The elliptic azimuthal anisotropy coefficient ($v_2$) of open-charm hadrons at midrapidity ($|\eta <1|$) was studied in $p$-Pb collisions at $\sqrt{s_{NN}}=8.16$ TeV using a multiphase transport (ampt) model including an additional charm quark–antiquark pair production trigger. The model provides a simultaneous description of the measured $p_{\mathrm{T}}$ spectrum and $v_2$ of the $D^0$ meson, as well as the $v_2$ of light flavor meson $K_s^0$. We found that the $D^0$ and $K_s^0 v_2$ are both significantly affected by different parton scatterings among charm and light quarks. In addition, the predictions for the $v_2$ of other charm hadrons including $D^{+}, D_s^{+}$, and ${\mathrm{\Lambda }}_c^{+}$ in $p$-Pb collisions are given for the first time. The $v_2$ of open-charm hadrons reasonably follows the number-of-constituent-quark (NCQ) scaling up to 2.5 GeV, strongly indicating the importance of partonic degrees of freedom for the collectivity of heavy flavors in high-multiplicity $p$-Pb collisions. These findings may hint at the formation of deconfined matter in small collision systems, and provide referential value for future measurements of azimuthal anisotropy at energies available at the CERN Large Hadron Collider.

We predict neutron-proton scattering cross sections and polarization observables up to next-to-next-to-next-to-leading order in a renormalization-group invariant description of the strong nucleon-nucleon interaction. Low-energy constants are calibrated to phase shifts, subleading corrections are computed in distorted-wave perturbation theory, and we employ momentum-cutoff values 500 and 2500 MeV. We find a steady order-by-order convergence and realistic descriptions of scattering observables up to a laboratory scattering energy of approximately 100 MeV. We also compare perturbative and nonperturbative calculations for phase shifts and cross sections and quantify how unitarity is gradually restored at higher orders. The perturbative approach offers an important diagnostic tool for any power counting and our results suggest that the breakdown scale in chiral effective field theory might be significantly lower than estimates obtained in nonperturbative calculations.

The influence of hyperons on localized clusters is studied in deformed nuclei ${}^{20}\mathrm{Ne}$ and ${}^{28}\mathrm{Si}$ and the spherical nucleus ${}^{40}\mathrm{Ca}$ by employing the deformed Skyrme-Hartree-Fock approach and the localization function. It is found that hyperons in the $p$ state initially tend to occupy the orbitals with shapes similar to that of the core nucleus. The nucleus ${}^{20}\mathrm{Ne}$ exhibits a robust prolate configuration characterized by an $\alpha {-}^{12}\mathrm{C}-\alpha$ cluster, while ${}^{28}\mathrm{Si}$ displays a less pronounced oblate ringlike cluster. A spherical shell-like cluster structure is possessed by the nucleus ${}^{40}\mathrm{Ca}$, and this spherical shape is also maintained in its hyperisotopes. For ${}_{8\mathrm{\Lambda }}^{28}\mathrm{Ne}$, the cluster structure retains sufficient strength to maintain its prolate shape even with an enhanced hyperon-nucleon ($YN$) interaction. In contrast, the cluster structure of ${}_{8\mathrm{\Lambda }}{}^{36}\mathrm{Si}$ is comparatively weak, and only a slight enhancement of the $YN$ interaction leads to its cluster structure and deformation collapse.

Charge radii measured with high accuracy provide a stringent benchmark for characterizing nuclear structure phenomena. In this work, the systematic evolution of charge radii for nuclei with $Z=19$–29 is investigated through relativistic mean-field theory with effective forces NL3, PK1, and $\mathrm{NL}{3}^{*}$. The neutron-proton ($np$) correlation around Fermi surface originated from the unpaired neutron and proton has been taken into account tentatively in order to reduce the overestimated odd-even staggering of charge radii. This improved method can give an available description of charge radii across $N=28$ shell closure. A remarkable observation is that the charge radii beyond $N=28$ shell closure follow the similarly steep increasing trend, namely irrespective of the number of protons in the nucleus. Especially, the latest results of charge radii for nickel and copper isotopes can be reproduced remarkably well. Along $N=28$ isotonic chain, the sudden increase of charge radii is weakened across $Z=20$, but presented evidently across $Z=28$ closed shell. The abrupt changes of charge radii across $Z=22$ are also shown along $N=32$ and 34 isotones, but the latter with a less slope. This seems to provide a sensitive indicator to identify the new magicity of a nucleus with universal trend of charge radii.

