The electromagnetic properties of ${}^{126,128}\mathrm{Xe}$ were studied in subbarrier Coulomb excitation measurements performed at the National Superconducting Cyclotron Laboratory Re-accelerator facility, ReA3, at Michigan State University (MSU). ${}^{126}\mathrm{Xe}$ and ${}^{128}\mathrm{Xe}$ nuclei were accelerated to 3.74 and 3.81 MeV/nucleon, respectively, and were impinged on ${}^{196}\mathrm{Pt}$ and ${}^{208}\mathrm{Pb}$ targets. The $\gamma$ rays deexciting the populated low-lying states were detected in coincidence with the scattered nuclei using the JANUS setup. Transition and diagonal matrix elements for low-lying states and transitions in ${}^{126,128}\mathrm{Xe}$ were extracted from the experimental data using the gosia and gosia2 codes. The experimental results were compared with the theoretical calculations by the microscopic shell model and the Davydov-Filippov $\gamma$-rigid rotor model. The calculated results from the newly established shell model (called the PMMU model), which is based on the advanced Hartree-Fock Bogoliubov plus generator coordinate method (HFB $+$ gcm) for a large model space, agree well with the measurements in both nuclei, except for the second $2^{+}$ state. Interpretation for the experimentally determined nearly vanishing electric-quadrupole moment of this state remains a challenge for theory.

Background: Recent experiments have confirmed that the neutron-rich isotopes ${}^{28,29}\mathrm{F}$ belong to the so-called island of inversion (IOI), a region of the nuclear chart around $Z=10$ and $N=20$ where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes ${}^{28\text{–}33}\mathrm{F}$ are basically unknown.

Purpose: In this work, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes ${}^{25\text{–}33}\mathrm{F}$, from a core of ${}^{24}\mathrm{O}$ and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels.

Methods: We develop two models adjusted on experimentally confirmed states in ${}^{25,26}\mathrm{O}$ and ${}^{25\text{–}27}\mathrm{F}$ based on different assumptions concerning the positions of the neutron $0d_{3/2}$ and $1p_{3/2}$ shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an $sd\text{−}fp$ model space.

Results: We obtain the first detailed spectroscopy of ${}^{25\text{–}33}\mathrm{F}$ in the continuum and show how the interplay between continuum effects and deformation explains the recent data on ${}^{28,29}\mathrm{F}$. Several deformed one- and two-neutron halo states are predicted in ${}^{29,31}\mathrm{F}$, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.

Conclusions: The complex structure of neutron-rich fluorine isotopes offers a trove of information about the formation of the southern shore of the IOI through a subtle interplay of emergent deformation via the neutron $p_{3/2}\text{−}{f}_{7/2}$ coupling, and continuum effects favoring the occupation of the $1p_{3/2}$ shell over the $0d_{3/2}$ shell. Further experimental studies of this region will be essential to assess the quality of future theoretical approaches.

The $2p$ radioactivity half-lives have been calculated within a tunneling process through the potential barrier determined from the original version of the generalized liquid drop model and quasimolecular shapes. The sparse experimental data on the $2p$ radioactivity half-lives of the ${}^{12}\mathrm{O}$, ${}^{16}\mathrm{Ne}$, ${}^{19}\mathrm{Mg}$, ${}^{45}\mathrm{Fe}$, ${}^{48}\mathrm{Ni}$, ${}^{54}\mathrm{Zn}$, and ${}^{67}\mathrm{Kr}$ nuclei are roughly reproduced when taking into account the $Q_{2p}^{exp}$ value. An analytic formula is provided to obtain rapidly these different half-lives. Using the $Q_{2p}$ values extracted from the recent Nubase2020 table, extrapolations to other perhaps possible $2p$ emitters are proposed. Within the same approach, formulas to determine the ${}^9\mathrm{Be}$, ${}^{6,7}\mathrm{Li}$, ${}^{3,6}\mathrm{He}$, and ${}^{2,3}\mathrm{H}$ decay half-lives at low excitation energy are also provided.

