A detailed level scheme of ${}^{213}\mathrm{Fr}_{126}$ following the $\mathrm{EC}/{\beta }^{+}$ decay of the $1/2^{-}{}^{213}\mathrm{Ra}$ parent ground state was built in an experiment performed at the ISOLDE Decay Station, CERN. The fragmented total $\beta$ decay strength favours the direct population of several low-spin ($J\le 7/2$) excited states. The analysis of the $\gamma$-singles spectrum and $\gamma \text{−}\gamma$ coincidences allowed us to identify many new $\gamma$-ray transitions and excited states in ${}^{213}\mathrm{Fr}$ up to about 3.6 MeV excitation energy. The spins and parities of the newly established levels, on top of the $(7/2_1^{-})$ state, were mainly assigned based on the systematics of the $N=126$ isotones and further compared with shell-model calculations. The level scheme displays a structural pattern, with several groups of states with negative parity, emerging from the well-defined, simple, $\pi \left(h_{9/2}^5\right)$, $\pi \left(h_{9/2}^4{f}_{7/2}^1\right)$ configurations or from their configuration mixing. The strength of the E2 transitions within the multiplets is compared with shell-model theoretical calculations performed with the KHPE and H208 effective interactions. A new $(3/2^{-})$ isomer with a half-life of 26(3) ns has been identified. An upper limit of 35 ps was determined for the half-life of the first excited state, $7/2^{-}$. The possibility of a mixed $M1+E2$ character is discussed for the $7/2_1^{-}\to 9/2_{\text{gs}}^{-}$ decay in ${}^{213}\mathrm{Fr}$, which leads to an $l$-forbidden nature of the $\pi f_{7/2}\to \pi h_{9/2}$ transition.

Background: Foster et al. measured total neutron cross sections ${\sigma }_{\mathrm{T}}$ of $n+{}^{208}\mathrm{Pb}$ scattering at $E_{\mathrm{lab}}=14.137\mathrm{MeV}$, where $E_{\mathrm{lab}}$ is an incident energy per nucleon. Carlson et al. measured reaction cross sections ${\sigma }_{\mathrm{R}}$ for $p+{}^{48}\mathrm{Ca}$ scattering in $E_{\mathrm{lab}}=23–48\mathrm{MeV}$. Tanaka et al. measured interaction cross sections ${\sigma }_{\mathrm{I}}$ for ${}^{42–51}\mathrm{Ca}+{}^{12}\mathrm{C}$ scattering at 280 MeV/nucleon. Ozawa et al. accumulated the measured values of ${\sigma }_{\mathrm{I}}$ and the extracted matter radii $r_{\mathrm{m}}$ from ${}^4\mathrm{He}$ to ${}^{32}\mathrm{Mg}$. Bagchi et al. measured the charge-changing (CC) cross sections and determined proton radii $r_{\mathrm{p}}\left(\mathrm{CC}\right)$ for ${}^{14,15,17–22}\mathrm{N}$ from the CC cross sections, and found a signal of ${}^{22}\mathrm{N}$ being a halo nucleus. Kanungo et al. measured the CC cross sections and extracted $r_{\mathrm{p}}\left(\mathrm{CC}\right)$ for ${}^{12–19}\mathrm{C}$. Kaur et al. measured the CC cross sections and determined $r_{\mathrm{p}}\left(\mathrm{CC}\right)$ for ${}^{16,18–24}\mathrm{O}$.

Purposes: Our first aim is to extract neutron skin thickness $r_{\mathrm{skin}}^{208}$ from the ${\sigma }_{\mathrm{T}}$ of $n+{}^{208}\mathrm{Pb}$ scattering at $E_{\mathrm{lab}}=14.137\mathrm{MeV}$. Our second aim is to determine $r_{\mathrm{skin}}^{48}\left(\mathrm{skin}\right)$ from ${\sigma }_{\mathrm{R}}$ on $p+{}^{48}\mathrm{Ca}$ scattering in $E_{\mathrm{lab}}=23–48\mathrm{MeV}$. Our third aim is to find light stable nuclei having nuclei having large $r_{\mathrm{skin}}$.

