We discuss critical approximations making the calculated results of the article by Bhuyan et al. [Phys. Rev. C 101, 044603 (2020)] unreliable. Namely, all target nuclei used for the calculations are strongly deformed, whereas, in the article they are considered to be spherical. In addition, we indicate other misleading points and missing/incorrect references.

A consistent microscopic theory for the response of strongly coupled superfluid fermionic systems is formulated. After defining the response as a two-point two-fermion correlation function in the basis of the Bogolyubov quasiparticles, the equation of motion (EOM) method is applied using the most general fermionic Hamiltonian with a bare two-body interaction, also transformed to the quasiparticle space. As a superfluid extension of the case of the normal phase, the resulting EOM is of the Bethe-Salpeter-Dyson form with the static and dynamical interaction kernels, where the former determines the short-range correlations and the latter is responsible for the long-range ones. Both kernels as well as the entire EOM have the double dimension as compared to that of the normal phase. Nonperturbative approximations via the cluster decomposition of the dynamical kernel are discussed, with the major focus on a continuous derivation of the quasiparticle-phonon coupling variant of the latter kernel, where the phonons (vibrations) are composite correlated two-quasiparticle states unifying both the normal and pairing modes. The developed theory is adopted for nuclear structure applications, such as the nuclear response in various channels. In particular, the finite-amplitude method generalized beyond the quasiparticle random phase approximation, taking into account the quasiparticle-vibration coupling, is formulated for prospective calculations in nonspherical nuclei.

Low-energy structure of even-even ${}^{108-116}\mathrm{Cd}$ isotopes is analyzed using a collective model that is based on the nuclear density functional theory. Spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with parameters determined by the constrained self-consistent mean-field calculations within the relativistic Hartree-Bogoliubov method employing a universal energy density functional and a pairing force. The collective Hamiltonian reproduces the observed quadrupole phonon states of vibrational character, which are based on the moderately deformed equilibrium minimum in the mean-field potential energy surface. In addition, the calculation yields a low-lying excited $0^{+}$ band and a $\gamma$-vibrational band that are associated with a deformed local minimum close in energy to the ground state, consistently with the empirical interpretation of these bands as intruder bands. Observed energy spectra, $B\left(E2\right)$, and ${\rho }^2\left(E0\right)$ values are, in general, reproduced reasonably well.

We propose a test-particle method to probe the transport dynamics of the establishment and development of collective flow in large and small systems of heavy-ion collisions. We place test particles as passengers into the partonic medium created by $\mathrm{Au}+\mathrm{Au}$ midcentral collisions at $\sqrt{s_{NN}}=200$ GeV and $p+\mathrm{Pb}$ central collisions at $\sqrt{s_{NN}}=5.02$ TeV, using a multiphase transport model. With the help of test particles in two extreme test cases, we demonstrate that parton collisions play an important role in establishing and developing collectivity in large and small colliding systems. The collectivity established by final state parton collisions is much stronger in large colliding systems compared to small colliding systems. The collectivity from the initial state can persist or survive more easily in small colliding systems than in large colliding systems due to fewer parton collisions. Our study provides a new method to understand the origin of collectivity in large and small colliding systems at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.

Spin alignment of vector mesons in noncentral relativistic heavy-ion collisions provides a novel probe of the global quark polarization and hadronization mechanism. In this paper, we discuss the spin alignment of a short-lived vector meson, namely $K^{*0}$, arising from the hadronic rescattering process using the UrQMD model. This spin alignment is not related to global quark polarization but cannot be distinguished from those arising from global quark polarization in experiment. The spin alignment parameter ${\rho }_{00}$ is found to deviate from 1/3 by up to $-0.008$ (0.03) with respect to the reaction (production) plane. These deviations are much larger than the expected signal from all the theoretical models implementing the conventional global quark polarization mechanism as well as the current experimental precision, and should be considered seriously when comparing measurements with theoretical calculations.