In the framework of the statistical multifragmentation model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the ratio between the probabilities of observing $n$ fragments in each event, for each of the sources, follows a scaling law, similar to the traditional nuclear isoscaling. However, the corresponding slope is sensitive to the source sizes. This property is explained analytically using the grand-canonical ensemble. The extent to which our findings are affected by finite size effects and by the deexcitation of the hot primary fragments is investigated. The scaling turns out to be robust and weakly affected by effects implied by these two aspects. We also find that the Poisson distribution is a fairly good approximation to the above mentioned probabilities, associated with both the primordial fragments, produced at the breakup stage, and the final ones, found at the end of the fragment deexcitation process.

Background: Average resonance spacing $D_0$ and spin dependence of nuclear level density (NLD) are essential quantities in nuclear physics, especially important for calculations of nuclear reactions and the normalization of NLD models.

Purpose: Neutron resonances with different spins in odd-mass targets can form close doublets that are often difficult to resolve. These doublets are not corrected for when accounting for subthreshold resonances during $D_0$ determination. Moreover, different literature sources disagree on the isotopic assignment of some resonances.

Methods: The $\gamma$ rays following radiative neutron capture on ${}^{161,163}\mathrm{Dy}$ and ${}^{167}\mathrm{Er}$ were measured with the highly segmented $\gamma$-ray calorimeter Detector for Advanced Neutron Capture Experiments (DANCE) at the Los Alamos Neutron Science Center. The analysis of spectra using the $\gamma$-multiplicity-based spin assignment method allows checking for the presence of the above-mentioned doublets. The calorimetric sensitivity provides unambiguous isotopic assignment.

Results: We were able to assign spin to tens of resonances as well as to identify new ones in all three isotopes. Some isotope assignments from the literature were corrected. Detailed analysis of the number of unobserved resonances, assuming that the resonance positions obey predictions of the Gaussian orthogonal ensemble and reduced neutron widths Porter-Thomas fluctuations, allowed determination of $D_0$ with an uncertainty of a few percent, $D_0=2.15\left(5\right)$, 6.39(24), and 3.86(12) eV for ${}^{161,163}\mathrm{Dy}$ and ${}^{167}\mathrm{Er}$, respectively. Thanks to the spin assignment, the spacings for the resonances with the two spins formed in $s$-wave neutron capture, $D_0^{-}$ and $D_0^{+}$, were determined. Their ratio was compared to different NLD models.

Conclusions: Our deduced $D_0$ for ${}^{163}\mathrm{Dy}$ is lower than any ${}^{163}\mathrm{Dy}$ value found in the literature. Good consistency was found with some literature values for ${}^{161}\mathrm{Dy}$ and ${}^{167}\mathrm{Er}$. The ratios $D_0^{-}/D_0^{+}$ are consistent with several models available in the literature, but in a clear contradiction with a few microscopic NLD models.

We have studied nuclear fusion reactions from the Coulomb explosion of deuterium clusters induced by high-intensity laser beams within a transport approach. By incorporating the D$+$D $\to n+{}^3\mathrm{He}$ channel, where D denotes deuterons, ${}^2\mathrm{H}$, as inelastic collisions based on the stochastic method, we have calibrated the neutron yield from the simulation in a box system with that from the reaction rate equation. After justifying the Coulomb explosion of a single cluster by comparing results with available theoretical limits, we then investigated the dynamics from Coulomb explosions of systems with different cluster numbers and different deuteron numbers in clusters. We find that the kinetic energy spectrum of deuterons at the final stage is different from that when neutrons are abundantly produced, corresponding to significantly different reaction rates. We also extrapolate the neutron yield result from small systems to large systems based on an intuitive parameterized form and compare with the available experimental result. The present framework can be extended by incorporating more channels, and useful for further studies of nuclear fusion reactions in plasma systems at higher energies reached in more recent experiments.

