We calculate the $n\mathrm{th}$ order of $2k$-particle azimuthal cumulants $c_n\left\{2k\right\}$ based on transverse momentum conservation (TMC) and collective flow $v_n$ ($n=2,3$). We demonstrate that the TMC effect only leads to a nonzero $c_n\left\{2k\right\}$ with the sign of ${(-1)}^{nk}$ and the magnitude inversely proportional to ${(N-2k)}^{nk}$. The interplay between TMC and collective flow can change the signs of $c_2\left\{4\right\}$, $c_3\left\{2\right\}$, and $c_3\left\{4\right\}$ at some values of multiplicity $N$, which could provide a good probe to study the onset of collectivity and search for the substructure of proton in small colliding systems.

We discuss a recently introduced model to evaluate complete and incomplete fusion in collisions of weakly bound nuclei. We propose a modification of the imaginary potential to deal with cross sections at energies well below the Coulomb barrier, and discuss the relation between the cross sections provided by a continuum discretized coupled-channel calculation and the ones measured in actual experiments. The new version of the model is used to make predictions of fusion cross sections in collisions of ${}^6\mathrm{Li}$ with a few heavy targets, and the results are compared to the available data. The overall agreement between theory and experiment is quite good.

Heavy-ion collisions provide a unique opportunity to study the nature of X(3872) compared with electron-positron and proton-proton (antiproton) collisions. We investigate the centrality and momentum dependence of $X\left(3872\right)$ in heavy-ion collisions via the Langevin equation and instant coalescence model (LICM). When $X\left(3872\right)$ is treated as a compact tetraquark state, the tetraquarks are produced via the coalescence of heavy and light quarks near the quantum chromodynamic phase transition due to the restoration of the heavy quark potential at $T\to T_c$. In the molecular scenario, loosely bound $X\left(3872\right)$ is produced via the coalescence of $D^0\text{−}{\overline{D}}^{*0}$ mesons in a hadronic medium after kinetic freeze-out. We employ the LICM to explain both $D^0$ and $J/\psi$ production as a benchmark. Then we give predictions regarding $X\left(3872\right)$ production and the nuclear modification factor $R_{AA}^{X\left(3872\right)}$. We find that the total yield of tetraquark is several times larger than the molecular production in Pb-Pb collisions. Although the geometric size of the hadronic molecule is huge, the coalescence probability is small due to strict constraints on the relative momentum between $D^0$ and ${\overline{D}}^{*0}$ in the molecular Wigner function, which significantly suppresses the molecular yield.

We carry out detailed calculations of jet production associated with $W$ gauge bosons in $\text{Pb}+\text{Pb}$ collisions at the Large Hadron Collider (LHC). In our calculations, the production of $W +$ jet in $p+p$ collisions as a reference is obtained by SHERPA, which performs next-to-leading-order matrix-element calculations matched to the resummation of parton shower simulations, while jet propagation and medium response in the quark-gluon plasma are simulated with the linear Boltzmann transport (LBT) model. We provide numerical predictions on seven observables of $W +$ jet production with jet quenching in $\text{Pb}+\text{Pb}$ collisions: the medium modification factor for the tagged jet cross sections $I_{AA}$, the distribution in invariant mass between the two leading jets in $N_{\text{jets}}\ge 2$ events $m_{jj}$, the missing $p_T$ or the vector sum of the lepton and jet transverse momentum $|{\vec{p}}_T^{\text{Miss}}|$, the summed scalar $p_T$ of all the jets in an event $S_T$, transverse momentum imbalance $x_{jW}$, average number of jets per $W$ boson $R_{jW}$, and azimuthal angle between the $W$ boson and jets $\mathrm{\Delta }{\varphi }_{jW}$. The distinct nuclear modifications of these seven observables in $\text{Pb}+\text{Pb}$ relative to that in $p+p$ collisions are presented with detailed discussions.

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking ${}^3\mathrm{He}$ as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the $p$-shell neutron halo nucleus ${}^6\mathrm{He}$.

Background: The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. Within a stationary framework rooted in a static collective Schrödinger equation, the collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments.

Purpose: We study the performance and precision of various methods to determine the minimum-action and minimum-energy fission trajectories in the collective space.

Methods: We apply the nudged elastic band method (NEB), grid-based methods, and the Euler-Lagrange approach to the collective action minimization in two- and three-dimensional collective spaces.

Results: The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential-energy surfaces obtained with the Skyrme-Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential-energy surface of the fissioning nucleus that determine the static fission path. The dynamic programming method also performs quite well and it can be used in many-dimensional cases to provide initial conditions for the NEB calculations.