The isoscalar single-pion production exhibits a broad bump in the energy dependence of the total cross section, which does not correspond to the usual opening of the $N^{*}\left(1440\right)$ production channel with subsequent pion decay. We reevaluate the current database and investigate whether the observed bump structure with a width of about 150 MeV points to the formation of dibaryon states with $I\left(J^P\right)=0\left(1^{+}\right)$ and $0\left(1^{-}\right)$ near the $N^{*}\left(1440\right)N$ threshold. This situation would be similar to the situation at the $\mathrm{\Delta }\left(1232\right)N$ threshold, where the signature of a number of dibaryonic resonances has been found.

We study the systematic deviations of the theoretical results (the Hartree-Fock-Bogoliubov, the relativistic mean field, the Duflo-Zuker, and Weizsäker-Skyrme models) and experimental values of atomic masses, one-nucleon separation energies, and nuclear charge radii. Strong correlations of these deviations, which has not been discerned hitherto, are highlighted, and are applied to improve the agreement of theoretical models with experimental experimental data. Substantial refinements of the consistency between theoretical models and experimental databases are achieved with additionally only one parameter which reflects the correlation reported in this Letter. The root mean square deviation values of these theoretical models in comparison with experimental databases are about 100–300 keV for atomic masses, 120–350 keV for one-nucleon separation energies, and 0.008–0.017 fm for nuclear charge radii, for nuclei with proton number $Z$ larger than 28.

The strength distributions, including giant resonances, of isovector and isoscalar spin-multipole transitions in the commonly studied double-$\beta$-decay triplets are computed in the framework of the quasiparticle random-phase approximation (QRPA) using the Bonn-$A$ two-body interaction in no-core single-particle valence spaces. The studied nuclei include the double-$\beta$ parent and daughter pairs (${}^{76}\mathrm{Ge}$, ${}^{76}\mathrm{Se}$), (${}^{82}\mathrm{Se}$, ${}^{82}\mathrm{Kr}$), (${}^{96}\mathrm{Zr}$, ${}^{96}\mathrm{Mo}$), (${}^{100}\mathrm{Mo}$, ${}^{100}\mathrm{Ru}$), (${}^{116}\mathrm{Cd}$, ${}^{116}\mathrm{Sn}$), (${}^{128}\mathrm{Te}$, ${}^{128}\mathrm{Xe}$), (${}^{130}\mathrm{Te}$, ${}^{130}\mathrm{Xe}$), and (${}^{136}\mathrm{Xe}$, ${}^{136}\mathrm{Ba}$). The studied transitions proceed from the ground states to the $J^{\pi }=0^{-},1^{-},2^{-}$ (spin-dipole transitions) and $J^{\pi }=1^{+},2^{+},3^{+}$ (spin-quadrupole transitions) excited states in these nuclei. Comparison of the present results with potential future data may, indirectly, shed light on the reliability of QRPA-based nuclear-structure frameworks in description of the wave functions of nuclear states relevant for the two-neutrino and neutrinoless double $\beta$ decays in the studied triplets.

${\beta }^{-}$ decay of very neutron-rich isotopes of P and S, studied at the National Superconducting Cyclotron Laboratory using the Beta Counting Station consisting of a Double Sided Strip Detector surrounded by clovers detectors for observing delayed $\gamma$ transitions, is reported here. $\beta$-decay half-lives and delayed neutron emission probabilities were extracted for ${}^{42,43,44}\mathrm{P}$ and ${}^{44,46}\mathrm{S}$ by analyzing spatial and temporal correlations between implants and decay events in the Si detector with further coincidence with $\gamma$ transitions. Detection of delayed $\gamma$ rays allowed for the identification of negative-parity 1p1h states in ${}^{42}\mathrm{S}$ for the first time, also constraining the parent (${}^{42}\mathrm{P}$) spin/parity to $2^{-}\text{or}{3}^{-}$. For the most exotic isotope studied, ${}^{46}\mathrm{S}$, no strong $\gamma$ transition was observed unlike lighter even-even S isotopes, thus implying the shift of Gamow-Teller strength distribution to higher energies. Comparison of experimental observations to detailed shell-model calculations using the SDPFSDG-MU interaction allowed us to infer the importance and role of first forbidden $\beta$ transitions as the neutron number approaches and then exceeds $N=28$.