Quark interactions with topological gluon configurations can induce local chirality imbalance and parity violation in quantum chromodynamics, which can lead to the chiral magnetic effect (CME)—an electric charge separation along the strong magnetic field in relativistic heavy-ion collisions. The CME-sensitive azimuthal correlator observable $\left(\mathrm{\Delta }\gamma \right)$ is contaminated by background arising, in part, from resonance decays coupled with elliptic anisotropy $\left(v_2\right)$. We report here differential measurements of the correlator as a function of the pair invariant mass $\left(m_{\mathrm{inv}}\right)$ in 20–50% centrality $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=200$ GeV by the STAR experiment at the BNL Relativistic Heavy Ion Collider. Strong resonance background contributions to $\mathrm{\Delta }\gamma$ are observed. At large $m_{\mathrm{inv}}$ where this background is significantly reduced, the $\mathrm{\Delta }\gamma$ value is found to be significantly smaller. An event-shape-engineering technique is deployed to determine the $v_2$ background shape as a function of $m_{\mathrm{inv}}$. We extract a $v_2$-independent and $m_{\mathrm{inv}}$-averaged signal $\mathrm{\Delta }{\gamma }_{\mathrm{sig}}=(0.03\pm 0.06\pm 0.08)\times {10}^{-4}$, or $(2\pm 4\pm 5)\%$ of the inclusive $\mathrm{\Delta }\gamma (m_{\mathrm{inv}}>0.4$ $\mathrm{GeV}/c^2)=(1.58\pm 0.02\pm 0.02)\times {10}^{-4}$, within pion $p_T=0.2$–0.8 $\mathrm{GeV}/c$ and averaged over pseudorapidity ranges of $-1<\eta <-0.05$ and $0.05<\eta <1$. This represents an upper limit of $0.23\times {10}^{-4}$, or $15\%$ of the inclusive result, at $95\%$ confidence level for the $m_{\mathrm{inv}}$-integrated CME contribution.

We study the role of chiral nuclear forces on the propagation of neutrinos in hot neutron matter. In particular, we analyze the convergence of the dynamical structure factor and the neutrino mean free path with the order of the power counting of the chiral forces, as well as the role of the regulator cutoff of these forces in the determination of these quantities. Single-particle energies and chemical potentials needed to calculate the dynamical structure factor are obtained within the Brueckner-Hartree-Fock approximation extended to finite temperature. Our results show that the dynamical structure factor and the neutrino mean free path depend on the cutoff only when the chiral potential is considered at leading order (LO) and next-to-leading order (NLO), with this dependence becoming strongly reduced at higher orders in the chiral power counting due to the role of three-nucleon forces that start to contribute at next-to-next-to-leading order $\left({\mathrm{N}}^2\mathrm{LO}\right)$ and being, in particular, almost negligible at next-to-next-to-next-to-leading order $\left({\mathrm{N}}^3\mathrm{LO}\right)$. The neutrino mean free path is found to converge up to densities slightly below $\approx$0.15 ${\mathrm{fm}}^{-3}$ when increasing the order of the chiral power counting, although no signal of convergence is found for densities above this value. The uncertainty associated with our order-by-order nuclear many-body calculation of the neutrino mean free path is roughly estimated from the difference between the results obtained at ${\mathrm{N}}^2\mathrm{LO}$ and ${\mathrm{N}}^3\mathrm{LO}$, finding that it varies from about a few centimeters at low densities up to a bit less than 2 m at the largest one considered in this work, $0.3{\mathrm{fm}}^{-3}$.

We study symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with the finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from the bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spins of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighboring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.

A delayed fission due to nuclear dissipation results in a drop of first-chance fission probability ($P_{f0}$) with respect to predictions by standard statistical models. Using the stochastic Langevin model, we calculate $P_{f0}$ as a function of presaddle dissipation strength ($\beta$) for fissioning nuclei ${}^{220}\mathrm{U}$, ${}^{230}\mathrm{U}$, ${}^{240}\mathrm{U}$, and ${}^{240}\mathrm{Cm}$. We find that with decreasing the isospin of the U nucleus, the sensitivity of $P_{f0}$ to $\beta$ is substantially enhanced, and that low-isospin ${}^{240}\mathrm{Cm}$ exhibits a significantly larger dependence on $\beta$ than high-isospin ${}^{240}\mathrm{U}$. Furthermore, it is shown that $P_{f0}$ becomes more sensitive to $\beta$ at low energy. These findings suggest that to accurately probe presaddle dissipation properties with first-chance fission probability, on the experimental side, it is best to produce those heavy fissioning systems with small isospin and low excitation energy.

