$) system named as KISO event in the KEK-E373 experiment, it is found that the ${\mathrm{\Xi }}^{-}$ binding energies are around $5.61–5.89$ MeV for $1s$ state and $0.94–1.21$ MeV for $1p$ state with QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets, whose single-$\mathrm{\Xi }$ potentials are $-12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the ${\mathrm{\Xi }}^{-}+{}^{12}\mathrm{Be}$ show that in the KISO event, the ${\mathrm{\Xi }}^{-}$ hyperon may occupy the $1p$ state. Furthermore, the ${\mathrm{\Xi }}^{-}$ binding energies are achieved around $27\mathrm{MeV}$ for the ${\mathrm{\Xi }}^{-}+{}^{207}\mathrm{Pb}$ (i.e., $\mathrm{Tl}$) system. The energies were nearly comparable to the single-$\mathrm{\Lambda }$ binding energy of $\mathrm{Pb}$ observed by experiments. It demonstrates that the $\mathrm{\Lambda }$ and ${\mathrm{\Xi }}^{-}$ hyperons seem to appear simultaneously in a neutron star.