Methods: We use the Kyushu $g$-matrix folding model for lower $E_{\mathrm{lab}}$ and the folding model based on the Love-Franey $t$ matrix for higher $E_{\mathrm{lab}}$. We tested the Kyushu (chiral) $g$-matrix folding model for reaction cross sections ${\sigma }_{\mathrm{R}}$ on $p+{}^{208}\mathrm{Pb}$ scattering in $20\lesssim E_{\mathrm{lab}}\lesssim 180\mathrm{MeV}$ and found that our folding model is reliable. For ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering, we tested the Kyushu $g$-matrix folding model and found that the folding model is reliable for ${\sigma }_{\mathrm{R}}$ in $30\lesssim E_{\mathrm{lab}}\lesssim 100\mathrm{MeV}/\mathrm{u}$ and $250\lesssim E_{\mathrm{lab}}\lesssim 400\mathrm{MeV}/\mathrm{u}$.

Results: We extract $r_{\mathrm{skin}}^{208}=0.309\pm 0.057$ fm from the ${\sigma }_{\mathrm{T}}$. For ${}^{48}\mathrm{Ca}$, we determine $r_{\mathrm{skin}}^{48}\left(\mathrm{skin}\right)=0.163\pm 0.037\mathrm{fm}$ from the ${\sigma }_{\mathrm{R}}$ on $p+{}^{48}\mathrm{Ca}$ scattering, using the Kyushu $g$-matrix folding model with the $\text{D1M-GHFB}+\text{AMP}$ proton and neutron densities, where $\text{D1M-GHFB}+\text{AMP}$ is Gogny-D1M HFB (D1M-GHFB) with angular momentum projection (AMP). We show that $\text{D1M-GHFB}+\text{AMP}$ is better than $\mathrm{D}1\text{S-GHFB}+\text{AMP}$ for the matter radius and the binding energy. Our skin value is consistent with $r_{\mathrm{skin}}^{48}\left(\mathrm{CREX}\right)$. For C, N, O isotopes, we find that ${}^{14}\mathrm{N}$ and ${}^{17}\mathrm{O}$ have large $r_{\mathrm{skin}}$, i.e., $r_{\mathrm{skin}}=0.267\pm 0.056$ fm for ${}^{14}\mathrm{N}$ and $r_{\mathrm{skin}}=0.197\pm 0.067$ fm for ${}^{17}\mathrm{O}$.

Conclusion: The value $r_{\mathrm{skin}}^{208}=0.309\pm 0.057$ fm agrees with $r_{\mathrm{skin}}^{208}\left(\mathrm{PREX}2\right)$.

We present a calculation of the spin polarization of spin-1/2 fermions in a relativistic fluid at local thermodynamic equilibrium at the second order in the gradient expansion, including second-order derivatives. The second-order derivative terms vanish if the local equilibrium hypersurface is the hyperplane $t=\mathrm{const}$ in the collision center-of-mass frame. However, since the freeze-out hypersurface has a nontrivial space-time structure, these terms may result in a nonvanishing contribution to the spin polarization, whose magnitude needs to be assessed with numerical computations.

Background: $\beta$-decay rates of neutron-rich nuclei are a crucial ingredient in simulations of the $r$-process nucleosynthesis. Up to now global calculations of these rates have been performed within the quasiparticle random-phase approximation (QRPA), which is known to have limited accuracy and predictive power due to a limited treatment of nuclear correlations. Although extensions of this approach have been developed to include a more precise description of correlations, and have been applied to the study of allowed $\beta$-decay of selected nuclei, no systematic calculations including first-forbidden transitions have so far been performed.

Purpose: The goal of this work is to compute $\beta$-decay half-lives of isotonic nuclear chains located at neutron shell closures $N=50$, 82, 126, and 184, which are of particular importance for the $r$-process nucleosynthesis, and to study the role of first-forbidden transitions in a framework that includes complex nucleonic correlations beyond the QRPA.

Method: The many-body approach based on the relativistic QRPA extended to account for the coupling between single-particle and collective degrees of freedom is applied. Both Gamow-Teller and first-forbidden contributions to the decay rates are considered.

Results: Overall, the fragmentation of the transition strength distributions due to the coupling between single particles and collective vibrations systematically increases the transition strength at low excitation energies and yields a decrease of the $\beta$-decay half-lives which is particularly important for low $Q$ values. Such effects are crucial to bring Gamow-Teller transitions within the decay energy window, and to reproduce the measured decay rates. Generally, quasiparticle-vibration coupling tends to decrease the probability of decay via FF transition near stability, due to the appearance of Gamow-Teller transitions within the decay $Q$ value. While in lighter systems allowed transitions dominate, the decay of $N=126$ and $N=184$ nuclei is found to occur to a large extent via first-forbidden transitions, and in particular those induced by $1^{-}$ and $0^{-}$ operators.