We report exclusive measurements for the $\eta$ photoproduction on a proton target. The differential cross sections and photon beam asymmetries of the $\gamma p\to \eta p$ reaction are measured in a center-of-mass energy ($W$) range of 1.82–2.32 GeV and a polar angle range of $-1.0<cos{\theta }_{\mathrm{c}.\mathrm{m}.}^{\eta }<0.6$ by using a large acceptance calorimeter (BGOegg) and forward-angle charged-particle detectors at the SPring-8 LEPS2 beamline. The reaction is identified with a kinematic fitting method to select a recoil proton and two photons produced in an $\eta$ meson decay. A bump structure at $W$ = 2.0–2.3 GeV in the differential cross section is confirmed at extremely backward $\eta$ polar angles, where the existing data are inconsistent with each other. This bump structure is likely associated with high-spin resonances that couple with $s\overline{s}$ quarks. The photon beam asymmetries in a wide $\eta$ polar angle range for the photon beam energies above 2.1 GeV are reported for the first time, providing an additional constraint to nucleon resonance studies at high energies.

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the CERN Large Hadron Collider (LHC), $d\sigma /dy(\text{Pb}+\text{Pb}\to \text{Pb}+J/\psi +\text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale choice and PDFs, and compare our results with ALICE, CMS, and LHCb $J/\psi$ photoproduction data in $\mathrm{Pb}+\mathrm{Pb}$ UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in $p+p$. The scale dependence in $d\sigma /dy(\text{Pb}+\text{Pb}\to \text{Pb}+J/\psi +\text{Pb})$ is significant, but we can find a scale choice that reproduces the $\mathrm{Pb}+\mathrm{Pb}$ UPC data at both 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner, where the relative signs of the LO and NLO terms in the amplitude play a significant role.

Lifetimes have been measured for the low-lying yrast levels of ${}^{130,132}\mathrm{Te}$ using $\gamma -\gamma$ fast timing methods. The excited states were populated in ${\beta }^{-}$ and IT decay of fission fragments, mass-separated by the Lohengrin separator at Institut Laue-Langevin. Four ${\mathrm{LaBr}}_3$(Ce) detectors, placed at the focal plane of the spectrometer, were used for the $\gamma -\gamma$ fast timing measurement. Lifetimes of $\mu \mathrm{s}$ isomers were measured using coincidence of an ionization chamber with two Clover HPGe detectors. The measured lifetimes and absolute transition probabilities are discussed in the light of systematics with the neighboring nuclei. Large basis shell model calculations have been performed to interpret the level structure and transition probabilities in these even mass Te isotopes.

The low-lying states of ${}^{146}\mathrm{Eu}$ populated in the decay of the $9^{+}$ isomer were studied. The $\gamma$-ray intensities were reanalyzed employing germanium detectors, and the lifetimes of the $6_1^{-}$ and $6_2^{-}$ states were measured using the mirror symmetric centroid difference (MSCD) method with fast-timing ${\mathrm{LaBr}}_3$(Ce) scintillator detectors. The $B\left(M1\right)$ values of the $6_1^{-}\to 5_1^{-}$ and $6_2^{-}\to 5_1^{-}$ transitions were deduced, and all observed states were interpreted as members of the $\pi d_{5/2}^{-1}\nu f_{7/2}$ and $\pi g_{7/2}^{-1}\nu f_{7/2}$ multiplets. In particular, the $5_1^{-}$ level is shown to be dominated by the $\pi d_{5/2}^{-1}\nu f_{7/2}$ configuration, solving the discrepancy in its configuration assignment proposed in previous works. These experimental results were compared with the shell model calculations using several different effective interactions. The systematics of low-lying structure in the $N=83$ isotones ${}^{142}\mathrm{Pr}$, ${}^{144}\mathrm{Pm}$, and ${}^{146}\mathrm{Eu}$ was established.

