The structure of the doubly magic ${}_{50}{}^{132}\mathrm{Sn}_{82}$ has been investigated at the ISOLDE facility at CERN, populated both by the ${\beta }^{-}\mathrm{decay}$ of ${}^{132}\mathrm{In}$ and ${\beta }^{-}$-delayed neutron emission of ${}^{133}\mathrm{In}$. The level scheme of ${}^{132}\mathrm{Sn}$ is greatly expanded with the addition of 68 $\gamma$ transitions and 17 levels observed for the first time in the $\beta$ decay. The information on the excited structure is completed by new $\gamma$ transitions and states populated in the $\beta \text{−}n$ decay of ${}^{133}\mathrm{In}$. Improved delayed neutron emission probabilities are obtained both for ${}^{132}\mathrm{In}$ and ${}^{133}\mathrm{In}$. Level lifetimes are measured via the advanced time-delayed $\beta \gamma \gamma$(t) fast-timing method. An interpretation of the level structure is given based on the experimental findings and the particle-hole configurations arising from core excitations both from the $N$ = 82 and $Z$ = 50 shells, leading to positive- and negative-parity particle-hole multiplets. The experimental information provides new data to challenge the theoretical description of ${}^{132}\mathrm{Sn}$.

We find an analytical solution to relativistic viscous hydrodynamics for a ($1+1$)-dimensional Landau flow profile. We consider relativistic Navier-Stokes form of the dissipative hydrodynamic equation, for a nonconformal system with a constant speed of sound, and employ the obtained solution to fit rapidity spectrum of observed pions in $\sqrt{s_{NN}}=200$, 17.3, 12.3, 8.76, 7.62, 6.27, 4.29, 3.83, 3.28, and 2.63 GeV collision energies. We find that at the freeze-out hypersurface with improved Landau's freeze-out prescription, the viscous corrections do not affect the rapidity spectra. We demonstrate that the solution of the nonconformal Landau flow leads to a better agreement with the experimental data compared to the conformal ideal solution. We also extract speed of sound from fit to the rapidity spectra for various collision energies and find a monotonous decrease with decreasing collision energies. Appealing to the fact that viscosity has negligible effect on rapidity spectra for Landau's freeze-out scenario, we argue that our calculations provides a framework for extracting the average value of speed of sound in relativistic heavy-ion collisions.

${}^{99}\mathrm{Tc}$ has been the subject of several experimental programs at the JRC-Geel since the late 1990s. This work presents new transmission data measured at the GELINA facility with the time-of-flight technique, whose simultaneous analysis with past transmission experiments provided a revised set of resonance parameters up to 5 keV. An iterative analysis between the resonance and “continuum” energy ranges leads to average resonance parameters $[S_0=0.51\left(3\right)$, $\langle {\mathrm{\Gamma }}_{{\gamma }_0}\rangle =137\left(7\right)$ meV, $D_0=12.8\left(2\right)$ eV] and theoretical average capture cross sections consistent with those reported in the literature. At $E=30$ keV, we obtain a capture cross section of 1076(45) mb and a Maxwellian-averaged cross section (MACS) of 1016(43) mb. The agreement with the recommended MACS value of 933(47) mb remains within the quoted uncertainties. This result demonstrates the performances of transmission experiments to provide reliable theoretical capture cross sections for long-lived fission products in the energy range of interest for $s$-process nucleosynthesis calculations.

The superdeformed rotational band in ${}^{40}\mathrm{Ca}$ is investigated in the framework of a shell-model-like approach based on cranking covariant density functional theory, in which the pairing correlations are treated with conserved particle number. A superdeformed state is obtained at the deformation $(\beta ,\gamma )=(0.70,9^{\circ })$ even though the depth of the superdeformation minimum is only about 0.2 MeV. With increasing rotational frequency, the potential around the superdeformed minimum becomes deeper. This indicates that the superdeformed state becomes more stable with increasing rotational frequency. Besides, the experimental data are well reproduced by the theoretical calculations with pairing correlations. Pairing correlations are important for the states with $I\le 10\hslash$ in the superdeformed rotational band of ${}^{40}\mathrm{Ca}$ in reproducing the experimental energy spectrum and transition quadrupole moments.