Conclusions: The relativistic approach based on the coupling between nucleons and vibrations has the ability to capture relevant correlations that are essential for an accurate predictions of $\beta$ decay and provides an ideal framework for future large-scale calculations. Upcoming experimental measurements of $\beta$-decay rates in the $N=126$ region by radioactive-beam facilities will be crucial in order to validate the approach.

The $B\left(E3\right)$ transition strengths in ${}^{90}\mathrm{Zr}$ and ${}^{91}\mathrm{Zr}$ isotopes were determined based on the half-life measurements of the first $3^{-}$ and ${(11/2)}^{-}$ states, i.e., $T_{1/2}=7.8\left(16\right)$ ps and 500(16) ps, respectively. The plunger method and fast-timing techniques were employed. The $B\left(E3\right)$ values of 16(3) and 20.5(7) W.u. for ${}^{90}\mathrm{Zr}$ and ${}^{91}\mathrm{Zr}$ were derived, pointing to a sizable octupole collectivity in both cases. The ${}^{90}\mathrm{Zr}$ value complements the systematics of the octupole strength in even-even Zr isotopic chain, revealing a smooth trend between $A=90$ and 96, which is in agreement with the pattern of octupole strength predicted by quasiparticle random phase approximation calculations. In ${}^{91}\mathrm{Zr}$, the hybrid configuration mixing model describes the ${(11/2)}^{-}$ low-energy strength in terms of a coupling of the unpaired neutron with the $3^{-}$ octupole excitation of the ${}^{90}\mathrm{Zr}$ core, predicting a slight decrease of octupole strength which is in contrast with the experimental result. This suggests a more complex structure for the ${(11/2)}^{-}$ state in ${}^{91}\mathrm{Zr}$ than predicted by the weak-coupling limit.

The depth of nuclear potential for $\alpha$ decay is systematically investigated using 178 measured $\alpha$-decay half-lives of even-even nuclei. We find that, by considering the shell effect in the depth of the potential, the results can be significantly improved. The root-mean-square deviation across the 178 data points is reduced from 0.278 to 0.188 by introducing a new formula that accounts for the shell correction dependence of potential depth. The $\alpha$-decay half-lives for unknown nuclei with charge numbers $Z=118$ and 120 are predicted with the proposed formula.

We investigate the ${}_{\varphi }{}^9\mathrm{Be}$ and ${}_{\varphi \varphi }{}^6\mathrm{He} \varphi$ mesic nuclei within the framework of the three-body cluster model as the $\varphi +\alpha +\alpha$ and $\varphi +\varphi +\alpha$ systems, using the Faddeev formalism in configuration space. The $\varphi \text{−}\alpha$ potential is determined through a folding procedure of the HAL QCD $\varphi \text{−}N$ interaction in the ${}^{4}S_{3/2}$ channel with the matter distribution of ${}^4\mathrm{He}$. The phenomenological $\alpha \text{−}\alpha$ and $\varphi \text{−}\varphi$ potentials are taken from the literature. Additionally, we construct a Wood-Saxon (WS) type interaction to simulate the $\varphi \text{−}\alpha$ potential, also taken from the literature, based on an effective Lagrangian approach that includes $K\overline{K}$ meson loops in the $\varphi$-meson self-energy. A comparison of binding energies obtained for both types of the $\varphi \text{−}\alpha$ interactions reveals qualitative agreement. We predict the binding energy for the ${}_{\varphi }{}^9\mathrm{Be}$ and ${}_{\varphi \varphi }{}^6\mathrm{He} \varphi$ mesic nuclei as the mirror $\varphi +\alpha +\alpha$ and $\varphi +\varphi +\alpha$ systems in the ranges of 1–11 and 3–10 MeV, respectively. The range of values of the binding energies relies on the choice of the WS $\varphi \text{−}\alpha$ interaction parameters.

Cross sections of ${}^{86}\mathrm{Sr}\left(d,x\right)$ reactions leading to the products ${}^{84m,g}\mathrm{Rb}, {}^{83}\mathrm{Rb}$, and ${}^{82m}\mathrm{Rb}$ were measured by the stacked-sample activation technique up to deuteron energies of 49 MeV. Nuclear model calculations were performed using the codes talys and empire, which combine the statistical, precompound, and direct interaction components. In all cases, the empire results were much higher than the talys calculation. Fairly good agreement was obtained between measured data and the talys calculation after some optimization of the input model parameters. Insight into competition between α-particle and multinucleon emission in the ${}^{88}\mathrm{Y}$ compound-nucleus system was also gained.