Parity-violating electron scattering (PVES) offers an important and model-independent method for probing the nuclear neutron density distributions. In this paper, a deformed PVES model is constructed, and detailed analyses of parity-violating asymmetry $A_{\mathrm{PV}}$ are presented for ${}^{208}\mathrm{Pb}$ and ${}^{27}\mathrm{Al}$. The impacts of the deformation of neutron and proton distributions (${\beta }_n$ and ${\beta }_p$) on $A_{\mathrm{PV}}$ are revealed by the plane- and distorted-wave Born approximations, respectively. It is demonstrated that ${\beta }_n$ mainly affects the depth of the diffraction minima of $A_{\mathrm{PV}}$, while ${\beta }_p$ influences the width of the diffraction minima of $A_{\mathrm{PV}}$. Furthermore, we combine the deformed mean-field model and deformed PVES calculations to modify the linear relation between the neutron skin thickness $\mathrm{\Delta }{R}_{\mathrm{np}}$ and $A_{\mathrm{PV}}$ that accommodates the correlation between the weak charge radius $R_W$ and $A_{\mathrm{PV}}$. Based on the latest PVES experimental measurements, $\mathrm{\Delta }{R}_{\mathrm{np}}$ and $R_W$ are extracted from the improved linear correlations. The studies in this paper provide new insights into determining ${\beta }_n$ and can serve as a useful guide for future PVES experiments.

Nuclear structure at short $NN$ distances is still poorly understood. In particular, the full quantum structure of the nucleus with a correlated $NN$ pair is a challenge to theory. So far, model descriptions have been limited to the average mean-field picture of the remaining nuclear system after removing the $NN$ pair. In the recent experiment of the BM@N Collaboration at JINR [M. Patsyuk et al., Nat. Phys. 17, 693 (2021)], the reactions ${}^{12}\mathrm{C}{(p,2p{n}_s)}^{10}\text{B}$ and ${}^{12}\mathrm{C}{(p,2p{p}_s)}^{10}\text{Be}$ induced by the hard elastic $pp$ scattering were studied. Here, $n_s$ or $p_s$ denote the undetected slow nucleon in the rest frame of ${}^{12}\mathrm{C}$. In contrast to the previous experiments, the residual bound nucleus was also detected which requires a new level of theoretical understanding. In the present work, we apply the technique of fractional parentage coefficients of the translationally invariant shell model to calculate the spectroscopic amplitude of the system $NN\text{−}B$ where $B$ is the remaining nuclear system. The spectroscopic amplitude enters the full amplitude of a nuclear reaction. The relative $NN\text{−}B$ wave function is no longer a free parameter of the model but is uniquely related to the internal state of $B$. The interaction of the target proton with the $NN$ pair is considered in the impulse approximation. We also include the initial- and final-state interactions of absorptive type as well as the single charge exchange processes. Our calculations are in a reasonable agreement with the BM@N data.

Quantum mechanics serves as the fundamental cornerstone for numerous areas of research. Finding simple and analytical quantum transmission coefficients for potentials is a rare occurrence. Notably, we have discovered a readily provable yet unreported symmetry tunneling law. For an infinite parabolic potential, it can be proved analytically that the sum of the one-dimensional tunneling probabilities at incident energies equal to the barrier height plus or minus any energy deviation is consistently 1. Based on this relationship, the original WKB approximation and the Kemble's formula can be generalized to the above-barrier energy region in a simplified but more accurate manner, referred to as the symmetric WKB approach in this context. For the realistic potential between two nuclei, numerical results demonstrate that the symmetry relationship at the above-barrier energy region and the sub-barrier energy is also well satisfied, as well as in the cases of the multichannel WKB method. The symmetry tunneling law has been effectively extended to the Eckart potential as well. Such symmetry in tunneling may have universal characteristics but its underlying reason remains to be uncovered, which may help us to further understand the quantum mechanisms.