This work incorporates the effect of short-range repulsion between particles into the Cooper-Frye hadron sampling procedure. This is achieved by means of a rejection sampling step, which prohibits any pair of particles from overlapping in the coordinate space, effectively modeling the effect of hard-core repulsion. The new procedure—called the fist sampler—is based on the package thermal-fist. It is used here to study the effect of excluded volume on cumulants of the (net-)proton number distribution in central collisions of heavy ions in a broad collision energy range in conjunction with exact global conservation of baryon number, electric charge, and strangeness. The results are compared with earlier calculations based on analytical approximations, quantifying the accuracy of the latter at different collision energies. An additional advantage of the new method over the analytic approaches is that it offers the flexibility provided by event generators, making it straightforwardly extendable to other observables.

The density-dependent cluster model combined with relativistic mean-field theory is used to explore the structure and $\alpha$ decay for the neutron-deficient nuclei with $89\le Z\le 94$, including two newly discovered nuclei ${}^{207}\mathrm{Th}$ [Phys. Rev. C 105, L051302 (2022)] and ${}^{214}\mathrm{U}$ [Phys. Rev. Lett. 126, 152502 (2021)]. The effective nucleon-nucleon interactions and matter density distributions from the relativistic mean field are employed to construct the $\alpha$-daughter potential with a double-folding model. The Pauli blocking effect is considered by normalizing the strength of the $\alpha$-daughter potential with the Bohr-Sommerfeld quantization condition. The $\alpha$-preformation factor is calculated with the cluster formation model. The calculated $\alpha$-decay half-lives for the 106 observed nuclei with $89\le Z\le 94$ are in excellent agreement with experimental data. Extending this model to the unknown nuclei ${}^{201–204}\mathrm{Ac}$, ${}^{205–206}\mathrm{Th}$, ${}^{209–210}\mathrm{Pa}$, ${}^{212–213,220}\mathrm{U}$, ${}^{215–218,221}\mathrm{Np}$, and ${}^{220–227}\mathrm{Pu}$, the evolution of the $N=126$ shell closure with neutron number is explored for the high-$Z$ isotopes. The available $\alpha$-decay energies, preformation factors, and $\alpha$-decay half-lives show a regular change with increasing neutron number. Especially, the robustness of the $N=126$ shell closure is shown up to the Pu isotopes.

The $\alpha$ decays of ${}^{207–209}\mathrm{Ac}$, located near the proton drip-line, were reinvestigated by means of $\alpha$-decay spectroscopy. They were produced in the fusion reaction ${}^{36}\mathrm{Ar}+{}^{176}\mathrm{Hf}$ and separated in flight using the gas-filled recoil separator SHANS. A new $\alpha$-decay line at 7483(15) keV was observed and assigned as the decay from the ground state of ${}^{208}\mathrm{Ac}$ to the excited ($2^{+}$) or ($4^{+}$) state in ${}^{204}\mathrm{Fr}$. In addition, the previously known $\alpha$-decay properties of ${}^{207–209}\mathrm{Ac}$ were measured with improved precision. The half-lives obtained, together with the existing decay data of other $N\le 126$ actinium isotopes, were compared with the values calculated with the Wentzel-Kramers-Brillouin approximation and without considering the $\alpha$-preformation factors. It is shown that the calculated half-lives exhibit a distinct odd-even staggering (OES) following the same trend as the experimental data, whereas the amplitudes of the exhibited OES are 30–60 % of the real ones. This implies that apart from the $\alpha$-preformation factors, the $\alpha$-decay energies also contribute significantly to the OES of $\alpha$-decay half-lives.

Deuteron elastic scattering from ${}^{15}\mathrm{C}$ and inelastic scattering reactions to the first excited state of ${}^{15}\mathrm{C}$ were studied using a radioactive beam of ${}^{15}\mathrm{C}$ in inverse kinematics. The scattered deuterons were measured using HELIOS. The elastic scattering differential cross sections were analyzed using the optical model. A matter deformation length ${\delta }_d=1.04\left(11\right)\mathrm{fm}$ has been extracted from the differential cross sections of inelastic scattering to the first excited state. The ratio of neutron and proton matrix elements $M_n/M_p=3.6\left(4\right)$ has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of ${}^{15}\mathrm{C}$ were determined and discussed. Results from ab initio no-core configuration interaction calculations were also compared with the experimental observations. This result supports a moderate core decoupling effect of the valence neutron in ${}^{15}\mathrm{C}$ similarly to its isotone ${}^{17}\mathrm{O}$, in line with the interpretation of other neutron-rich carbon isotopes.