We investigate photon emission at the hadronization stage from a quark-gluon plasma created in relativistic heavy-ion collisions. A recombination-model picture suggests that a quark and an antiquark bind into a meson state in hadronization, which would apparently violate the energy conservation if there is nothing else involved. We consider here a hadronization process where the recombination accompanies a photon emission. This is an analog of the “radiative recombination” known in plasma physics, such as $e^{-}+p^{+}\to {\mathrm{H}}^0+\gamma$, which occurs when an electromagnetic plasma goes back to a neutral atomic gas. The “radiative hadronization” picture will bring about (i) an enhancement of the photon yield, (ii) significant flow of photons similar to that of hadrons, and (iii) the photon transverse momentum ($p_T$) distribution with a thermal profile whose effective temperature is given by the blue-shifted temperature of quarks. Here as a simplest and phenomenological realization of the radiative hadronization, we modify the recombination model to involve a photon emission and evaluate the photon yield with this modified model. Adding this contribution to the direct photon yield along with the thermal photon contribution calculated with a hydrodynamic model and a parametrized contribution of prompt photons, we study the $p_T$ spectrum and elliptic flow of the photons produced in heavy-ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider.

The production of $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ mesons in proton–proton $\left(pp\right)$ and lead–lead (Pb–Pb) collisions at $\sqrt{s_{NN}}$ $=$ 5.02 TeV has been measured using the ALICE detector at the Large Hadron Collider (LHC). The transverse momentum $\left(p_{\mathrm{T}}\right)$ distributions of $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ mesons have been measured at midrapidity $\left(\right|y|<0.5)$ up to $p_{\mathrm{T}}=$ 20 $\mathrm{GeV}/c$ in inelastic $pp$ collisions and for several Pb–Pb collision centralities. The collision centrality and collision energy dependence of the average transverse momenta agree with the radial flow scenario observed with stable hadrons, showing that the effect is stronger for more central collisions and higher collision energies. The $K^{*0}/K$ ratio is found to be suppressed in Pb–Pb collisions relative to $pp$ collisions: this indicates a loss of the measured $K^{*}{\left(892\right)}^0$ signal due to rescattering of its decay products in the hadronic phase. In contrast, for the longer-lived $\varphi \left(1020\right)$ mesons, no such suppression is observed. The nuclear modification factors ($R_{AA}$) of $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ mesons are calculated using $pp$ reference spectra at the same collision energy. In central Pb–Pb collisions for $p_{\mathrm{T}}$ $>$ 8 $\mathrm{GeV}/c$, the $R_{AA}$ values of $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ are below unity and observed to be similar to those of pions, kaons, and (anti)protons. The $R_{AA}$ values at high $p_{\mathrm{T}}$ ($>$8 $\mathrm{GeV}/c$) for $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ mesons are in agreement within uncertainties for $\sqrt{s_{NN}}=$ 5.02 and 2.76 TeV.

A new two-dimensional procedure for extrapolation of the values of matter, neutron, and proton radii obtained in no-core shell model (NCSM) calculations to infinite size of its basis is proposed. A relationship between the radii is used as an additional test. Together with the JISP16 potential, which is frequently used in NCSM calculations of the radii, the Daejeon16 potential is applied for these purposes. Halo nucleus ${}^6\mathrm{He}$ is the object of studies. The small spread of radii values and reasonable agreement between the obtained results and experimental data as well as the results of other advanced ab initio calculations demonstrate the high efficiency of the developed approach and, therefore, good prospects for its application. The performed investigations and analysis of the results of other studies indicate that the halo of ${}^6\mathrm{He}$ has a large size: 0.7–0.8 fm.

