We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number nonconserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for ${}^{122}\mathrm{Xe}$, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^{+}$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.

The JETSCAPE framework is a modular and versatile Monte Carlo software package for the simulation of high energy nuclear collisions. In this work we present a new tune of JETSCAPE, called PP19, and validate it by comparison to jet-based measurements in $p+p$ collisions, including inclusive single jet cross sections, jet shape observables, fragmentation functions, charged hadron cross sections, and dijet mass cross sections. These observables in $p+p$ collisions provide the baseline for their counterparts in nuclear collisions. Quantifying the level of agreement of JETSCAPE results with $p+p$ data is thus necessary for meaningful applications of JETSCAPE to $A+A$ collisions. The calculations use the JETSCAPE PP19 tune, defined in this paper, based on version 1.0 of the JETSCAPE framework. For the observables discussed in this work calculations using JETSCAPE PP19 agree with data over a wide range of collision energies at a level comparable to standard Monte Carlo codes. These results demonstrate the physics capabilities of the JETSCAPE framework and provide benchmarks for JETSCAPE users.

We report the first measurement of the magnetic dipole and electric quadrupole moment of the exotic nucleus ${}^{133}\mathrm{Sn}$ by high-resolution laser spectroscopy at ISOLDE/CERN. These, in combination with state-of-the-art shell-model calculations, demonstrate the single-particle character of the ground state of this short-lived isotope and, hence, the doubly-magic character of its immediate neighbor ${}^{132}\mathrm{Sn}$. The trend of the electromagnetic moments along the $N=83$ isotonic chain, now enriched with the values of tin, are discussed on the basis of realistic shell-model calculations.

The low lying structure of deformed nuclei has long been actively investigated. One particular issue has been how to distinguish axial $\gamma$ rigidity from $\gamma$ softness in axially asymmetric nuclei. In this study, we discuss a new signature based solely on low spin ground and $\gamma$-band energies as a function of spin in deformed nuclei that illuminates some of these questions and apply it to the well-deformed Gd through W isotopes and the transitional, axially asymmetric, Os and Pt nuclei. The simplicity of the new approach suggests that it may have a wide range of use.

By using isochronous mass spectrometry at the experimental cooler storage ring in Lanzhou, China, masses of short-lived ${}^{44}\mathrm{Cr}$, ${}^{46}\mathrm{Mn}$, ${}^{48}\mathrm{Fe}$, ${}^{50}\mathrm{Co}$, and ${}^{52}\mathrm{Ni}$ were measured for the first time and the precision of the mass of ${}^{40}\mathrm{Ti}$ was improved by a factor of about 2. Relative precisions of $\delta m/m=\left(1\text{–}2\right)\times {10}^{-6}$ have been achieved. Details of the measurements and data analysis are given. The obtained masses are compared with the Atomic-Mass Evaluation 2016 and with theoretical model predictions. The new mass data enable us to extract the higher-order coefficients, $d$ and $e$, of the quartic form of the isobaric multiplet mass equation for the $fp$-shell isospin quintets. Unexpectedly large $d$ and $e$ values for the $A=44$ quintet are found. By revisiting the previous experimental data on $\beta$-delayed protons from ${}^{44}\mathrm{Cr}$ decay, it is suggested that the observed anomaly could be due to the misidentification of the $T=2$, $J^{\pi }=0^{+}$ isobaric analog state in ${}^{44}\mathrm{V}$.

We investigated the effects of the pairing correlation on the quasiparticle resonant energy and width in the neutron-rich Ca isotopes by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method. The resonant energy and width can be read from three kinds of quasiparticle spectra, including the quasiparticle-state probability density, the occupation probability density, and the pair probability density. The results read from different quasiparticle spectra calculated with the same potential are exactly the same for the narrow resonances, while for the broad resonances, the difference among the results are relatively larger. From the comparison between the quasiparticle-state probability density calculated with and without the pairing field, we could separate the effect only from the pairing correlation on the quasiparticle resonances. We found that the pairing correlation can increase the resonant energy and width for both the hole-like and particle-like quasiparticle resonances. And this increase is larger when the state is closer to the Fermi energy, especially for the particle-like quasiparticle resonance originated from the unbound single-particle states with smaller angular momentum $l$ in weakly bound nucleus.