The cross section for one-proton knockout from ${}^{17}\mathrm{N}$ on a carbon target at 245 MeV/nucleon has been measured. The experimental result is compared to the predictions based on the Glauber reaction model combined with shell model structure inputs. The experimental to theoretical cross section ratio $R_s$ is consistent with the well established $R_s\text{−}\mathrm{\Delta }S$ systematics. The experimental one-proton knockout cross section for ${}^{17}\mathrm{N}$ projectile is found to be smaller than those for the neighboring isotones ${}^{16}\mathrm{C}$ and ${}^{18}\mathrm{O}$. The observed small cross section for ${}^{17}\mathrm{N}$ can be attributed to the small spectroscopic factors from ${}^{17}\mathrm{N}$ to the bound states of ${}^{16}\mathrm{C}$ residue. The shell model calculations show that one-proton removal from the $\pi 0p_{3/2}$ orbital of ${}^{17}\mathrm{N}$ mainly leads to unbound states of ${}^{16}\mathrm{C}$, and the spectroscopic factor from ${}^{17}\mathrm{N}$ to the ${}^{16}\mathrm{C} 2_1^{+}$ state is negligibly small, indicating that the proton configuration $\pi {\left(0p_{3/2}\right)}^3{\left(0p_{1/2}\right)}^1$ contributes little to the ${}^{16}\mathrm{C} 2_1^{+}$ state and neutron excitation configuration plays dominant role.

The general intuition that heavier partons suffer weaker energy loss inside a quark-gluon plasma (QGP) medium is critically re-examined. Within a linear Boltzmann transport model that includes both Yukawa and string types of interactions between heavy quarks and the QGP, we find that while the radiative energy loss is suppressed by the parton mass, heavier partons can experience stronger string potential scatterings with the medium. Their competition may result in less energy loss of bottom quarks than charm quarks at low transverse momentum ($p_{\mathrm{T}}$) but an inverse order at high $p_{\mathrm{T}}$. Our model calculation shows a weaker nuclear modification on bottom particles than charm particles at low $p_{\mathrm{T}}$, as observed by both BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider experiments, but predicts an opposite hierarchy at high $p_{\mathrm{T}}$. A larger momentum space transport coefficient ($\widehat{q}$) and a smaller spatial diffusion coefficient ($D_{\mathrm{s}}$) are found for bottom quarks than for charm quarks.

Cooling curves of a neutron star are investigated within the minimal cooling scenario based on the Akmal- Pandharipande-Ravenhall (APR) equation of state. The Fermi surface depletion ($Z$ factor) of $\beta$-stable nuclear matter is calculated by employing a Brueckner-Hartree-Fock approach with the AV18 two-body force supplemented by a microscopic three-body force. The $Z$ factor of $\beta$-stable nuclear matter is computed to study its effects on three physical properties (superfluidity, neutrino emissivity, and heat capacity) which determine the neutron star thermal evolution. The calculated cooling curves reproduce well the mostly observed data when the $Z$ factor was taken into account in the gap energies, neutrino emissivity, and heat capacity.

Indirect methods have become the predominant approach in experimental nuclear astrophysics for studying several low-energy nuclear reactions occurring in stars, as direct measurements of many of these relevant reactions are rendered infeasible due to their low reaction probability. Such indirect methods, however, require theoretical input that in turn can have significant poorly quantified uncertainties, which can then be propagated to the reaction rates and have a large effect on our quantitative understanding of stellar evolution and nucleosynthesis processes. We present two such examples involving $\alpha$-induced reactions, ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$, for which the low-energy cross sections have been constrained with $({}^6\mathrm{Li},d)$ transfer data. In this Letter, we discuss how a first-principle calculation of ${}^6\mathrm{Li}$ leads to a 21% reduction of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ cross sections with respect to a previous estimation. This calculation further resolves the discrepancy between recent measurements of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction and points to the need for improved theoretical formulations of nuclear reactions.

