We introduce a global analysis of relativistic heavy ion collisions using Trajectum of a significantly higher precision and including a new option to vary the normalization of the centrality estimator. We use the posterior distribution of our parameters to generate a set of high-statistics samples that allows us to make precise predictions including statistical and systematic uncertainties estimated from the model parameter distribution. The results are systematically compared with experiment whereby we also include many observables not included in the global analysis. This includes in particular (extremely) ultracentral anisotropic flow and mean transverse momentum, whereby we find satisfactory agreement with experiment where data are available. Lastly, we compute spectra and anisotropic flow for oxygen-oxygen collisions performed at the BNL Relativistic Heavy Ion Collider (RHIC) and to be performed at the the CERN Large Hadron Collider (LHC) and comment on how these collisions may inform us on properties of the quark-gluon plasma.

Starting from the relativistic realistic nucleon-nucleon ($NN$) interactions, the relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space is employed to study neutron star properties. First, the one-to-one correspondence relation for gravitational redshift and mass is established and used to infer the masses of isolated neutron stars by combining gravitational redshift measurements. Next, the ratio of the moment of inertia $I$ to mass times radius squared $M{R}^2$ as a function of the compactness $M/R$ is obtained, and is consistent with the universal relations in the literature. The moment of inertia for $1.338M_{\odot }$ pulsar PSR J0737$-$3039A $I_{1.338M_{\odot }}$ is predicted to be $1.356\times {10}^{45}, 1.381\times {10}^{45}$, and $1.407\times {10}^{45}\mathrm{g}{\mathrm{cm}}^2$ by the RBHF theory in the full Dirac space with $NN$ interactions Bonn A, B, and C, respectively. Finally, the quadrupole moment of neutron star is calculated under the slow-rotation and small-tidal-deformation approximation. The equations of state constructed by the RBHF theory in the full Dirac space, together with those by the projection method and momentum-independence approximation, conform to universal $I$-Love-$Q$ relations as well. By combing the tidal deformability from GW170817 and the universal relations from relativistic ab initio methods, the moment of inertia of a neutron star with 1.4 solar mass is also deduced as $I_{1.4M_{\odot }}=1.{22}_{-0.25}^{+0.40}\times {10}^{45}\mathrm{g}{\mathrm{cm}}^2$.

Spectroscopic amplitudes (SAs) in the interacting boson fermion fermion model (IBFFM) are necessary for the computation of $0\nu \beta \beta$ decay but also for cross sections of heavy-ion reactions, in particular, double charge exchange reactions for the NUMEN Collaboration, if one does not want to use the closure limit. We present for the first time (i) the formalism and operators to compute in a general case the spectroscopic amplitudes in the IBFFM scheme from even-even to odd-odd nuclei, in a way suited to be used in reaction code, i.e., extracting the contribution of each orbital; (2) the odd-odd nuclei as described by the old IBFFM are obtained for the first time with the new implementation of machine learning (ML) techniques for fitting the parameters, getting a more realistic description. The one-body transition densities for ${}^{116}\mathrm{Cd}\to {}^{116}\mathrm{In}$ and ${}^{116}\mathrm{In}\to {}^{116}\mathrm{Sn}$ are part of the experimental program of the NUMEN experiment, which aims to find constraints on $0\nu \beta \beta$ decay matrix elements. As a first application of the spectroscopic amplitudes we present the calculation of the $0\nu \beta \beta$ nuclear matrix elements in the IBFFM formalism in closure approximation.

We have implemented an energy-variance extrapolation method with the variation after projection (VAP) wave functions which are fully optimized. Thanks to the adopted VAP wave functions which are simplified by taking only one projected state for each selected reference state, the present energy variance extrapolation calculation can be easily applied to high-spin states, even over the backbending. Moreover, the energy variance can be calculated very quickly because the required matrix elements are already available in our previous VAP calculations. The calculated results in $pf$ model space have clearly shown that the extrapolated energies for all calculated spin states are very close to the exacted shell model ones within 20 keV.

Background: Establishing computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations.

Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum.

Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast.

Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: ${}^{44,46,48}\mathrm{Ti}$, ${}^{48,50}\mathrm{Cr}$, ${}^{52}\mathrm{Fe}$, ${}^{60,62,64}\mathrm{Zn}$, ${}^{66,68}\mathrm{Ge}$, ${}^{68}\mathrm{Se}$, and ${}^{108,110}\mathrm{Xe}$. We predict low-lying states of ${}^{112–114}\mathrm{Ba}$ and ${}^{116–120}\mathrm{Ce}$, nuclei difficult to reach by large-scale SM calculations.

Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

The shell evolution of neutron-rich nuclei with temperature is studied in a beyond-mean-field framework rooted in the meson-nucleon Lagrangian. The temperature-dependent Dyson equation with a dynamical kernel taking into account the particle-vibration coupling (PVC) is solved for the fermionic propagators in the basis of the thermal relativistic mean-field Dirac spinors. The calculations are performed for ${}^{68–78}\mathrm{Ni}$ in a broad range of temperatures $0\le T\le 4$ MeV. Special focus is put on the fragmentation pattern of the single-particle states, which is further investigated within toy models in truncated model spaces. Such models allow for quantifying the sensitivity of the fragmentation to the phonon frequencies, the PVC strength, and the mean-field level density. This study provides insights into the temperature evolution of the PVC mechanism in real nuclear systems under the conditions which occur in astrophysical environments. In this connection, we discuss the temperature-dependent nucleon effective mass and symmetry energy coefficient, which are key ingredients of the nuclear equation of state.

We have extended the compressible liquid-drop model with a density-dependent surface term which allows for a unified description of both the nuclear ground-state energies and the incompressibility modulus in finite nuclei $K_A$. We analyze the role of the nuclear empirical parameters, e.g., $K_{\mathrm{sat}}$, $Q_{\mathrm{sat}}$, $L_{\mathrm{sym}}$, and $K_{\mathrm{sym}}$, which contribute to the bulk properties, as well as the role of the finite-size contributions. For the bulk properties, the density and isospin dependencies of the nuclear incompressibility in infinite matter are characterized by introducing new empirical parameters, and two new constraints for the value of $K_{\mathrm{sym}}$ are suggested. For finite nuclei, we employ a Bayesian approach coupled to a Markov-Chain Monte Carlo exploration of the parameter space to confront the model predictions of $K_A$ in Zr, Sn, and Pb isotopes to the experimental data. We show that $Q_{\mathrm{sat}}\approx -950\pm 200\mathrm{MeV}$ describes the experimental measurements of $K_A$ in these isotopes. This value is different from those deduced from phenomenological nuclear energy density functionals, suggesting a possible explanation of their difficulty to accurately describe Zr, Sn, and Pb data all together. In addition we explore the impact of a fictitious measurement of the giant monopole resonance energy in ${}^{132}\mathrm{Sn}$. We show that this measurement, provided it is accurate enough, will allow us to better determine $K_{\mathrm{sym}}$ and $K_{\tau }$. Finally we explore the properties of the speed of sound around saturation density and show the important role of finite-size terms in finite nuclei since they reduce the speed of sound to approximately half compared with nuclear matter.

The effects of deformation and the change of the nuclear core on the hyperon binding and halo structure in single-$\mathrm{\Lambda }$ $p$-shell hypernuclei are studied for the C hyperisotopes and $N=6$ hyperisotones in the framework of the deformed Skyrme-Hartree-Fock approach with combinations of the $NN$ interactions SIII, SGII, SkI4 and the $\mathrm{\Lambda }N$ interactions LY1 and SLL4, respectively. Deformation causes more deeply bound states with smaller extension of the density distributions and radii. The possibility of deformed halo structures of $\mathrm{\Lambda }$ $1p$ states in hypernuclei up to a mass number $A=15$ is found.

