$\beta$-delayed neutron emission is one of the key ingredients for astrophysical $r$-process nucleosynthesis, and theoretical model predictions have still large uncertainties. In this work, we apply a novel feed-forward neural network model to calculate accurately $\beta$-delayed one-neutron emission probabilities. A model is trained with a set of input data of known physical quantities; one-neutron emission $Q$ value, the $Q$-value difference between the one- and two-neutron emissions, $\beta$-decay half-life, the distance from the least neutron-rich nucleus with $Q_{\beta 1n}>0$ in each isotope, and the exponential form of the ratio of $Q$-value $\exp (-Q_{\beta 2n}/Q_{\beta 1n})$. The results give improvements for predictions of medium heavy isotopes and provide reasonable results in $r$-process nuclei, especially in the waiting point nuclei for neutron magic numbers $N=50$ and 82, in comparison with other microscopic models.

The transport properties of the strongly coupled quark-gluon plasma created in ultrarelativistic heavy-ion collisions are extracted by Bayesian parameter estimate methods with the latest collision beam energy data from the CERN Large Hadron Collider. This Bayesian analysis includes sophisticated flow harmonic observables for the first time. We found that the temperature dependence of specific shear viscosity appears weaker than in the previous studies. The results prefer a lower value of specific bulk viscosity and a higher switching temperature to reproduce additional observables. However, the improved statistical uncertainties both on the experimental data and hydrodynamic calculations with additional observables do not help to reduce the final credibility ranges much, indicating a need for improving the dynamical collision model before the hydrodynamic takes place. In addition, the sensitivities of experimental observables to the parameters in hydrodynamic model calculations are quantified. It is found that the analysis benefits most from the symmetric cumulants and nonlinear flow modes, which mostly reflect nonlinear hydrodynamic responses, in constraining the temperature dependence of the specific shear and bulk viscosities in addition to the previously used flow coefficients.

The single-particle properties of ${}^{29}\mathrm{Mg}$ have been investigated via a measurement of the ${}^{28}\mathrm{Mg}(d,p){}^{29}\mathrm{Mg}$ reaction, in inverse kinematics, using the ISOLDE Solenoidal Spectrometer. The negative-parity intruder states from the $fp$ shell have been identified and used to benchmark modern shell-model calculations. The systematic data on the single-particle centroids along the $N=17$ isotones show good agreement with shell-model predictions in describing the observed trends from stability toward ${}^{25}\mathrm{O}$. However, there is also evidence that the effect of the finite geometry of the nuclear potential is playing a role on the behavior of the $p$ orbitals near the particle-emission threshold.

We investigate the applicability of machine learning techniques in studying the finite-size effects associated with many-body physics. These techniques have an emerging presence in many-body theory as they have been used for interpolations, extrapolations, and in modeling wave functions. We will resolve several issues associated with machine learning and many-body calculations such as small datasets, outliers, and discontinuities, for the purpose of extrapolating finite calculations to macroscopic scales. We carry out a systematic investigation of two related systems by developing metrics that aim to avoid spurious effects and capture desired features. This work uses neural networks to extrapolate the unitary gas to the thermodynamic limit at zero range, which is otherwise difficult to reach. The effective mass of strongly interacting neutron matter is also studied and makes use of the noninteracting problem to resolve discontinuous predictions. For this investigation, we also carried out new auxiliary field diffusion Monte Carlo (AFDMC) calculations for a variety of densities and particle numbers. Ultimately, we demonstrate an effective utility for neural networks in this context.

${}^{162}\mathrm{Er}$ and ${}^{164}\mathrm{Er}$ are two of the 35 $p$ nuclei, and their ($n,\gamma$) cross sections are important input parameters in nuclear astrophysics network calculations. The neutron capture cross section in the resonance region of isotopes and even the natural erbium (${}^{\mathrm{nat}}\mathrm{Er}$) sample has not been measured experimentally according to the EXFOR database. The ($n,\gamma$) cross section of ${}^{\mathrm{nat}}\mathrm{Er}$, using ${\mathrm{C}}_6{\mathrm{D}}_6$ liquid scintillator and pulse height weighting techniques to measure prompt $\gamma$ rays, has been measured in the energy range of 1–100 eV using a back streaming white neutron facility at China Spallation Neutron Source. The deduced neutron capture cross sections matches the evaluation databases ENDF/B-VIII.0, ENDF/B-VII.1, JENDL-4.0, and ROSFOND-2010, and resonance parameters extracted from the $R$-matrix code in the 1–100 eV region.