We investigate the ground-state structures of ${}^{12-14}\mathrm{C}$ isotopes, which exhibit the coexistence of the cluster and shell-like states, using the cluster breaking Tohsaki-Horiuchi-Schuck-Röpke (CB-THSR) wave function. This approach incorporates cluster breaking nucleon-nucleon pairs, making it particularly suitable for describing the cluster states that feature mixed configurations and dynamic cluster motion. Through variational optimization of THSR bases, we find the coupling between the motions of clusters and valence neutrons in different configurations of ${}^{12-14}\mathrm{C}$ isotopes, e.g., dumbbell-like molecular orbits of valence neutrons coupled with an oblate 3-$\alpha$ core, and a prolate 3-$\alpha$ core surrounded by ringlike valence neutron distributions. For describing the coexistence of shell-like structures and cluster formation in the compact cores of ${}^{12-14}\mathrm{C}$ isotopes, we introduce CB pairs into the THSR approach to formulate the CB-THSR wave function, which allows a further optimization of the variational wave function and the binding energy. The results suggest oblate and shell-like structures for the ground states of ${}^{12}\mathrm{C}$ and ${}^{13-14}\mathrm{C}$, respectively. As compared to the original THSR calculation, our new model yields relatively more accurate spectra for ${}^{12-14}\mathrm{C}$ isotopes, as well as their matter rms radii. The improved results show that $\alpha$ clusters are broken by the CB pairs, and the CB-THSR wave functions describe a more compact spatial extension of cluster motion, while such strong overlaps between $\alpha$ clusters are not energetically favored in pure cluster models. Finally, we discuss the breaking of $\alpha$ clusters in ${}^{12-14}\mathrm{C}$ isotopes via the calculations of momentum distributions and form factors, and it is found that both the particle exchange and the paired excitation should be included for describing the compact cluster states.

The matter distribution is systematically studied for neutron-rich carbon isotopes with $N=6–16$ from the available measured reaction cross sections with ${}^{12}\mathrm{C}$ reaction target, using the finite-range Glauber model with Coulomb correction. We have first studied the energy dependence of the ${}^{12}\mathrm{C}\text{−}{}^{12}\mathrm{C}$ reaction cross sections in a wide range of incident energies from 30–950 MeV/nucleon. A good agreement with the experimental data measured at low and high incident energy is obtained by considering the nuclear density distribution of two Fermi (2pF) parameters, where the two optimized parameters are the size parameter $r_{2pF}$ and the diffusivity parameter $a_{2pF}$. We have therefore extracted the necessary parameters of the proton, neutron, and matter distributions for the whole range of ${}^{12-20,22}\mathrm{C}$ isotopes. With a set of calculations of four freely adjustable parameters (proton: $r_{2pF,p}, a_{2pF,p}$) and (neutron: $r_{2pF,n}, a_{2pF,n}$), we present for the first time an accurate determination of the neutron radii together with the proton radii, which are in excellent agreement with the charge radii directly extracted from the measured charge-changing cross sections. The evolution of the central density and diffuseness is studied as a function of the number of neutrons and shows the persistence of the $N=8$ shell closure for ${}^{14}\mathrm{C}$. However, an anomalous halo structure is studied for the ${}^{16,19,22}\mathrm{C}$ isotopes, where the effect of proton-neutron nuclear interaction could be manifested by the decrease of the central density with large expansion at large distance, leading to a sharp increase of the radii with respect to the neighboring nuclei.

A separable expansion of the two-particle free resolvent in terms of two-particle pseudostates is used to convert Alt-Grassberger-Sandhas (AGS) integral equations into a set of effective two-body equations in spectator degrees of freedom. The resulting effective two-body equations are much like the multichannel Lippmann-Schwinger (LS) equations of inelastic scattering with real, energy independent, nonsingular potential matrices. Hence, they are more conducive to computations than the effective equations that ensue in the conventional approach based on separable expansions of two-particle transition operators. In particular, the problem of moving singularities of the conventional approach is avoided. The effective propagator matrix is complex and nondiagonal, and exhibits simple-pole singularities in diagonal elements corresponding to open rearrangement channels. These singularities can be handled by simple subtraction procedures well known from two-particle scattering. After regularization of the kernel, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly via the Nyström method in which the integrals over spectator momenta are discretized using suitable quadrature rules. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. This proposed method has been tested on two models: (i) particle-dimer collisions in a three-boson model with $s$-wave separable pair potentials and (ii) an $s$-wave benchmark model with local pair potentials of the $n+d$ collisions. Calculations reported in the present article show that rather accurate results for elastic and breakup amplitudes can be obtained with pseudostates generated from a relatively small number of local basis functions in momentum space.