We report the measurement of the total kinetic energy (TKE) release in the fast neutron induced fission of ${}^{240}\mathrm{Pu}$ and ${}^{242}\mathrm{Pu}$. The results are compared to the predictions of the GEF model, the CGMF model, and the model of Denisov and Sedykh as well as previous experimental work on these reactions. Our absolute measurements of the TKE release are in good agreement with the previous measurements of Nethaway et al. for the interaction of 14.8 MeV neutrons with ${}^{240}\mathrm{Pu}$ [Phys. Rev. C 16, 1907 (1977)] and of Winkelmann and Aumann for the interaction of 15 MeV neutrons with ${}^{242}\mathrm{Pu}$ [Phys. Rev. C 30, 934 (1984)]. The general trends of the measured TKE values agree with phenomenological models but the variances of the TKE distributions are significantly less than predicted by various models. The mean postneutron emission TKE release decreases nonlinearly with increasing neutron energy and can be represented as $\mathrm{TKE}\left(\mathrm{MeV}\right)=175.8\pm 0.3-\left(2.4\pm 0.8\right)\mathrm{lo}{\mathrm{g}}_{10}{E}_n-\left(1.4\pm 0.4\right)\mathrm{lo}{\mathrm{g}}_{10}{E}_n^2$ for ${}^{240}\mathrm{Pu}$ and $\mathrm{TKE}\left(\mathrm{MeV}\right)=177.1\pm 0.3-\left(1.2\pm 0.9\right)\mathrm{lo}{\mathrm{g}}_{10}{E}_n-\left(1.8\pm 0.5\right)\mathrm{lo}{\mathrm{g}}_{10}{E}_n^2$ for ${}^{242}\mathrm{Pu}$.

Type-Ia supernovas are powerful stellar explosions that provide important distance indicators in cosmology. Recently, we proposed a new Type-Ia supernova mechanism that involves a nuclear fission chain-reaction in an isolated white dwarf [Phys. Rev. Lett. 126, 131101 (2021)]. Here we perform novel reaction network simulations of the actinide-rich first solids in a cooling white dwarf. The network includes neutron-capture and fission reactions on a range of U and Th isotopes with various possible values for ${}^{235}\mathrm{U}$ enrichment. We find, for modest ${}^{235}\mathrm{U}$ enrichments, neutron capture on ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ can breed additional fissile nuclei so that a significant fraction of all U and Th nuclei may fission during the chain reaction. Finally, we compute the energy release from the fission chain reaction for various uranium enrichments; a novel result that is a necessary input for thermal diffusion simulations of carbon ignition.

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($\chi \mathrm{EFT}$) up to one loop are determined by a simultaneous fit to the $A=2-3$ nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the ${}^3\mathrm{He}/{}^3\mathrm{H}$ magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ $\mathrm{GeV}/c$, beyond the expected regime of validity of the $\chi \mathrm{EFT}$ approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Machleidt, and Nosyk [Phys. Rev. C 96, 024004 (2017)] and by Piarulli et al. [Phys. Rev. C 94, 054007 (2016)], using different $\chi \mathrm{EFT}$ formulations. In the $A=3$ calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below $\approx 0.8$ $\mathrm{GeV}/c$. An analysis of the convergence of the chiral expansion is also provided.

Background: The lowest-lying shape oscillations of deformed nuclei have been described as quadrupole in nature $(\lambda =2)$, resulting in two types of vibrations or oscillations: $\beta$ vibrations with oscillations along the symmetry axis $(K^{\pi }=0^{+})$ and $\gamma$ vibrations breaking axial symmetry with a projection of $K^{\pi }=2^{+}$ on the symmetry axis. The $\gamma$ vibration seems to be well characterized as the first $K^{\pi }=2_1^{+}$ (or $2_{\gamma }^{+}$) band in deformed nuclei and exhibits a systematic behavior across the region. The nature of the $K^{\pi }=0^{+}$ excitations, however, has remained poorly understood and has been open to debate for some decades.

Purpose: The goal of this work is to understand the nature of $0^{+}$ states observed in ${}^{168}\mathrm{Er}$ through measurements of the lifetimes of these states and to determine if they are consistent with oscillations built on a deformed ground state, the minima of other coexisting shapes, single-particle states, or a mixture of effects.

Method: Lifetimes of excited states in the ${}^{168}\mathrm{Er}$ nucleus were measured with the Doppler shift attenuation method (DSAM) and the inelastic neutron scattering reaction, $(n,n^{\prime }\gamma )$, at the University of Kentucky Accelerator Laboratory.