Background: The recent surprising experimental discovery of asymmetric fission in the nucleus ${}^{180}\mathrm{Hg}$ at low excitation energy has renewed interest concerning our understanding of the role of nuclear shell effects in the dynamics of the fission process. New theoretical models have been developed that claim to successfully explain the observed asymmetric fission of ${}^{180}\mathrm{Hg}$ and also predict the nature of mass distributions of several other preactinide nuclei for which experimental data are scarce.

Purpose: We investigated fragment-mass distributions in the fission of the preactinide nucleus ${}^{214}\mathrm{At}$ at different excitation energies near the Coulomb barrier. The present results were compared with the predictions from a recent state-of-the-art theoretical calculation, as well as with our previous measurement for the nearby nucleus ${}^{210}\mathrm{Po}$.

Methods: A pulsed heavy-ion beam was used in the experiment. Fission fragments were detected with two large-area position-sensitive multiwire proportional counters placed at the folding angle. Mass distributions were extracted from time-of-flight differences and position information ($\theta ,\varphi$) for the fission fragments.

Results: An asymmetry in fragment-mass distribution in the fission of ${}^{214}\mathrm{At}$ was observed at an excitation energy of $\approx 31$ MeV, where a shell effect is found to influence the potential energy surface. At higher excitation energies, mass distributions are predominantly symmetric indicating the absence of shell effects.

Conclusion: This finding is consistent with the prediction of a recent macroscopic-microscopic dynamical model. However, for the preactinides, static models with nascent fragment shell structure are likely to produce similar results.

$\alpha$-Particle evaporation spectra were measured at backward angles in ${}^{16}\mathrm{O}+{}^{94,100}\mathrm{Mo}$ reactions at multiple beam energies. Inverse level-density parameter, $K$, was determined for Cd nuclei of different isospins by simulating high-energy tail of the measured $\alpha$-particle evaporation spectra with statistical model code pace2. An overall increasing behavior of the $K$ value is observed with increasing temperature in the range of 1 to 2.5 MeV. It is observed that in the temperature region below 1.8 MeV, the parameter $K$ is higher for the neutron-rich nuclei by around 1 MeV. Semiclassical calculations were performed which treat single-particle level density of neutron and proton on different footing and this can account for the isospin effects. These calculations reproduce the $K$ values as determined from the statistical model analysis of $\alpha$-particle evaporation spectra. Present results clearly demonstrate the isospin dependence of the level-density parameter as conjectured by theoretical works.

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of ${}^{129}\mathrm{Xe}$ collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In ${}^{208}\mathrm{Pb}$ collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted by hydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that ${}^{208}\mathrm{Pb}$ nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the $v_2$-to-$v_3$ puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio $v_3\left\{4\right\}/v_3\left\{2\right\}$ and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between $v_2$ and $v_3$, it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with ${\beta }_3\lesssim 0.0375$ for ${}^{208}\mathrm{Pb}$, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. The $v_2$-to-$v_3$ puzzle remains a challenge for hydrodynamic models.

Hindrance at deep subbarrier energies for the symmetric ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}, {}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, and asymmetric ${}^{12}\mathrm{C}+{}^{198}\mathrm{Pt}$ systems is investigated using microscopic energy and the density-dependent $G$-matrix effective interaction. The proton and neutron density distributions of target and projectile are derived from Skyrme-Hartree-Fock calculations. A fair agreement with the data of the fusion excitation functions and astrophysical $S$ factors have been obtained without any fitting parameters. Hindrance is naturally reproduced at deep subbarrier energies, which is consistent with experimental observations.