The ground-state bands (GSBs) in the even-even hafnium isotopes ${}^{170–184}\mathrm{Hf}$ are investigated by using the cranked shell model with pairing correlations treated by the particle-number conserving method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hslash \omega \approx 0.5$ MeV observed (predicted) in ${}^{172}\mathrm{Hf}$ (${}^{170,174–178}\mathrm{Hf}$) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi 1i_{13/2} (1/2^{+}\left[660\right]),\pi 1h_{9/2} (1/2^{-}\left[541\right])$ and orbital $\pi 1h_{11/2} (7/2^{-}\left[523\right])$. The first upbendings of GSBs at low frequency $\hslash \omega =0.2–0.3$ MeV in ${}^{170–178}\mathrm{Hf}$, which locate below the deformed neutron shell $N=108$, attribute to the alignment of the neutron orbital $\nu 1i_{13/2}$. For the heavier even-even isotopes ${}^{180–184}\mathrm{Hf}$, compared to the lighter isotopes, the first band cross is delayed to the high frequency due to the existence of the deformed shells $N=108,116$. The upbendings of GSBs in ${}^{180–184}\mathrm{Hf}$ are predicted to occur at $\hslash \omega \approx 0.5$ MeV, which come from the sharp raise of the simultaneous alignments of both proton $\pi 1i_{13/2},\pi 1h_{9/2}$ and neutron $\nu 2g_{9/2}$ orbitals. The pairing correlation plays a very important role in the rotational properties of GSBs in even-even isotopes ${}^{180–184}\mathrm{Hf}$. Its effects on upbendings and band-crossing frequencies are investigated.

Reduced transition probabilities have been measured for the neutron-rich ${}^{73,74,75}\mathrm{Ni}$ nuclei with relativistic Coulomb excitation performed at the RIKEN Nishina Center. For the even-even Ni isotope the determined $B(E2;0^{+}\to 2^{+})$ value is compatible within errors with the result of a previous intermediate energy Coulomb excitation experiment, although being somewhat larger. For the odd Ni isotopes $B\left(E2\right)$ values have been determined for the first time. In the middle $\nu g_{9/2}$ shell nucleus ${}^{73}\mathrm{Ni}$ three peak candidates have been observed and tentatively assigned to the ($5/2^{+}$), ($13/2^{+}$), and ($11/2^{+}$) excitations. Two peak candidates have been observed in ${}^{75}\mathrm{Ni}$ and tentatively assigned to the ($13/2^{+}$) and ($11/2^{+}$) levels. The measured $B\left(E2\right)$ values are in line with the large $B\left(E2\right)$ reported in ${}^{70}\mathrm{Ni}$ and at variance with the small strength measured in ${}^{72}\mathrm{Ni}$. Excitation energies compare well with the result of large-scale shell-model calculations, while $B\left(E2\right)$ values are larger than predicted. This could indicate an increasing contribution of proton excitations across the $Z=28$ shell closure when approaching ${}^{78}\mathrm{Ni}$.

A lifetime measurement of excited states in ${}^{144}\mathrm{Ce}$ using the ${}^{142}\mathrm{Ce}({}^{18}\mathrm{O},{}^{16}\mathrm{O})$ reaction with a beam energy of 67 MeV and the recoil distance Doppler-shift method was performed at the Cologne FN Tandem accelerator. Lifetimes of the three lowest yrast states in ${}^{144}\mathrm{Ce}$ have been measured as well as for the $3_1^{-}$ state and an effective lifetime of the $4_2^{+}$ state. Reduced $E2$ transition strengths determined using these results have been compared to predictions from recent shell-model calculations. From the interband transitions reduced $E1$ strengths could be determined, which are strongly enhanced.

In the framework of a multiphase transport model, fluctuation and correlation of the azimuthal anisotropies in ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{S_{NN}}=200\mathrm{GeV}$ are explored. Properties of the initial eccentricity and final harmonic flow fluctuation resulted from ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions with Woods-Saxon configuration and triangular $\alpha$-clustering configurations of ${}^{12}\mathrm{C}$ are investigated via scaled variance, skewness, and kurtosis. Comparisons are made between results from $\alpha$-clustered configurations and Woods-Saxon configuration. The triangular flow fluctuation is found to have particular sensitivity in distinguishing triangular $\alpha$-clustering structure of ${}^{12}\mathrm{C}$. Furthermore, correlations between initial eccentricities and final flow harmonics are studied with strong multiplicity dependence observed for the correlation functions.

We demonstrate the ability to calculate electromagnetic sum rules with the ab initio symmetry-adapted no-core shell model. By implementing the Lanczos algorithm, we compute nonenergy weighted, energy weighted, and inverse energy weighted sum rules for electric monopole, dipole, and quadrupole transitions in ${}^4\mathrm{He}$ using realistic interactions. We benchmark the results with the hyperspherical harmonics method and show agreement within $2\sigma$, where the uncertainties are estimated from the use of the many-body technique. We investigate the dependence of the results on three different interactions, including chiral potentials, and we report on the ${}^4\mathrm{He}$ electric dipole polarizability calculated in the SA-NCSM that reproduces the experimental data and earlier theoretical outcomes. We also detail a novel use of the Lawson procedure to remove the spurious center-of-mass contribution to the sum rules that arises from using laboratory-frame coordinates. We further show that this same technique can be applied in the Lorentz integral transform method, with a view toward studies of electromagnetic reactions for light through medium-mass nuclei.