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases.

Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier.

Methods: Fusion excitation functions for the ${}^{16}\mathrm{O}+{}^{142,150}\mathrm{Nd}$ reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range $12\%$ below to $50\%$ above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using ccfull code. The cross sections are also compared with reactions using ${}^{16}\mathrm{O}$ beams with other isotopes of Nd to explore the systematic behavior of fusion.

Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ and ${}^{16}\mathrm{O}+{}^{150}\mathrm{Nd}$ reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Akyüz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier.

Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using ${}^{150}\mathrm{Nd}$ target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

We have studied systematically microscopic properties of a quantum vortex in neutron matter at finite temperatures and densities corresponding to different layers of the inner crust of a neutron star. To this end and in preparation of future simulations of the vortex dynamics, we have carried out fully self-consistent three-dimensional (3D) Hartree-Fock-Bogoliubov calculations, using one of the latest nuclear energy-density functionals from the Brussels-Montreal family, which has been developed specifically for applications to neutron superfluidity in neutron-star crusts. By analyzing the flow around the vortex, we have determined the effective radius relevant for the vortex filament model. We have also calculated the specific heat in the presence of the quantum vortex and have shown that it is substantially larger than for a uniform system at low temperatures. The low temperature limit of the specific heat has been identified as being determined by Andreev states inside the vortex core. We have shown that the specific heat in this limit does not scale linearly with temperature. The typical energy scale associated with Andreev states is defined by the minigap, which we have extracted for various neutron-matter densities. Our results suggest that vortices may be spin-polarized in the crust of magnetars. Finally, we have obtained a lower bound for the specific heat of a collection of vortices with given surface density, taking into account both the contributions from the vortex core states and from the hydrodynamic flow.

A new $\beta$-decaying state in ${}^{214}\mathrm{Bi}$ has been identified at the ISOLDE Decay Station at the CERN-ISOLDE facility. A preferred $I^{\pi }=\left(8^{-}\right)$ assignment was suggested for this state based on the $\beta$-decay feeding pattern to levels in ${}^{214}\mathrm{Po}$ and shell-model calculations. The half-life of the $I^{\pi }=\left(8^{-}\right)$ state was deduced to be $T_{1/2}=9.39\left(10\right)$ min. The deexcitation of the levels populated in ${}^{214}\mathrm{Po}$ by the $\beta$ decay of this state was investigated via $\gamma \text{−}\gamma$ coincidences and a number of new levels and transitions was identified. Shell-model calculations for excited states in ${}^{214}\mathrm{Bi}$ and ${}^{214}\mathrm{Po}$ were performed using two different effective interactions: the H208 and the modified Kuo-Herling particle interaction. Both calculations agree on the interpretation of the new $\beta$-decaying state as an $I^{\pi }=8^{-}$ isomer and allow for tentative assignment of shell-model states to several high-spin states in ${}^{214}\mathrm{Po}$.

We demonstrate that the $p_T$ dependence of the $\eta /{\pi }^0$ ratio at midrapidity is universal within a few percent for high-energy $p+p, p+A$, and $d+A$ collisions, over a broad range of collision energies. The $\eta /{\pi }^0$ ratio increases with $p_T$ up to 4 to 5 GeV/$c$ where it saturates at a nearly constant value of $0.487\pm 0.024$. Above $p_T=5$ GeV/$c$, the same constant value is also observed in $A+A$ collisions independent of collision system, energy, and centrality. At lower $p_T$, where accurate $\eta /{\pi }^0$ data are absent for $A+A$ collisions, we estimate possible deviations from the universal behavior, which could arise due to the rapid radial hydrodynamic expansion of the $A+A$ collision system. For $A+A$ collisions at the BNL Relativistic Heavy Ion Collider we find that possible deviations are limited to the $p_T$ range from 0.4 to 3 GeV/$c$ and remain less than 20% for the most central collisions.