Results: Numerous $0^{+}$ states had been observed by the ($p,t$) reaction [D. Bucurescu et al., Phys. Rev. C 73, 064309 (2006).]. We confirm the $0^{+}$ states at 1217.2, 1421.5, 1833.6, 2364.9, 2392.1, and 2643.0 keV in ${}^{168}\mathrm{Er}$. We could not, however, support the previous assignments of $0^{+}$ levels at 2114.1, 2200.6, 2572.5, and 2617.4 keV. We report measured lifetimes for six confirmed $0^{+}$ excitations and additional members of $0^{+}$ bands.

Conclusions: The results for ${}^{168}\mathrm{Er}$ show that it is the third excited $K^{\pi }=0^{+}$ $\left(0_4^{+}\right)$ excitation that carries the collective strength and, therefore, the potential to be an oscillation on the ground state. This result is similar to the case in ${}^{166}\mathrm{Er}$, where it was also the $0_4^{+}$ state that exhibited greater collectivity than the first excited $K^{\pi }=0^{+}$ band. The Delaroche et al. [J.-P Delaroche et al., Phys. Rev. C 81, 014303 (2010).] prediction for a collective $K^{\pi }=0^{+}$ band is at $E_T=1.818\mathrm{MeV}$, which corresponds the third excited $K^{\pi }=0^{+}$ band.

We report a new half-life measurement of the 188-keV isomeric state in ${}^{184}\mathrm{Re}$. The ${}^{184m}\mathrm{R}\mathrm{e}$ isomer was produced by means of neutron activation of natural rhenium foil in the MARIA nuclear reactor at the National Centre for Nuclear Research (NCBJ). The observation of the ${}^{184m}\mathrm{R}\mathrm{e}$ decay for over two half-life periods has yielded the new value of $T_{1/2}=177.25\pm 0.07$ d. Our result is the most precise determination of the half-life of the ${}^{184m}\mathrm{Re}$ isomer and improves the precision of the previously known value of $T_{1/2}=169\pm 8$ d by two orders of magnitude.

We investigate the sensitivity of the $\mathrm{\Lambda }$ directed flow to the $\mathrm{\Lambda }$ potential in midcentral Au $+$ Au collisions at $\sqrt{s_{NN}}\approx 3.0\text{–}30\mathrm{GeV}$. The $\mathrm{\Lambda }$ potential obtained from the chiral effective field theory ($\chi \mathrm{EFT}$) is used in a microscopic transport model, a vector version of relativistic quantum molecular dynamics. We find that the density-dependent $\mathrm{\Lambda }$ potentials, obtained from the $\chi \mathrm{EFT}$ assuming weak momentum dependence of the potential, reproduce the rapidity and the beam-energy dependence of the $\mathrm{\Lambda }$ directed flow measured by the STAR collaboration in the beam energy scan program. Although the $\mathrm{\Lambda }$ directed flow is insensitive to the density dependence of the potential, it is susceptible to the momentum dependence. We also show that a hydrodynamics picture based on the blast-wave model predicts a similarity of the proton, $\mathrm{\Lambda }$, and $\mathrm{\Xi }$ directed flows, but the directed flow of $\mathrm{\Omega }$ baryons slightly deviates from other baryons. We also show that the quark coalescence predicts different rapidity dependence of the directed flows for hyperons. These investigations suggest that measurements of a wide range of the rapidity dependence of the directed flow of hyperons may provide important information about the properties of hot and dense matter created in high-energy heavy-ion collisions.

$R$-matrix analyses have been performed for the ${}^7\mathrm{Li}(t,n){}^9\mathrm{Be}$ and ${}^7\mathrm{Li}({}^3\mathrm{He},p){}^9\mathrm{Be}$ reactions, which are thought to be of importance in primordial abundance of ${}^9\mathrm{Be}$. All available data were compiled and used in the $R$-matrix analysis. The resonance parameters are compared with previous works. The resulting fit was used to extract an improved determination of the reaction rate for both reactions. The present rates of ${}^7\mathrm{Li}(t,n_0){}^9\mathrm{Be}$ at $T=0.3\text{–}3$ GK are about 7.5–28.9% lower than the values of Brune et al. and are larger than the rates of Barhoumi et al. by up to 28.1%. Our ${}^7\mathrm{Li}({}^3\mathrm{He},p_0){}^9\mathrm{Be}$ rates are higher than those of Yan et al. by no more than 29% and differ within 21% from those of Rath et al. over 0.1–3.0 GK.