The evaluated ${}^{16}\mathrm{O}(n,\alpha )$ cross sections in the ENDF/B-VIII.0 nuclear data library remain uncertain because of systematic discrepancies in the measured data. In the energy region below the first excited state, $R$-matrix analyses rely heavily on the inverse reaction, and in particular, they rely on the measured ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ cross sections reported by Bair et al. in 1973 and Harissopulos et al. in 2005. The Harissopulos cross section values are systematically lower than those previously reported by Bair. Drawing on the available experimental information, this paper briefly describes and demonstrates that the two sets of measured cross sections are consistent.

The hindrances in the $n\alpha$-nucleus-induced fusion reactions at deep subbarrier energies are investigated by using the coupled-channels model. Inspired by the microscopic Pauli-blocking effects of $\alpha$-cluster decay in radioactive nuclei, a Pauli blocking potential is constructed in the $n\alpha$-nucleus-induced fusion reactions by using a single folding procedure, in which the $n\alpha$ nuclei are assumed to be consisted of $\alpha$ particles. A shallow pocket is formed in the inner part of the potential between two colliding nuclei as compared to the one obtained from the double-folding potential with standard Michigan-3-Yukawa effective nucleon-nucleon interaction. The experimental fusion cross sections are described well for fusion systems ${}^{12}\mathrm{C}+{}^{198}\mathrm{Pt}$, ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$, ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$, and ${}^{28}\mathrm{Si}+{}^{30}\mathrm{Si}$. At deep subbarrier energies, it is found that this shallow pocket potential reduces the partial fusion cross sections and shields the contributions of high-angular-momentum partial waves to fusion cross sections. In addition, a detailed comparison of fusion processes with different projectiles ${}^{12}\mathrm{C}$, ${}^{24}\mathrm{Mg}$, and ${}^{28}\mathrm{Si}$ on the same target ${}^{30}\mathrm{Si}$ shows the hindrance effect is stronger for heavier projectiles.

Background: In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power.

Purpose: This paper aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ at $E_{\mathrm{c}.\mathrm{m}.}$ $=$ 268 MeV and ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ at $E_{\mathrm{c}.\mathrm{m}.}$ $=$ 270 MeV and are compared with available experimental data.

Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++.

Results: Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed.

Conclusions: The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

We explore the properties of nuclear pasta appearing in supernova matter, i.e., matter at finite temperature with a fixed proton fraction. The pasta phases with a series of geometric shapes are studied using the compressible liquid-drop (CLD) model, where nuclear matter separates into a dense liquid phase of nucleons and a dilute gas phase of nucleons and $\alpha$ particles. The equilibrium conditions for two coexisting phases are derived by minimization of the total free energy including the surface and Coulomb contributions, which are clearly different from the Gibbs conditions for phase equilibrium due to the finite-size effects. Compared to the results considering only spherical nuclei, the inclusion of pasta phases can delay the transition to uniform matter and enlarge the region of nonuniform matter in the phase diagram. The thermodynamic quantities obtained in the present calculation with the CLD model are consistent with those in the realistic equation of state table for astrophysical simulations using the Thomas-Fermi approximation. It is found that the density ranges of various pasta shapes depend on both the temperature $T$ and the proton fraction $Y_p$. Furthermore, the nuclear symmetry energy and its density dependence may play crucial roles in determining the properties of pasta phases. Our results suggest that the pasta phase diagram is most sensitively dependent on the symmetry energy slope $L$ especially in the low-$Y_p$ and high-$T$ region.

$\beta$-delayed fission ($\beta$DF) decay of a low-spin (ls) and a high-spin (hs) isomer in ${}^{188}\mathrm{Bi}$ was studied at the ISOLDE facility at CERN. Isomer-selective laser ionization and time gating were employed to investigate each isomer separately and their $\beta$DF partial half-lives were determined: $T_{1/2\mathrm{p},\beta \mathrm{DF}}{(}^{188}{\mathrm{Bi}}^{\mathrm{hs}})=5.6\left(8\right)\times {10}^3$ s and $T_{1/2\mathrm{p},\beta \mathrm{DF}}{(}^{188}{\mathrm{Bi}}^{\mathrm{ls}})=1.7\left(6\right)\times {10}^3$ s. This work is the first $\beta$DF study of two states in one isotope and allows the spin dependence of low-energy fission to be explored. The fission fragment mass distribution of a daughter nuclide ${}^{188}\mathrm{Pb}$, following the $\beta$ decay of the high-spin isomer, was deduced and indicates a mixture of symmetric and asymmetric fission modes. Experimental results were compared with self-consistent mean-field calculations based on the finite-range Gogny D1M interaction. To reproduce the measured $T_{1/2\mathrm{p},\beta \mathrm{DF}}{(}^{188}{\mathrm{Bi}}^{\mathrm{hs}})$, the calculated fission barrier of ${}^{188}\mathrm{Pb}$ had to be reduced by $\approx 30\%$. After this reduction, the measured $T_{1/2\mathrm{p},\beta \mathrm{DF}}{(}^{188}{\mathrm{Bi}}^{\mathrm{ls}})$ was in agreement with calculations for a few possible configurations for ${}^{188}\mathrm{Bi}^{\mathrm{ls}}$. Theoretical $\beta$DF probabilities for these configurations were found to be lower by a factor of 4–9 than the $\beta$DF probability of ${}^{188}\mathrm{Bi}^{\mathrm{hs}}$. The fission fragment mass distribution of ${}^{188}\mathrm{Pb}$ was compared to the scission-point model SPY and the calculations based on the finite-range liquid-drop model. The first observation of $\beta$DF for ${}^{190}\mathrm{Bi}$ is also reported.