We study the behavior of four types of vorticities in noncentral $\text{Au}+\text{Au}$ collisions at energies $\sqrt{S_{NN}}=5\text{–}200$ GeV using a microscopic transport model PACIAE. The results show that the vorticities decay faster at lower energy and smaller impact parameter. The nonmonotonic dependence of the initial vorticities on the collision energies is reconfirmed and the turning point is 10–15 GeV for different vorticities. The global $\mathrm{\Lambda }$ polarization at energies $\sqrt{S_{NN}}=7.7\text{–}200$ GeV is reproduced by introducing an energy density freeze-out criterion.

In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well-defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle numbers of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry-restored densities and total energies. These formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.

A first $\gamma$-ray study of ${}^{47,49}\mathrm{Cl}$ spectroscopy was performed at the Radioactive Isotope Beam Factory with ${}^{50}\mathrm{Ar}$ projectiles at 217 MeV/nucleon, impinging on the liquid hydrogen target of the MINOS device. Prompt deexcitation $\gamma$ rays were measured with the NaI(Tl) array DALI2${}^{+}$. Through the one-proton knockout reaction ${}^{50}\mathrm{Ar}(p,2p)$, a spin assignment could be determined for the low-lying states of ${}^{49}\mathrm{Cl}$ from the momentum distribution obtained with the SAMURAI spectrometer. A spin-parity $J^{\pi }=3/2^{+}$ is deduced for the ground state of ${}^{49}\mathrm{Cl}$, similar to the recently studied $N=32$ isotope ${}^{51}\mathrm{K}$. The evolution of the energy difference $E(1/2_1^{+})-E(3/2_1^{+})$ is compared to state-of-the-art theoretical predictions.

The temperature evolution of electric dipole transition strengths of Sn isotopes is studied using self-consistent quasiparticle random phase approximation (QRPA) and finite-temperature RPA models based on a relativistic density functional. For tin isotopes lighter than ${}^{132}\mathrm{Sn}$, temperature only shows its effect at high values of 2 MeV, while for neutron-rich tin isotopes heavier than ${}^{132}\mathrm{Sn}$, the low-lying strength distributions get fragmented and spread to the lower-energy region already at temperature of 1 MeV. Using these electric dipole transition strengths as inputs for the talys code, the temperature effects on $(n,\gamma )$ cross sections are studied. For tin isotopes lighter than ${}^{132}\mathrm{Sn}$, temperature causes an enhancement of neutron-capture cross section at high temperatures of 2 MeV, while for neutron-rich tin isotopes heavier than ${}^{132}\mathrm{Sn}$, the cross section is largely enhanced already at temperature $T=1.0$ MeV, and the bump of cross section caused by the pygmy dipole resonance also becomes broader. The change in neutron-capture rate can be as large as 70% for ${}^{136}\mathrm{Sn}$, considering the temperature effects on electric dipole transition strength in the final compound nucleus with a temperature of 0.86 MeV (corresponding to $T=10$ GK in the astrophysical environment). The change is around 20% for tin isotopes lighter than ${}^{132}\mathrm{Sn}$ and above 40% for those heavier than ${}^{132}\mathrm{Sn}$.

Background: Significant enhancement in sub-barrier fusion cross sections by several orders of magnitude, in the frame of one-dimensional barrier penetration models, is observed for a variety of nuclear systems. To understand this, one needs to find the fundamental degrees of freedom relevant in the sub-barrier fusion region by incorporating nonelastic channels such as coupling of the excited target and/or projectile nuclei, particle transfer channels, threshold variation of nuclear potential, etc.

Purpose: We probe what degrees of freedoms are associated with the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ reaction at energies $\approx 18\%$ below to $\approx 12\%$ above the Coulomb barrier.

Method: An online $\gamma$-ray spectroscopy technique is used to determine the populated excitation functions in the ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ reaction. The reaction cross sections obtained from these $\gamma$ rays are compared with the statistical model to explore the mechanism of fusion reactions.