The importance of the constraints imposed by finite nuclei properties in unveiling the correlations of the tidal deformability with the symmetry energy parameters is investigated within the ${\chi }^2$-based covariance approach (CCA). The Hessian matrix, a quantity central to the CCA, contains implicitly in-built knowledge of the distributions of the nuclear matter parameters (NMPs) consistent with the fit data. Using an extensive set of fit data on finite nuclei together with the maximum mass of neutron stars in the CCA, the correlation of the tidal deformability of a neutron star with the slope and the curvature parameters of the nuclear symmetry energy is studied. Comparing these results with those obtained from completely uncorrelated distributions of NMPs, but filtered by high-density constraints coming from observations, it is shown that the additional constraints on the NMPs induced by the finite nuclei properties are instrumental in strengthening the correlations of the tidal deformability with the symmetry energy parameters.

Background: The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce—or rather re-introduce—the “Dirac oscillator,” a fully relativistic basis that has all the desired attributes of the ordinary harmonic oscillator while naturally incorporating a strong spin-orbit coupling.

Purpose: To assess the power and flexibility of the Dirac oscillator basis in the solution of nuclear structure problems within the framework of covariant density-functional theory.

Methods: Self-consistent calculations of binding energies and ground-state densities for a selected set of doubly magic nuclei are performed using the Dirac oscillator basis and are then compared against results obtained with the often-used Runge-Kutta method.

Results: Results obtained using the Dirac oscillator basis reproduce with high accuracy those derived using the Runge-Kutta method and suggest a clear path for a generalization to systems with axial symmetry.

Conclusions: Although the harmonic oscillator with spin-orbit corrections has been the staple of the nuclear shell model since the beginning, the Dirac oscillator is practically unknown among the nuclear physics community. In this paper we illustrate the power and flexibility of the Dirac oscillator and suggest extensions to the study of systems without spherical symmetry, as required in constrained calculations of nuclear excitations.

We have investigated the production yields of charged pions, kaons, and (anti)protons (restricted to midrapidity of $\left|y\right|<0.1$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV, from the STAR experiment in the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC), within an improved heavy-ion jet interaction generator (ImHIJING) code plus a relativistic transport (ART) model. Improvements of the dynamical content of ImHIJING code include (i) sampling of initial momenta of nuclear ground state, (ii) a Regge cascade for initial-state interaction effects, and (iii) an advanced popcorn mechanism for baryon production. It is found that the implementation of initial-state interactions in the $\mathrm{ImHIJING}+\mathrm{ART}$ model is crucial for the description of collision centrality dependence of bulk hadron observables in peripheral and semicentral ($\approx 10\%$–$70\%$) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}>11.5$ GeV.

We propose a new, model-independent approach that appropriately incorporates the resonant and threshold behaviors. We show that when choosing the appropriate variable, the complete Green's function and the $T$ matrix can be expressed as single-valued functions (uniformization) in the form of a simple series explicitly written by the bound and resonant poles: the uniformized Mittag-Leffler expansion. The poles' symmetries, arising from the unitarity of the $S$ matrix, impose the series to obey the proper threshold behaviors. We then demonstrate this method in a model case of a double-channel meson-baryon scattering, with channels, $\overline{K}N(I=0)$, and $\pi \mathrm{\Sigma }(I=0)$, by fitting the numerically calculated $T$ matrix with the simple series and comparing the fitted results to the exact results.

A simple model to study the collective coupling between pairing and rotational degrees of freedom in well-deformed even-even nuclei is proposed. It relies on the description of the effects of pairing correlations on the rotational motion in terms of intrinsic vortical currents. As a result, an expression of the rotational energy within a band is provided as a polynomial of order three in the square of the angular velocity. The coefficients of this polynomial have a well-defined analytical form and their values are determined from merely three experimental pieces of data: the energy of the first $2^{+}$ state, the ground-state charge quadrupole moment as deduced from $B(E2,2^{+}\to 0^{+})$ measurements, and a quantity deduced from the odd-even mass differences in neighboring odd nuclei. This model is tested in 24 deformed nuclei chosen across the rare-earth and actinide regions. In spite of the very restricted input of data, and moreover which is limited to nuclear properties at zero or very low excitation energies, the agreement with the data within the yrast line is in many cases, especially in actinide nuclei, excellent up to angular momenta of the order of $30\hslash$ or more. Of course, such an approach is by construction unable to reproduce physical effects which do not result from this Coriolis antipairing (CAP) type of collective quenching of pairing correlations. This is especially the case in the rare-earth region, where a backbending effect is often observed. In such cases our model may be considered as a baseline in order to disentangle the effect of the CAP collective mode from those of other existing spectroscopic phenomena.