The synthesis of new nuclides is an important direction in nuclear physics research. This article explores the optimal methods for producing new nuclides in the transuranic nuclear region. Based on the dinuclear system model, the influence of the isospin effect on the synthesis of actinide neutron-deficient nuclides through fusion evaporation reactions is studied. It is found that, for the same compound nucleus, using projectile-target combinations with a smaller neutron asymmetry can result in a larger capture cross section. Subsequently, taking the synthesis of curium element isotopes as an example, the best method for producing new actinide nuclides is explored. It is found that fusion evaporation reactions can achieve a larger reaction cross section under extremely neutron-deficient conditions, while multinucleon transfer reactions have a larger cross section in the neutron-rich region. Finally, the possibility of producing superheavy neutron-rich nuclides using multinucleon transfer reactions is theoretically predicted.

We demonstrate, in the context of a scalar version of the chiral effective-field theory, that the multisea quark contribution to the nucleon is significant and highly nontrivial, in sharp contrast with the prediction of perturbation theory. The nonperturbative calculation is performed in the Fock sector dependent renormalization scheme on the light front, in which the nonperturbative renormalization is incorporated. The calculation suggests that a fully nonperturbative calculation of the chiral EFT is needed to obtain a robust result to be compared with the recent experimental measurement of flavor asymmetry in the proton.

The ratio of the transverse and longitudinal components of polarization transfer to protons in the quasielastic $(\vec{e},e^{\prime }\vec{p})$ reaction, $P_x^{\prime }/P_z^{\prime }$, is sensitive to the proton's electromagnetic form factor ratio, $G_E/G_M$. To explore density-dependent in-medium modifications, a comparison of polarization transfer ratios involving protons from distinct nuclear shells, each with different local nuclear densities, has been proposed. In this study, we present such comparisons between four shells, $1s_{1/2},1p_{3/2}$ in ${}^{12}\mathrm{C}$ and $1d_{3/2},2s_{1/2}$ in ${}^{40}\mathrm{Ca}$. In an effort to account for other many-body effects that may differ between shells, we use a state-of-the-art relativistic distorted-wave impulse-approximation (RDWIA) calculation and present the double ratios ${(P_x^{\prime }/P_z^{\prime })}_{\mathrm{Data}}/{(P_x^{\prime }/P_z^{\prime })}_{\mathrm{RDWIA}}$ as well as the super-ratios ${[{(P_x^{\prime }/P_z^{\prime })}_{\mathrm{A}}/{(P_x^{\prime }/P_z^{\prime })}_{\mathrm{B}}]}_{\mathrm{Data}}/{[{(P_x^{\prime }/P_z^{\prime })}_{\mathrm{A}}/{(P_x^{\prime }/P_z^{\prime })}_{\mathrm{B}}]}_{\mathrm{RDWIA}}$, for chosen shells A and B, as a function of effective local nuclear densities. We find that double ratios for individual shells show a dependence on the probed effective nuclear densities. Studying the super-ratios, we observed a systematic variation between pairs of higher- and lower-density shells.

This work presents a formalism to compute spatial $n$-point correlations of a conserved charge density in a large thermal system in the canonical ensemble, with explicit results presented up to fourth order. The resulting correlators contain local and balancing terms expressed through the grand-canonical susceptibilities for any equation of state. The new formalism is used to introduce a Gaussian local baryon number conservation in (spatial) rapidity in heavy-ion collisions at CERN Large Hadron Collider conditions through a modulation of the balancing term. Connection to the conservation volume $V_c$ approach is established, indicating that the latter is appropriate for observables within a limited range around midrapidity. Quantitative analysis of the experimental data of the ALICE Collaboration on net proton cumulants in central Pb-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV shows significant evidence for local baryon conservation.

Ultrarelativistic isobar collisions have been proposed as a useful tool to investigate nuclear structure. These systems are not created in equilibrium, rather they undergo a pre-thermalization stage. In this stage, some of the initial structure information may be lost and additional effects introduced. The objective of this paper is to study this possibility in the extreme case of a “free-streaming” pre-equilibrium stage. We do this by computing estimators for ratios of various measured (or measurable) quantities (elliptic and triangular flows, mean transverse momentum and associated cumulants, correlators between elliptic or triangular flows and mean transverse momentum, symmetric cumulant, and two-plane correlator) and study their sensitivity to the duration of the free-streaming stage. We find that the correlators between elliptic or triangular flows and mean transverse momentum, the so-called ${\rho }_2$ and ${\rho }_3$, are indeed sensitive to the duration of the free-streaming stage and that the normalized symmetric cumulant, $\varepsilon \text{NSC}(2,3)$ might also depend on this duration.