Uncertainty propagation of model parameters through nuclear reaction models is critical for nuclear data evaluation and other applications. Nuclear reaction models generally contain nonlinear functions of the model parameters, making the process of uncertainty propagation difficult. Usually stochastic approaches like the Monte Carlo method are employed to propagate the uncertainties through nuclear reaction models. The Monte Carlo method does provide proper results, but it takes a lot of computational power and time, which makes the process of uncertainty propagation difficult. Deterministic sampling approaches may provide results with accuracy using less computational time making the process of uncertainty propagation fast. In this study we have explored the use of a deterministic sampling approach called the unscented transform method for the uncertainty propagation in the nuclear reaction models. As a test case we have propagated the uncertainties of correlated optical model parameters through the optical model calculations for total and reaction cross sections of the $n+{}^{56}\mathrm{Fe}$ reaction. The results obtained using the unscented transform method are then compared with the results of the Monte Carlo method. It has been observed that the unscented transform method provides results practically similar to the Monte Carlo method in less computational time. It is concluded in this study that the unscented transform method can propagate uncertainties effectively through optical model calculations and there should be further investigation of the use of this method for other nuclear reaction models.

The one-nucleon separation energy $S_n$, two-nucleon separation energy $S_{2n}$, one-proton separation energy $S_p$, two-proton separation energy $S_{2p}, \alpha$-decay energy $Q_{\alpha }, \alpha$-decay half-life and spontaneous fission half-life of $Z=114$ isotopes and $N=184$ isotones are calculated by the finite-range droplet model (FRDM2012). It is found that $N=184$ is a neutron magic number, and $Z=114$ is a proton magic number. The properties of $Z=114$ isotopes and $N=184$ isotones provide a vital signal that ${}_{114}{}^{298}\mathrm{Fl}$ may be a spherical double-magic nucleus and also the center of the stability island of superheavy nuclei. Based on this, we began to investigate the optimal conditions for the synthesis of superheavy nucleus ${}_{114}{}^{298}\mathrm{Fl}$ within the dinuclear system model. To produce such neutron-rich compound nucleus, we consider using the extremely neutron-rich radioactive beams to bombard actinide targets. The evaporation residue cross section of superheavy nuclei synthesized by radioactive beam is analyzed in detail. Finally, we suggest that for the synthesis of ${}_{114}{}^{298}\mathrm{Fl}$, the radioactive beam-induced fusion reaction ${}^{64}\mathrm{Ti}+{}^{238}\mathrm{U}$ in the $4n$ evaporation channel with an excitation energy of 43 MeV is optimal.

In-medium effects are introduced in the microscopic description of the effective nucleon-nucleon ($\mathit{NN}$) interaction potential entitled DDR3Y in terms of the density-dependent nucleon-meson couplings within the relativistic-Hartree-Bogoliubov (RHB) approach. The nuclear densities of the interacting target and projectile nuclei and $\mathit{NN}$ potentials are obtained for nonlinear $\mathrm{NL}{3}^{*}$ and TM1 parameter sets within the relativistic mean-field approach and density-dependent DDME1 and DDME2 parameter sets within the RHB formalism. The DDR3Y $\mathit{NN}$ potential and the densities are used to obtain the nuclear potential by adopting the double-folding approach. This nuclear potential is further used to probe the fusion dynamics within the $\ell$-summed Wong model for a few even-even systems leading to the formation of light, heavy, and superheavy nuclei. The calculations are also performed for the relativistic R3Y, density-dependent and -independent Michigan 3 Yukawa (M3Y) interaction potentials for the comparison. We observed that the DDR3Y $\mathit{NN}$ potential gives a better overlap with the experimental data as compared to nonrelativistic M3Y and DDM3Y $\mathit{NN}$ potentials. From the comparison of R3Y and DDR3Y interactions, it is manifested that the inclusion of in-medium effects in terms of density-dependent nucleon-meson couplings raises the fusion barrier and consequently decreases the fusion and/or capture cross-section. Moreover, the nuclear densities, as well as the relativistic R3Y $\mathit{NN}$ potential obtained for the $\mathrm{NL}{3}^{*}$ parameter set, are observed to give a comparatively better fit to the experimental data.