Results: At energies near and below the Coulomb barrier, two isotopes of sulfur (${}^{34}\mathrm{S}$ and ${}^{32}\mathrm{S}$) were found to reproduce cross section within the frame of the pace2 model based on Hauser-Feshbach calculations, whereas isotopes of chlorine (${}^{35}\mathrm{Cl}$), sulfur (${}^{35}\mathrm{S}$), and phosphorous (${}^{32}\mathrm{P}$) agree well but at above-barrier energies. Isotopes of Ar, Cl, S, P, and Si show significant enhancement over an entire band of energies. This enhancement (suppression) in the experimental cross section at energies above (below) the barrier points towards the involvement of some nuclear reaction mechanism other than fusion-evaporation. Distorted-wave Born approximation calculations strongly support the population of ${}^{28}\mathrm{Si}$ residue via the one-proton transfer process. The total fusion cross section is found to follow the theory after the inclusion of coupling of low lying excited states of projectile and target. Calculations concerning the astrophysical $S$ factor and the logarithmic derivative factor support the idea of no fusion hindrance at the studied energies. The universal fusion function benchmark shows consistency with previous data for lithium (or Li isotopes) induced systems.

Conclusions: The inclusion of inelastic couplings associated with both target and projectile is important to understand the behavior of total fusion cross section. The formation of ${}^{28}\mathrm{Si}$ via the one-proton transfer reaction supports the present experimental technique to make inclusive transfer measurements. The calculations with the universal fusion function present a slight suppression in the higher energy region, indicating possible breakup effects in this region. The present calculations show that till $18\%$ below the barrier there is no fusion hindrance. On extrapolating the theoretical values we further observed that the present system has no fusion hindrance. No connection of ${}^{10}\mathrm{B}+{}^{27}\mathrm{Al}$ fusion with astrophysics has been made, which raises the question to think of cosmic ray reactions and perhaps reactions in the early solar system, but how the fusion reaction would fit into the picture is not clear at all.

The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained. Similarly to the case of zero temperature, it is decomposed into the static and dynamical components, where the former is given by the contraction of the bare interaction with the two-fermion density and the latter is represented by the double contraction of the four-fermion two-time correlation function, or propagator, with two interaction matrix elements. The dynamical kernel with the four-body propagator, being formally exact, requires approximations to avoid generating prohibitively complicated hierarchy of equations. We focus on the approximation where the dynamical interaction kernel is truncated on the level of two-body correlation functions, neglecting the irreducible three-body and higher-rank correlations. Such a truncation leads to the dynamical kernel with the coupling between correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, or phonons, of normal and superfluid nature. The latter ones are, thus, the mediators of the dynamical superfluid pairing. In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators. This allows us to study the temperature dependence of the pairing gap beyond the Bardeen-Cooper-Schrieffer approximation that is implemented for medium-heavy nuclear systems. The cases of ${}^{68}\mathrm{Ni}$ and ${}^{44,46}\mathrm{Ca}$ are discussed in detail.

We calculate volume-independent ratios of cumulants of the net-proton number distribution up to sixth order in a fireball that cools down after the chemical freeze-out. A hadron resonance gas model is used together with the assumption of partial chemical equilibrium, which fixes the number of observed stable hadrons after the chemical freeze-out. It is shown that, due to only weak departure from the statistical Boltzmann distribution, also the volume-independent ratios of higher-order cumulants of the net-proton number show only weak dependence on the temperature. This observation supports the possibility to measure noncritical cumulants at chemical freeze-out even after subsequent cooling in the hadronic phase. Cumulants of the net-baryon number behave similarly, while those for the kaon number vary more strongly with the temperature. Our results are relevant for the current fluctuation studies of runs of the Beam Energy Scan program at the BNL Relativistic Heavy Ion Collider.

A high statistics $\mathrm{\Sigma }p$ scattering experiment is performed at the J-PARC Hadron Experimental Facility. Momentum-tagged ${\mathrm{\Sigma }}^{-}\mathrm{s}$ running in a liquid hydrogen target are accumulated by detecting the ${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction with a high intensity ${\pi }^{-}$ beam of 20 M/spill. The differential cross sections of the ${\mathrm{\Sigma }}^{-}p$ elastic scattering were derived with a drastically improved accuracy by identifying approximately 4500 events from $1.72\times {10}^7{\mathrm{\Sigma }}^{-}$. The derived differential cross section shows a clear forward-peaking angular distribution for a ${\mathrm{\Sigma }}^{-}$ momentum range from 470 to 850 $\mathrm{MeV}/c$. The accurate data will impose a strong constraint on the theoretical models of the baryon-baryon interactions.