The main aim of the present paper is to solve the eigenvalues problem with the Bohr collective Hamiltonian for $\gamma$-rigid nuclei within a model we have elaborated by combining two model approaches: the quantum mechanical formalism, namely, deformation-dependent mass formalism (DDM), and the anharmonic sextic oscillator potential for the variable $\beta$ and $\gamma =0$. The model developed in this way is conventionally called the sextic and DDM approach. Analytical expressions for energy spectra are conjointly derived by means of quasiexact solvability and a quantum perturbation method. Due to the scaling property of the problem, the energy and $B\left(E2\right)$ transition ratios depend on two free parameters apart from an integer number which limits the number of allowed states. Numerical results are given for 35 nuclei—${}^{98–108}\mathrm{Ru}, {}^{100–102}\mathrm{Mo}, {}^{116–130}\mathrm{Xe}, {}^{180–196}\mathrm{Pt}, {}^{172}\mathrm{Os}, {}^{146–150}\mathrm{Nd}, {}^{132–134}\mathrm{Ce}, {}^{154}\mathrm{Gd}, {}^{156}\mathrm{Dy}$, and ${}^{150–152}\mathrm{Sm}$—revealing a good agreement with experiment. Moreover, as proved for the first time by Bonatsos et al. [D. Bonatsos, P. Georgoudis, D. Lenis, N. Minkov, and C. Quesne, Phys. Lett. B 683, 264 (2010)], the dependence of the mass on the deformation with the sextic potential moderates the increase of the moment of inertia with the deformation, removing an important drawback that has been revealed in the constant mass case [Buganu and Budaca, J. Phys. G: Nucl. Part. Phys. 42, 105106 (2015)]. Additionally, the correlation between the DDM and the minimal length formalism persists for the sextic potential. Finally, the DDM effects on the shape phase transition for the most numerous isotopic chains, namely, Ru, Xe, Nd, and Pt, have been duly investigated.

The nucleus of ${}^{235}\mathrm{U}$ has a low-lying isomeric state of energy about 76.7 eV. Excitation cross sections of the nucleus from the ground state to the isomeric state by inelastic electron scattering are calculated on the level of the Dirac distorted-wave Born approximation. The cross sections are about six orders of magnitude higher than known values based on the Dirac plane-wave Born approximation, emphasizing the vital importance of wave function distortion in the nuclear excitation. In addition, we find that even with low-energy electrons on the order of 100 eV, relativistic effects are significant without which the excitation cross sections drop by an order of magnitude.

Charm hadrons possess versatile hadro-chemistry as characterized by various transverse-momentum-dependent ratios between their different species. In particular, the charm hadro-chemistry may be modified in relativistic heavy-ion collisions with respect to proton-proton collisions at the same energy, as caused by novel diffusion and hadronization mechanisms of charm quarks in the environment of the created quark-gluon plasma in the former. Inspired by recent measurements of leptons from charm-hadron decays (separated from bottom decays) in Pb-Pb and Au-Au collisions, we investigate the effects of the charm hadro-chemistry on the leptonic observables. We find that full consideration of charm hadro-chemistry in both proton-proton and heavy-ion collisions causes only mild change of charm-leptons' suppression factor with respect to previous calculations hadronizing charm quarks into $D$ mesons only, whereas the resulting change (increase) in the charm-leptons' elliptic flow turns out to be more pronounced as a consequence of the larger collectivity of ${\mathrm{\Lambda }}_c$ baryons than $D$ mesons.