We present some analytic results that describe the gluon field, or glasma, that exists at very early times after a collision of relativistic heavy ions at proper time $\tau =0$. We use a color glass condensate approach, and perform an expansion in $\tau$. The full details of our calculational method are described in our previous paper [Carrington, Czajka, and Mrówczyński, Eur. Phys. J. A 58, 5 (2022)], where we have explained all of the steps that are necessary to obtain the energy-momentum tensor up to sixth order in $\tau$. In this paper we present an analysis of various physical quantities that can be obtained from this energy-momentum tensor. We show that the expansion to order ${\tau }^6$ can be trusted to about $\tau =0.05$ fm. We calculate the transverse and longitudinal pressures and show that, for times small enough that the expansion converges, they move towards their equilibrium values of one third of the energy density. We also study the spatial eccentricity of the glasma and the Fourier coefficients of the azimuthal flow. Our results for the Fourier coefficients are larger than expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial asymmetry introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are characteristic of the onset of hydrodynamic behavior. Finally, we have calculated the angular momentum of the glasma and obtained results that are many orders of magnitude smaller than the angular momentum of the initial system of colliding ions in a configuration with nonzero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma. The result is significant because it contradicts the picture of a rapidly rotating initial glasma state that has been proposed by several authors, but agrees with the current lack of experimental evidence for a significant polarization effect of the hyperons and vector mesons produced in heavy ion collisions at the highest accessible energies.

The light-nuclei yield ratio is one of the candidates to probe the critical fluctuations of hot QCD matter. In this paper, we investigate the background effects, namely, the noncritical effects coming from the nontrivial thermal background, on the light-nuclei production within the framework of the coalescence model. Specifically, we analyze the impact of the equilibrium phase-space distribution function of nucleons, $f(\mathit{r},\mathit{p})$, on the light-nuclei yield ratio $N_t{N}_p/N_d^2$, where $N_t, N_p$, and $N_d$ denote triton, proton, and deuteron yields. By considering the characteristic function of the phase-space distribution, we systematically expand the yield of light nuclei of $A$-constituent nucleons, $N_A$, in terms of the phase-space cumulants, ${\langle {\mathit{r}}^n{\mathit{p}}^m\rangle }_c$. We find that the cumulants up to the second-order are canceled out in the generalized ratio $N_p^{B-A}{N}_B^{A-1}/N_A^{B-1}$. This means that the dominant background effects including the fireball size, the kinetic freeze-out temperature, and the coordinate-momentum correlations caused by the radial expansion play an insignificant role in the yield ratio, which supports the yield ratio as a useful tool for the critical-point search. We also show several examples of background phase-space distributions for the qualitative illustration. The higher-order cumulants, which correspond to the non-Gaussian shape of the phase-space profile, play an important role in the variation of the yield ratio, particularly for smaller fireball sizes. Qualitatively, the spatial structure of the background decreases the yield ratio, and the azimuthal anisotropy $v_n$ increases it. The higher order of the azimuthal anisotropy causes a larger effect on the yield ratio. These results call for the comprehensive future studies of the yield ratio using sophisticated dynamical models.

Background: Although microscopic models are frequently used to investigate giant resonances built on the ground state of a nucleus, similar calculations at nonzero temperature are limited. Approaches based on the classical thermal shape-fluctuation model (TSFM) are often utilized to analyze the properties of giant dipole resonance at finite temperature. However, TSFM fails to predict the correct trend of resonance width over a wide range of temperature starting from zero.

Purpose: To study the isovector giant dipole resonance (IVGDR) at finite temperature, we present an improved version of TSFM, where driving potential and IVGDR centroid energies are obtained self-consistently using the nuclear energy density functional formalism. The temperature dependence of IVGDR width in ${}^{120}\mathrm{Sn}$ is calculated to benchmark the proposed method.

Method: Nuclear free energy surfaces and entropy surfaces are simulated at different temperatures for two different parametrizations of Skyrme energy density functionals. Moreover, IVGDR centroid energies are calculated by incorporating nuclear deformations extracted from the corresponding self-consistent densities. Subsequently, IVGDR widths are obtained within TSFM. Also, we demonstrate the role of pairing fluctuation in improving the low temperature behavior of IVGDR width.

Result: We found good overall agreement of our results with the measured IVGDR widths. Specifically, except at a very low temperature, unprecedented accuracy has been achieved in TSFM. Calculated IVGDR widths are shown to be robust against the choices of driving potential and Skyrme parametrization.

Conclusion: The present paper provides guidance on using TSFM based calculations in predicting the IVGDR width over a broad range of temperature. For a more consistent calculation, pairing fluctuations are required to be included as additional degrees of freedom.