Conclusions: The NEB method is the tool of choice for finding the least-action and minimum-energy fission trajectories. It will be particularly useful in large-scale static fission calculations of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical $r$-process recycling.

We establish bounds on the maximum possible specific latent heat of cold neutron-star matter derived from hadron physics alone. Existing chiral perturbation theory computations for the equation of state, together with perturbative quantum chromodynamics (QCD), relevant at highest densities (even if they would turn out not to be physically realizable) bind the maximum latent heat which is possible in actual neutron stars. Because these are already near gravitational collapse in general relativity, no denser form of cold matter can exist: thus, the bounds are a generic physical limit. Even in scenarios that modify the theory of gravity, the existence of a family of latent-heat maxima is relevant to diagnose progress in the knowledge of the equation of state of neutron matter, by quantifying the maximum possible (presumed) phase transition that its error bands would allow. Thus, latent heat is a natural benchmark for the equation of state in cold QCD.

The $2\nu \beta \beta$-decay nuclear matrix elements (NMEs) for 11 nuclei are studied with the self-consistent quasiparticle random phase approximation (QRPA) based on the Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common feature pointed out by Šimkovic, Smetana, and Vogel [Phys. Rev. C 98, 064325 (2018)], negative contributions in the running sums of NMEs are found, and play important roles in the fulfillment of the single-state dominance or low-lying-states dominance hypothesis. By comparing the results of the QRPA model and the quasiparticle Tamm-Dancoff approximation (QTDA) model, we find that the negative contributions are due to the enhanced ground-state correlations, which are brought by the backward amplitude in the QRPA model and tuned by strong isoscalar pairing interaction. The enhancement of ground-state correlations will change the signs of ${\mathrm{GT}}^{+}$ (Gamow-Teller) transition amplitudes of higher-lying states and leads to the negative contributions in the running sum.

Nucleon pair shell model truncated to $SD$ collective pair subspace (SDPSM) was applied to study the properties of the low-lying states of the even-even ${}^{144–156}\mathrm{Nd}$ isotopes. It is found that, within the $M$ scheme, the systems with the number $N_{\nu }=7$ of neutron pairs (or the number $N_{\pi }=7$ of proton pairs) can be studied in the SDPSM for the first time. The results show that the properties of the low-lying states of the even-even Nd isotopes can be reproduced approximately, and the even-even ${}^{144–156}\mathrm{Nd}$ isotopes may be a good candidate for the first-order shape phase transition.

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, $a_f$, as well as those for neutron, $a_n$, proton, $a_p$, and $\alpha$-particle, $a_{\alpha }$, emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$ = 112–120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the “immersion water flow” technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the $a_f/a_n$ ratio, the $a_p/a_n$ and $a_{\alpha }/a_n$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of $\alpha$ decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.

We study excited states of two-quasiparticle (2qp) character in well-deformed even-even actinide and heavier nuclei exhibiting $K$ isomerism within the framework of the Skyrme energy-density functional (SEDF) approach, including BCS pairing correlations with self-consistent blocking. We use the SIII SEDF parametrization with time-odd terms and seniority pairing residual interaction as in a previous study of magnetic moments in odd-mass nuclei [Phys. Rev. C 91, 054307 (2015)]. The strength of the seniority interaction is determined through an overall fit on the $2_1^{+}$ excitation energies along the lines of Phys. Rev. C 99, 064306 (2019). Our calculations confirm the 2qp configurations reported in the literature providing an overall good agreement with the available data on isomeric energies. One notes, however, a few significant deviations such as in the $N=142$ uranium and $N=152$ nobelium isotopes, which are explained through known single-particle features of the SEDF used. Given the good predictive capability of the approach, we expect it to serve as a reliable tool in the search for similar kinds of qp excitations and to suggest additional or alternative qp configurations.

Background: The Gorkov approach to self-consistent Green's function theory has been formulated by Somà, Duguet, and Barbieri in [Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principles computations of semimagic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number nonconserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences (i.e., two neutron separation energies, excitation energies of states dominating the one-nucleon spectral function), ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of $N\pm 1$ particle systems or delicate quantities such as second-order energy differences associated with pairing gaps, requires going to higher truncation orders.

Purpose: The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians.

Methods: The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy.

Results: Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian.

Conclusions: Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.