It was first noted during the 1970s that finite-range distorted wave Born approximation (FR-DWBA) calculations were unable satisfactorily to describe the shape of the angular distributions of many single-proton (and some single-neutron) transfer reactions induced by heavy ions, with calculations shifted to larger angles by up to $\sim 4^{\circ }$ compared with the data. These reactions exhibited a significant mismatch, either of the reaction $Q$ value or the grazing angular momentum of the entrance and exit channels, and it was speculated that the inclusion of multistep transfer paths via excited state(s) of the projectile and/or ejectile could compensate for the effect of this mismatch and yield good descriptions of the data by shifting the calculated peaks to smaller angles. However, to date this has not been explicitly demonstrated for many reactions. In this work we show that inclusion of the two-step transfer path via the 4.44-MeV $2^{+}$ excited state of the ${}^{12}\mathrm{C}$ projectile in coupled channel Born approximation calculations enables a good description of the ${}^{208}\mathrm{Pb}({}^{12}\mathrm{C},{}^{11}\mathrm{B}){}^{209}\mathrm{Bi}$ single-proton stripping data at four incident energies which could not be described by the FR-DWBA. We also show that inclusion of a similar reaction path for the ${}^{208}\mathrm{Pb}({}^{12}\mathrm{C},{}^{13}\mathrm{C}){}^{207}\mathrm{Pb}$ single-neutron pickup reaction has a relatively minor influence, slightly improving the already good description obtained with the FR-DWBA.

Masses of neutron-rich, odd-odd Pm, Eu, and Tb nuclei near $N=98$ were measured using the Canadian Penning Trap mass spectrometer at the Californium Rare Isotope Breeder Upgrade (CARIBU) facility. High-resolution mass measurements yielded the discovery of spin-trap isomers at $N=97$ in ${}^{162}\mathrm{Tb}$, and in the $N=99$ isotones of ${}^{160}\mathrm{Pm}$ and ${}^{164}\mathrm{Tb}$. Furthermore, no evidence of long-lived isomers were observed at $N=95$ in ${}^{158}\mathrm{Eu}$, at $N=97$ in ${}^{158}\mathrm{Pm}$, nor at $N=101$ in ${}^{164}\mathrm{Eu}$ and ${}^{166}\mathrm{Tb}$. These experimental observations are compared to results from multiquasiparticle blocking calculations.

A new method for computing the density of states in nuclei making use of an extrapolated form of the tridiagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire Lanczos matrix can be predicted from just four Lanczos iterations. The extrapolated Lanczos matrix (ELM) approach provides for an accurate computation of the density of states described within the configuration space, which, in some cases, is sufficient to accurately calculate the density of states at, or near, the neutron separation energy. Comparisons between theory and experiment are shown for ${}^{57}\mathrm{Fe}, {}^{74}\mathrm{Ge}$, and ${}^{76}\mathrm{Ge}$. In addition, we show results for the $J$-dependence of moments and the level density for these three nuclei.

The thermomagnetic behavior of quark-gluon plasma has recently received a great deal of attention. In this work we make use of the extended self-consistent quasiparticle model to study the thermodynamic properties, magnetic response, and screening properties of magnetized (2$+$1)-flavor quark-gluon plasma (QGP). The system is considered as a noninteracting system of quasiparticles with masses depending on both temperature and magnetic fields. This allows us to obtain the equation of state of the system and other thermodynamic properties such as the speed of sound. We use the extended self-consistent model to obtain the magnetization and show that QGP has a paramagnetic nature. In addition, we study the pressure anisotropy and calculate the transverse pressure. The obtained anisotropic pressure may be used in hydrodynamic studies of magnetized QGP produced in heavy-ion collisions. We then study the total pressure in both directions, taking pure-field contributions into consideration. Finally we examine the screening properties of magnetized QGP in the longitudinal direction by calculating the Debye screening mass. We go on to compare our results for Debye mass with the results from other approaches.