Lifetimes of excited nuclear states were determined in ${}^{59}\mathrm{Ni}$ and ${}^{57}\mathrm{Fe}$ utilizing the recoil distance Doppler-shift technique. The results are based on the fusion-evaporation reactions ${}^{51}\mathrm{V}({}^{12}\mathrm{C},\mathrm{pn}\alpha ){}^{57}\mathrm{Fe}$ and ${}^{51}\mathrm{V}({}^{12}\mathrm{C}$,p3n)${}^{59}\mathrm{Ni}$ measured at the FN Tandem accelerator in Cologne. Reduced transition strengths were deduced from the lifetime values and compared to shell-model calculations employing the GXPF1A interaction along the $N=31$ isotonic chain and for several $Z=28$ even-odd Ni isotopes. Existing large discrepancies between previous experimental $E2$ strength values and the corresponding GXPF1A values in ${}^{59}\mathrm{Ni}$ were resolved by the new experimental results. The shell closure for the $Z=28$ isotope ${}^{59}\mathrm{Ni}$, indicated by a drop in the $B(E2;9/2_1^{-}\to 5/2_1^{-})$ value, is clearly observed, in contrast to evaluated data. Despite the good agreement between experiment and theory for most $B\left(E2\right)$ values, considerable deviations remain for the new experimental $B\left(M1\right)$ values and results from GXPF1A calculations.

Background: Masses of neutron-rich exotic nuclei are important for both nuclear physics and nuclear astrophysics, yet most of them remain beyond the current experimental capabilities. The relativistic continuum Hartree-Bogoliubov (RCHB) theory has achieved great success in the study of exotic nuclei. In the first paper of this series [Phys. Rev. C 109, 024310 (2024)], the kernel ridge regression (KRR) approach has been employed to refine the RCHB mass model, and the predictive power has been validated through comparison with the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for even-even nuclei. Recently, the mass data for even-odd nuclei have been released by the DRHBc Mass Table Collaboration [At. Data Nucl. Data Tables 158, 101661 (2024)]. The KRR approach has been extended to incorporate odd-even effects [Phys. Lett. B 819, 136387 (2021)], thereby enhancing its capability in nuclear mass predictions.

Purpose: The aim of this work is to combine the RCHB mass model and the extended KRR approach with odd-even effects (KRRoe) to improve the predictions of masses and separation energies for neutron-rich exotic nuclei.

Method: In the KRRoe approach, the odd-even effect is incorporated by remodulating the kernel function in the KRR framework. The KRRoe network is trained with the RCHB mass residuals, i.e., deviations between experimental and calculated masses. Four hyperparameters contained in the KRRoe approach are optimized through the leave-one-out cross validation. The mass data in different AME series are employed to validate the generalization ability of the KRRoe approach. The DRHBc mass model for even-even and even-odd nuclei is employed to help pin down the capacity of the KRRoe extrapolations.

Results: The refined RCHB mass model with KRRoe corrections can achieve a mass accuracy with a root-mean-square deviation of 177 keV from the experimental data. Especially, it improves the accuracy of separation energy from approximately 500 keV, given by the KRR approach, to the level of 200 keV. The generalization and extrapolation of the KRRoe approach in refining the RCHB predictions are found reliable and extensive.

Conclusions: A mass model incorporating the RCHB theory with properly treated continuum effects and the KRRoe approach with properly included odd-even effects has been developed. This model demonstrates accuracy in the reproduction of experimentally known masses and separation energies, as well as reliability in generalization and extrapolation to experimentally unknown neutron-rich regions.

A study of the $N=81$ odd-odd nucleus ${}^{140}\mathrm{Pr}$ with the ${}^{142}\mathrm{Nd}(d,\alpha )$ reaction at 18-MeV incident energy is presented. A distorted-wave Born approximation analysis of measured angular distributions has been performed for 23 excited states up to $E_x=1.35$ MeV, yielding information on the spin, parity, and sometimes on the simple proton-neutron structure of these states. The observed structure is discussed in comparison with that of other $N=81$ isotones, from ${}^{136}\mathrm{Cs}$ to ${}^{144}\mathrm{Eu}$, and with shell-odel calculations.