Evaporation residue (ER) cross sections are measured for the reaction ${}^{30}\mathrm{Si}+{}^{176}\mathrm{Yb}$, which forms the compound nucleus ${}^{206}\mathrm{Po}^{*}$, over the excitation energy range from 47.68 to 113.73 MeV. Dependence of noncompound nuclear reaction on entrance channel parameters such as charge product ($Z_1{Z}_2$), mass asymmetry ($\alpha$), deformation (${\beta }_2$) of the target, and isospin asymmetry ($\mathrm{\Delta }\frac{N}{Z}$) is explored. To analyze the experimental data the coupled-channels and the statistical model calculations are used. The measured ER cross sections are compared with the system,${}^{12}\mathrm{C}+{}^{194}\mathrm{Pt}$ forming the same compound nucleus and also with ${}^{28}\mathrm{Si}+{}^{176}\mathrm{Yb}$, forming ${}^{204}\mathrm{Po}^{*}$ in the neighborhood. Observed suppression in the evaporation residue cross sections at higher energies may be attributed to the presence of the noncompound nuclear process.

We study helicity polarization through the $(3+1)$-dimensional relativistic viscous hydrodynamic models at $\sqrt{s_{NN}}=200$ GeV $\text{Au}+\text{Au}$ collisions. Similar to the local spin polarization, we consider the helicity polarization beyond global equilibrium and investigate the contributions induced by thermal vorticity, shear viscous tensor, and the fluid acceleration. We find that the local helicity polarization induced by thermal vorticity dominates over other contributions. It also implies that, in low-energy collisions, the fluid vorticity as part of thermal vorticity may play the crucial role in the total helicity polarization. Such a finding could be useful for probing the local strength of vorticity in rotational quark gluon plasmas by measuring helicity polarization. Our simulation confirms the strict space reversal symmetry, whereas we also compare our numerical results with approximated relations derived from ideal Bjorken flow. Our studies also provide a baseline for the future investigation on local parity violation through the correlations of helicity polarization.

The number spectrum of nonequilibrium neutrinos resulting from neutron star matter deviation from beta equilibrium is calculated. For this purpose, the chemical potential gap ($\delta \mu$) in a typical density change and in the high degeneracy regime ($k_{B}T\le 0.1\text{MeV}$) is estimated. This is done under the application of realistic descriptions of nuclear matter and the assumption of the presence of free hyperons (${\mathrm{\Sigma }}^{-}, {\mathrm{\Lambda }}^0$) in the neutron star core. Realistic nuclear interactions are taken into account by a microscopic many-body approach—the lowest order constrained variational (LOCV) method—for asymmetric nuclear matter. We find that addition of a three-body force interaction leads to a dramatic change in the trend of the symmetry energy at high densities and consequently the change in the sign of $\delta \mu$. This, as a result, changes the dominant flavor of the nonequilibrium neutrinos. By accounting for the hyperons' presence, we see that apart from the sign change of $\delta \mu$ its value can change noticeably. In hypernuclear matter, the effect of particle fractions is also very important. We have also investigated the effect of deviation from beta equilibrium on the dynamic part of the number spectra of nonequilibrium neutrinos produced in the neutron branch of the modified Urca process. It is shown that this part of the number spectra is not affected significantly by the nonequilibrium process and can be replaced by its equilibrium value.

Accumulated experimental data on the binding energies for single-particle states in a broad range of nuclei is examined as a function of the constituent number of neutrons and protons and a simple pattern emerges. The dependence of the energies of neutron states on the number of constituent protons, or of proton states on the number of neutrons, behave similar to each other across the nuclear chart, and the sign reflects the well-known strong attraction. The change in energy of neutron states with neutron number or proton states with protons is approximately a factor of four weaker in magnitude and slightly repulsive, except when the changing nucleons are only within the same orbit as the state. These patterns in the experimental data underlie much of what is implicitly understood from nuclear models, but the consistency throughout the periodic table is remarkable.

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in nonspherical geometries. In this paper, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of ${}^{38}\mathrm{Si}$ and ${}^{250}\mathrm{Cf}$ are presented and discussed.