Background: Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence.

Purpose: Through comparison with the nuclear shell model, the question of convergence is addressed.

Methods: Shell-model calculations performed in the $sd$- and $pf$-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined.

Results: It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $〈\widehat{Q^2}〉$, converging to within 10% of its true value and the triaxiality term, $cos\left(3\delta \right)$, converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly.

Conclusions: The convergence of quadrupole rotationally invariant sum rules was quantified in the $sd$- and $pf$-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Larger spaces, such as the rare-earth region, potentially offer faster convergence.

Hyperfine structure (HFS) measurements of neutron-rich iridium isotopes ${}^{196,197,198}\mathrm{Ir}$ ($Z=77,N=119$–121) were performed via in-gas-cell laser resonance ionization spectroscopy at the KEK Isotope Separation System. Magnetic dipole moments $\mu$ and isotope shifts were determined from the HFS spectra. The variation of mean-square charge radii and quadrupole deformation parameters of these isotopes were evaluated from the isotope shifts. The $\mu$ value of ${}^{197}\mathrm{Ir}$ agreed with a theoretical value based on the strong coupling model, and the Ir nucleus was interpreted as prolately deformed by the theoretical calculations. The $\mu$ values of ${}^{196,198}\mathrm{Ir}$ were also compared with semiempirical values calculated based on the strong coupling model. From the comparison, we can suggest the possible spin values of $I^{\pi }=1,2^{-}$ for ${}^{196}\mathrm{Ir}$ and $I^{\pi }=1^{-}$ for ${}^{198}\mathrm{Ir}$.

We show that the transverse-mass and rapidity spectra of protons and pions produced in Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=2.4$ GeV can be well reproduced in a thermodynamic model assuming single freeze-out of particles from a spherically symmetric hypersurface. This scenario corresponds to a physical picture used by Siemens and Rasmussen in the original formulation of the blast-wave model. Our framework modifies and extends this approach by incorporation of a Hubble-like expansion of QCD matter and inclusion of resonance decays. In particular, the $\mathrm{\Delta }\left(1232\right)$ resonance is taken into account, with a width obtained from the virial expansion. Altogether, our results bring evidence for substantial thermalization of the matter produced in heavy-ion collisions in the few-GeV energy regime and its nearly spherical expansion.

Low-lying states in the isotope ${}^{130}\mathrm{Xe}$ were populated in a Coulomb-excitation experiment performed at CERN's HIE-ISOLDE facility. The magnitudes and relative signs of seven $E2$ matrix elements and one $M1$ matrix element coupling five low-lying states in ${}^{130}\mathrm{Xe}$ were determined using the semiclassical coupled-channel Coulomb-excitation least-squares search code gosia. The diagonal $E2$ matrix elements of both the $2_1^{+}$ and $4_1^{+}$ states were extracted for the first time. The reduced transition strengths are in line with those obtained from previous measurements. Experimental results were compared with the general Bohr Hamiltonian with the microscopic input from mean-field theory utilizing universal nuclear energy density functional (UNEDF0), shell-model calculations using the GCN50:82 and SN100PN interactions, and simple phenomenological models (Davydov-Filippov and $\gamma$-soft). The extracted shape parameters indicate triaxial-prolate deformation in the ground-state band. In general, good agreement between theoretical predictions and experimental values was found, while neither phenomenological model was found to provide an adequate description of ${}^{130}\mathrm{Xe}$.