Reactions on proton-rich nuclides drive the nucleosynthesis in core collapse supernovae (CCSNe) and in x-ray bursts (XRBs). CCSNe eject the nucleosynthesis products to the interstellar medium and hence are a potential inventory of $p$ nuclei, whereas in XRBs nucleosynthesis powers the light curves. In both astrophysical sites the Ni-Cu cycle, which features a competition between ${}^{59}\mathrm{Cu}(p,\alpha ){}^{56}\mathrm{Ni}$ and ${}^{59}\mathrm{Cu}(p,\gamma ){}^{60}\mathrm{Zn}$, could potentially halt the production of heavier elements. Here, we report the first direct measurement of ${}^{59}\mathrm{Cu}(p,\alpha ){}^{56}\mathrm{Ni}$ using a reaccelerated ${}^{59}\mathrm{Cu}$ beam and a cryogenic solid hydrogen target. Our results show that the reaction proceeds predominantly to the ground state of ${}^{56}\mathrm{Ni}$, and the experimental rate has been found to be lower than Hauser-Feshbach based statistical model predictions. New results hints that the $\nu p$ process could operate at higher temperatures than previously inferred and therefore remains a viable site for synthesizing the heavier elements.

The role of pairing interactions on fission barriers and static fission paths in Th, U and Pu isotopes is investigated by using the deformed mean-field plus standard pairing model. It is found that pairing interaction plays different roles in different stages of the fission process. The first and second saddle point of the fission process are sensitive to the pairing interaction strength, while the ground-state and prescission points are mainly driven by nuclear deformation. It is also demonstrated that pairing interactions play a crucial role in the region of the inner and outer barriers. The barrier heights obtained by using the present model are found to reproduce the experimental data remarkably well and yield better results than those obtained by using the BCS approximation, thus indicating the importance of exact solutions of pairing interactions. Through numerical analysis, we provide possible microscopic pictures of spontaneous fission in the current pairing model.

The $\beta$ decay of the neutron-rich ${}^{134}\mathrm{In}$ and ${}^{135}\mathrm{In}$ was investigated experimentally in order to provide new insights into the nuclear structure of the tin isotopes with magic proton number $Z=50$ above the $N=82$ shell. The $\beta$-delayed $\gamma$-ray spectroscopy measurement was performed at the ISOLDE facility at CERN, where indium isotopes were selectively laser-ionized and on-line mass separated. Three $\beta$-decay branches of ${}^{134}\mathrm{In}$ were established, two of which were observed for the first time. Population of neutron-unbound states decaying via $\gamma$ rays was identified in the two daughter nuclei of ${}^{134}\mathrm{In}, {}^{134}\mathrm{Sn}$ and ${}^{133}\mathrm{Sn}$, at excitation energies exceeding the neutron separation energy by 1 MeV. The $\beta$-delayed one- and two-neutron emission branching ratios of ${}^{134}\mathrm{In}$ were determined and compared with theoretical calculations. The $\beta$-delayed one-neutron decay was observed to be dominant $\beta$-decay branch of ${}^{134}\mathrm{In}$ even though the Gamow-Teller resonance is located substantially above the two-neutron separation energy of ${}^{134}\mathrm{Sn}$. Transitions following the $\beta$ decay of ${}^{135}\mathrm{In}$ are reported for the first time, including $\gamma$ rays tentatively attributed to ${}^{135}\mathrm{Sn}$. In total, six new levels were identified in ${}^{134}\mathrm{Sn}$ on the basis of the $\beta \gamma \gamma$ coincidences observed in the ${}^{134}\mathrm{In}$ and ${}^{135}\mathrm{In}\beta$ decays. A transition that might be a candidate for deexciting the missing neutron single-particle $13/2^{+}$ state in ${}^{133}\mathrm{Sn}$ was observed in both $\beta$ decays and its assignment is discussed. Experimental level schemes of ${}^{134}\mathrm{Sn}$ and ${}^{135}\mathrm{Sn}$ are compared with shell-model predictions. Using the fast timing technique, half-lives of the $2^{+}, 4^{+}$, and $6^{+}$ levels in ${}^{134}\mathrm{Sn}$ were determined. From the lifetime of the $4^{+}$ state measured for the first time, an unexpectedly large $B(E2;4^{+}\to 2^{+})$ transition strength was deduced, which is not reproduced by the shell-model calculations.