Isomers with three- and five-nucleon-hole configurations have been established in ${}^{203}\mathrm{Tl}$. These include newly identified levels with a three-nucleon-hole structure: $I^{\pi }$ = ($15/2^{-}$) with $T_{1/2}$ = 7.9(5) ns and $I^{\pi }$ = ($35/2^{-}$) with $T_{1/2}$ = 4.0(5) ns. In addition, five-nucleon-hole states have also been established: $I^{\pi }$ = ($39/2^{-}$) with $T_{1/2}$ = 1.9(2) ns and $I^{\pi }$ = ($49/2^{+}$) with $T_{1/2}$ = 3.4(4) ns. The previously determined long-lived decay, $T_{1/2}$ = 6.6(3) $\mu \mathrm{s}$ from this work, is associated with isomerism of the $I^{\pi }$ = ($29/2^{+}$) state. Levels above this long-lived isomer have been identified through a delayed-prompt $\gamma -\gamma$ coincidence measurement. Five-nucleon-hole states with excitation energies $E_x\approx$ 7 MeV have been established as well as possible octupole excitations of the ${}^{208}\mathrm{Pb}$ core built on these levels. The level scheme of ${}^{203}\mathrm{Tl}$ is extended up to $E_x\approx$ 11 MeV with the inclusion of 25 new transitions. Empirical and shell-model calculations have been performed to aid in the description of the observed states which are found to be of intrinsic character.

In the environment of a hot plasma, as achieved in stellar explosions, capture and photodisintegration reactions proceeding on excited states in the nucleus can considerably contribute to the astrophysical reaction rate. Usually, such reaction rates including the excited-state contribution are obtained from theoretical calculations as the direct experimental determination of these astrophysical rates is currently unfeasible. Future experiments could provide constraining information on the current reaction models which would improve the predictive power of the theoretical reaction rates. In the present study, experiments of photodisintegration with charged-particle emission leading to specific excited states in the residual nucleus are proposed. The expected experimental results can be used to determine the particle-transmission coefficients in the model calculations of photodisintegration and capture reactions. With such constrained transmission coefficients, the astrophysical reaction rates especially involving the excited-state contributions can be better predicted and implemented in astrophysical simulations. In particular, ($\gamma ,p$) and ($\gamma ,\alpha$) reactions in the mass and energy range relevant to the astrophysical $p$ process are considered and the feasibility of measuring them with the ELISSA detector system at the future Variable Energy $\gamma$-ray (VEGA) facility at Extreme Light Infrastructure–Nuclear Physics is investigated. To this end, in a first step 17 reactions with proton emission and 17 reactions with $\alpha$ emission are selected and the dependence of calculated partial cross sections on the variation of nuclear property input is tested. The simulation results reveal that, for the ($\gamma ,p$) reaction on 12 targets of ${}^{29}\mathrm{Si}$, ${}^{56}\mathrm{Fe},{}^{74}\mathrm{Se},{}^{84}\mathrm{Sr},{}^{91}\mathrm{Zr},{}^{96,98}\mathrm{Ru},{}^{102}\mathrm{Pd},{}^{106}\mathrm{Cd}$, and ${}^{115,117,119}\mathrm{Sn}$, and the ($\gamma ,\alpha$) reaction on five targets of ${}^{50}\mathrm{V},{}^{87}\mathrm{Sr},{}^{123,125}\mathrm{Te}$, and ${}^{149}\mathrm{Sm}$, the yields of the reaction channels with the transitions to the excited states in the residual nucleus, namely ($\gamma ,X_i$) with $i\ne 0$, are relevant and even dominant. Therefore, these 17 reactions are considered in the further feasibility study. For each of the 17 photon-induced reactions, in order to attain the detectable limit of 100 counts per day for the total proton or $\alpha$-particle yields, the minimum required $\gamma$-beam energies $E_{\mathrm{low}}$ for the measurements are estimated. It is further found that for each considered reaction, the total yields of the charged-particle $X$ may be dominantly contributed from one, two, or three ($\gamma ,X_i$) channels within a specific, narrow energy range of the incident $\gamma$ beam. If the actual measurements of these photon-induced reactions are performed in this energy range, the sum of the yields of the dominant ($\gamma ,X_i$) channels can be approximated by the measured yields of the charged particle $X$ within acceptable uncertainty. This allows to experimentally obtain the yields of the ($\gamma ,X_i$) channels which dominantly contribute to the total yields of $X$. Using the simulated yields, these energy ranges for each of the 17 photon-induced reactions are derived. Furthermore, the energy spectra of the ($\gamma ,X_i$) channels with $0\le i\le 10$ are simulated for each considered reaction, with the incident $\gamma$-beam energies in the respective energy range as derived before. Based on the energy spectra, the identification of the individual dominant ($\gamma ,X_i$) channels is discussed. It becomes evident that measurements of the photon-induced reactions with charged-particle emissions considered in this work are feasible with the VEGA+ELISSA system and will provide knowledge useful for nuclear astrophysics.