High-spin positive parity states of ${}^{50}\mathrm{V}$, populated through the ${}^{48}\mathrm{Ti}({}^4\mathrm{He},np){}^{50}\mathrm{V}$ reaction with a 48 MeV $\alpha$ beam, have been studied using the Indian National Gamma Array (INGA) facility. A few new levels and $\gamma$-ray transitions have been added to the level scheme utilizing the results of intensity, directional correlation, and linear polarization measurements. Lifetimes of a few excited states have been measured for the first time using the Doppler shift attenuation method (DSAM). Large basis shell model calculations have been performed within the $fp$ valence space to understand the microscopic origin of the excited states. Apart from the ground state yrast band [having a $\pi \left(1f_{7/2}^3\right)\otimes \nu \left(1f_{7/2}^7\right)$ particle configuration], a non-yrast band with a $\pi \left(1f_{7/2}^3\right)\otimes \nu (1f_{7/2}^6,2p_{3/2}^1)$ particle configuration has also been identified. The interplay between single-particle and collective modes of excitation have been investigated in the observed bands by analyzing the particle partitions and spectroscopic quadrupole moments, both calculated using large basis shell model calculations.

Based on an extended Skyrme momentum-dependent interaction (MDI), we derive an isospin asymmetric equation of state, isospin-dependent single-particle potential and the Hamiltonian which can be used in the Boltzmann-Uehling-Uhlenbeck model and the quantum molecular dynamics (QMD) model at the beam energy less than 1 GeV/u. As an example of the applications of extended Skyrme MDI, we also present the results obtained with the extended Skyrme momentum-dependent interaction in the improved quantum molecular dynamics model (ImQMD), and the influence of the effective-mass splitting on the isospin sensitive observables, i.e., the single and double neutron-to-proton ratios, is discussed again.

Here, we consider nuclear excitation by electron capture (NEEC) in a beam-based experiment for the ${}^{84m}\mathrm{Rb}$ isomer ($I^{\pi }$ = $6^{-}, T_{1/2}=20.26$ min). The NEEC process for the ${}^{84m}\mathrm{Rb}$ isomer allows an excitation by magnetic-dipole ($M1$) and electric-quadrupole ($E2$) transitions into a depletion level ($I^{\pi }$ = $5^{-}$), which subsequently decays, releasing a substantial amount of stored energy. To ensure effective production of the ${}^{84m}\mathrm{Rb}$ isomer, the fusion-evaporation reaction ${}^{82}\mathrm{Se} + {}^7\mathrm{Li}$ is considered. In the multiconfigurational Dirac-Fock calculations of energy released by electron capture into the $M, N, O, P$, and $Q$ shells, we have used the ground-state configurations for ${}^{84m}\mathrm{Rb}$ ions. To focus on the role of $M1$ and $E2$ transition multipolarities, Compton profiles, and excited-state configurations are neglected here. The predictions of the mean equilibrium charge state for the ${}^{84m}\mathrm{Rb}$ recoil ion as a function of its kinetic energy in the C target and the analysis of potentially possible NEEC resonance kinetic energies have been performed. The NEEC resonance strengths and probabilities have been estimated by a theoretical model applied for the $M1$ and $E2$ excitations. It was found that the $M1$ contribution for the NEEC process clearly dominates over the $E2$ one. Moreover, the total NEEC probability ($M1$ plus $E2$) for ${}^{84m}\mathrm{Rb}$ isomer is almost three orders of magnitude higher than that predicted for the ${}^{93m}\mathrm{Mo}$ isomer. This result makes the ${}^{84m}\mathrm{Rb}$ isomer a good candidate for new NEEC beam-based experiment.