High-energy heavy-ion collisions contain enormous angular momentum, $|\vec{J}|$, which is $O({10}^3–{10}^6\hslash )$ in the range of collision energy, $\sqrt{s_{\mathrm{NN}}}$, spanned experimentally by the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). A fraction of $\vec{J}$ is transferred to the overlapping collision region, which is indispensable for measuring observables such as vorticity-driven hadron spin alignment with $\widehat{J}$. Experiments estimate the orientation of $\widehat{J}$ of the participant nucleons within the collision overlap region, ${\widehat{J}}_{\mathrm{part}}$, by using that of the forward- and backward-going spectating nucleons ${\widehat{J}}_{\mathrm{spec}}$. Using two models, we study the decorrelation between ${\widehat{J}}_{\mathrm{part}}$ and ${\widehat{J}}_{\mathrm{spec}}$, driven both by angular-momentum conservation and event-by-event fluctuations, as well as by the decorrelation between the orientation of the elliptic overlap region and the ${\widehat{J}}_{\mathrm{part}}$. $\sqrt{s_{\mathrm{NN}}}$-dependent decorrelation is observed in both of these cases and is large enough to be an important corrective factor used when experimentally observing phenomena driven by $\vec{J}$.

Having in mind the pre-equilibrium stage in peripheral heavy-ion collisions as a possible scenario for the production of electromagnetic radiation, we compute the two-gluon one-photon vertex in the presence of an intense magnetic field at one-loop order. The quarks in the loop are taken such that two of them occupy the lowest Landau level, with the third one occupying the first excited Landau level. When the field strength is the largest of the energy (squared) scales, the tensor basis describing this vertex corresponds to two of the three-vector particles polarized in the longitudinal direction whereas the third one is polarized in the transverse direction. However, when the photon energy is of the same order as or larger than the field strength, the explicit one-loop computation contains extra tensor structures that spoil the properties of the basis compared with the case when the field strength is the largest of the energy scales, which signals that the calculation is incomplete. Nevertheless, by projecting the result onto the would-be basis, we show that the squared amplitude for processes involving two gluons and one photon exhibits the expected properties such as a preferred in-plane photon emission and a slightly decreasing strength for an increasing magnetic-field strength. We comment on possible venues to improve the one-loop calculation that include accounting for progressive occupation of the three quarks of the lowest and first-excited Landau levels such that, still working in the large field limit, a more complete description can be achieved when the photon energy increases.

The Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) is used to measure the absolute proton beam polarization, ${\sigma }_P^{\text{syst}}/P\lesssim 0.5\%$, at the Relativistic Heavy Ion Collider. Here I consider the possibility of employing HJET to measure the ${}^3\mathrm{He}$ ($h$) beam polarization at the Electron-Ion Collider (EIC). The dominant contribution to the ratio of the $h^{\uparrow }p$ and $p^{\uparrow }h$ analyzing powers, which is needed for such measurements, can be easily calculated using well-known values of the proton and helion magnetic moments, but some corrections should be applied to achieve the required accuracy. It was found that corrections due to absorption and ${}^3\mathrm{He}$ breakup effectively cancel in the ratio and a correction due to hadronic spin-flip amplitudes can be derived from the proton beam measurements. As a result, the anticipated systematic uncertainty in the measured ${}^3\mathrm{He}$ beam polarization can satisfy the EIC requirement ${\sigma }_P^{\text{syst}}/P\lesssim 1\%$.

Requirements for hadron polarimetry at the future Electron-Ion Collider (EIC) include measurements of absolute ${}^3\mathrm{He}\left(h\right)$ beam polarization with systematic uncertainties better than ${\sigma }_P^{\text{syst}}/P\lesssim 1\%$. Due to the successful use, since 2005, of the polarized hydrogen jet target polarimeter (HJET) to measure proton beam polarization at the Relativistic Heavy Ion Collider (RHIC), the HJET technique promises to be suitable for the ${}^3\mathrm{He}$ polarimetry at EIC. For that, however, one needs to know the ratio of the $h^{\uparrow }p$ and $p^{\uparrow }h$ analyzing powers. For elastic scattering, this ratio can be evaluated with sufficient accuracy if $p^{\uparrow }p$ analyzing power is precisely known. In this paper, the deuteron beam data acquired at HJET in RHIC Run 16 was used to evaluate corrections to the measured helion beam polarization due to the ${}^3\mathrm{He}$ breakup. The breakup effect was found to be negligible if the ratio of the beam and target (jet) single spin asymmetries are concurrently measured to determine the ${}^3\mathrm{He}$ beam polarization.