Background: Quantum shell effects are crucial for the stability and structure of atomic nuclei and play a key role in the discovery of superheavy elements. However, during nuclear collisions, the dynamical evolution of these shell effects disrupts the equilibration process necessary for forming a compound nucleus, leading to the breakup of the initial composite as a result of quasifission. As such, quasifission reactions hinder the formation of a superheavy element.

Purpose: In our previous study [L. Li et al., Phys. Lett. B 833, 137349 (2022)], we identified that tensor forces significantly influence the evolution of dynamical shell effects in quasifission reactions of the ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ system, particularly affecting the competition between spherical and deformed shell gaps. This paper aims to extend our previous findings by employing TIJ parametrizations of the Skyrme interaction to investigate the effects of isoscalar and isovector tensor coupling constants on quasifission products. Additionally, we aim to validate our conclusions by analyzing the ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ system, for which experimental data are available.

Method: We employ the microscopic time-dependent Hartree-Fock theory to study the ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ and ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ systems, taking into account the dependence on orientation for deformed nuclei and full range of impact parameters. By analyzing fragment distributions of neutron and proton numbers, we assess the influence of different isoscalar and isovector tensor coupling constants of the effective nucleon-nucleon interaction.

Results: The quasifission yield distributions of a ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ collision system utilizing SLy5t and T31 parametrizations exhibit more pronounced spherical shell effects compared to those using SLy5, T44, and T62 sets. Furthermore, within each parametrization group, the distributions for SLy5t and T31 are closely aligned, as are those for SLy5, T44, and T62. Similarly, the yield distributions for the ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ system using SLy5t and T31 also reflect the more pronounced spherical shell effects relative to SLy5 and T62, while the charge distribution shows much better agreement with experimental results for the SLy5t and T62 parametrizations compared to SLy5 and T31.

Conclusions: The yield distributions for the ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ and ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ systems, when compared across the SLy5, SLy5t, T31, T44, and T62 parametrizations, indicate that the influence of tensor forces on quasifission fragments is reflected in the prominence of shell effects. This influence appears to be sensitive only in specific regions within the isoscalar and isovector coupling constant parameter space. In the ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ system, the prominence of shell effects is manifested not only through shifts in peak positions, but also through narrower yield distributions.

Peculiar phenomena have been observed in analyses of anisotropic flow ($v_n$) fluctuations in ultracentral nucleus-nucleus collisions: The fourth-order cumulant of the elliptic flow ($v_2$) distribution changes sign. In addition, the ATLAS Collaboration has shown that cumulants of $v_n$ fluctuations of all orders depend significantly on the centrality estimator. We show that these peculiarities are due to the fact that the impact parameter $b$ always spans a finite range for a fixed value of the centrality estimator. We provide a quantitative determination of this range through a simple Bayesian analysis. We obtain excellent fits of STAR and ATLAS data, with a few parameters, by assuming that the probability distribution of $v_n$ solely depends on $b$ at a given centrality. This probability distribution is almost Gaussian, and its parameters depend smoothly on $b$, in a way that is constrained by symmetry and scaling laws. We reconstruct, thus, the impact parameter dependence of the mean elliptic flow in the reaction plane in a model-independent manner, and assess the robustness of the extraction using Monte Carlo simulations of the collisions where the impact parameter is known. We argue that the non-Gaussianity of $v_n$ fluctuations gives direct information on the hydrodynamic response to initial anisotropies, ATLAS data being consistent with a smaller response for $n=4$ than for $n=2$ and $n=3$, in agreement with hydrodynamic calculations.

In this work, we construct a unified equation of state (EOS) for neutron stars with a microscopic approach to describe both the core and the crust of these compact objects. For this aim, we calculate the composition and EOS of crust using compressible liquid drop approximation and the metamodeling of asymmetric nuclear matter approach. Such approach is calculated by applying the lowest-order constrained variational method using ${\mathrm{AV}}_{18}$ potential plus different sets of three-nucleon interactions. Furthermore, we determine the structural properties of neutron star and its crust like mass, radius, and moment of inertia for the selected EOSs. We also compare our results with various astrophysical constraints including the mass measurements of binary pulsars, measurements of radius of pulsars by NICER, and tidal deformability relevant to gravitational wave detection GW170817.