The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters $\beta$ and $\gamma$ is a classical theme in nuclear structure. Here we use the quadrupole invariants, calculated within the framework of the configuration-interaction shell model, to clarify the meaning and limitations of nuclear shapes. We introduce a novel method that enables us to calculate accurately higher-order invariants and, therefore, the fluctuations in both $\beta$ and $\gamma$. We find that the shape parameter $\beta$ often has a non-negligible degree of softness and that the angle $\gamma$ is usually characterized by large fluctuations, rendering its effective value not meaningful. Contrary to common belief, we conclude that doubly magic nuclei are not spherical, because the notion of a well-defined shape does not apply to them.

Using the Bernard-Kaiser-Lee-Meissner (BKLM) parametrization of the hadronic vertex ${\gamma }^{*}N\to \pi N^{\prime }$, with ${\gamma }^{*}$ being a virtual photon, we analyze the restrictions imposed on the form factors (FF) in the limit at which the pion three-momentum and mass go to zero, which is known as the soft-pion limit. We obtain information about the normalization of the FF in this limit using current algebra methods and the hypothesis of partially conserved axial-vector current (PCAC) which is a way to implement chiral symmetry. We relate these FF with those of the $W^{\pm }N\to N^{\prime }$ weak interaction. The present work provides a useful tool to decide whether a certain model is better than another, checking whether the corresponding FF satisfy the conditions imposed in the soft-pion limit, which are model independent.

Recent experimental results in proton-proton and in proton-nucleus collisions at Large Hadron Collider energies show a strong similarity to those observed in nucleus-nucleus collisions, where the formation of a quark-gluon plasma is expected. We discuss the comparison between small colliding systems and nucleus-nucleus collisions, for (a) the strangeness suppression factor ${\gamma }_s$ and yields of multi-strange hadrons; (b) the average transverse momentum, $p_t$, with particular attention to the low $p_t$ region where soft, nonperturbative effects are important; and (c) the elliptic flow scaled by the participant eccentricity. The universal behavior in hadronic and nuclear high energy collisions emerges for all these observables in terms of a specific dynamical variable which corresponds to the entropy density of initial system in the collision and which takes into account the transverse size of the initial configuration and its fluctuations.

The octupole deformation $\left({\beta }_3\right)$ distorts the spherically symmetric or quadrupole deformed $\left({\beta }_2\right)$ nuclei into a pear shape. In the present work, the optimum (or uniquely fixed) orientations obtained for the ‘elongated’ and ‘compact’ fusion configurations of octupole $\left({\beta }_3\right)$ deformed nuclei differ significantly from the ones reported for the quadrupole deformed nuclei. The soft-pear shape nuclei with small ${\beta }_3$ deformations show a maximum deviation of ${20}^{\circ }$ in the elongated and compact configurations, respectively, of oblate and prolate cases, whereas for rigid-pear shape nuclei with strong ${\beta }_3$ deformation, the deviation is of ${90}^{\circ }$. The optimum orientations obtained are also dependent on ‘$+$’ and ‘$-$’ signs of ${\beta }_3$. Thus, octupole deformations significantly modify the optimum orientations for the cold and hot fusion reactions and hence leads to modification of the barrier characteristics. In addition to this, the effects of ${\beta }_3$ have also been observed in the calculation of fusion cross section for the formation of heavy $\left({}^{190}\mathrm{Ir}^{*}\right)$ and superheavy $\left({}^{268}\mathrm{Sg}^{*}\right)$ elements from the octupole-based reactions, i.e., ${}^{48}\mathrm{Ca}$(sph.)$+{}^{142}\mathrm{La}\left({\beta }_2=0.108,{\beta }_3=-0.083\right)$ and ${}^{220}\mathrm{Ra}\left({\beta }_2=0.110,{\beta }_3=-0.125\right)$, respectively.

We present a new extraction of the positron-proton and electron-proton elastic-scattering cross sections ratio $R_{e^{+}{e}^{-}}$ based on a new phenomenological parametrization of the two-photon-exchange (TPE) corrections to electron-proton $\left(ep\right)$ elastic-scattering cross section ${\sigma }_R$. We compare our results to several previous phenomenological extractions, TPE hadronic calculations, and world data on the ratio $R_{e^{+}{e}^{-}}$, including the recent direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments. The ratio $R_{e^{+}{e}^{-}}$ as extracted from this work is consistent with unity, and shows little sensitivity to $\varepsilon$ and essentially no $Q^2$ dependence, suggesting a smaller hard-TPE contribution to $R_{e^{+}{e}^{-}}$ than that predicted by several previous phenomenological extractions and TPE hadronic calculations. In this work, we show that, under certain assumptions and constraints imposed on the TPE amplitudes $Y_E$ and $Y_3$, the proton magnetic form factor squared ${\left(G_M^p\right)}^2$, and the proton form factors ratio ${\mu }_p{R}_p={\mu }_p{G}_E^p/G_M^p$, the TPE corrections to ${\sigma }_R$ can be suppressed, yielding a small hard-TPE contribution to $R_{e^{+}{e}^{-}}$. Our results are in agreement with the recent analysis by Bytev and Tomasi-Gustafsson [Phys. Rev. C 99, 025205 (2019)]. We believe that the assumption that hard-TPE corrections could account for the discrepancy in the ratio ${\mu }_p{R}_p$ is still an open question.

Photoproduction of the $\omega$ meson on the proton has been experimentally studied near the threshold. The total cross sections are determined at incident energies ranging from 1.09 to 1.15 GeV. The 1/2 and 3/2 spin-averaged scattering length $a_{\omega p}$ and effective range $r_{\omega p}$ between the $\omega$ meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $a_{\omega p}=(-0.{97}_{-0.{16}_{\mathrm{stat}}-0.{00}_{\mathrm{syst}}}^{+0.{16}_{\mathrm{stat}}+0.{03}_{\mathrm{syst}}})+i(0.{07}_{-0.{14}_{\mathrm{stat}}-0.{09}_{\mathrm{syst}}}^{+0.{15}_{\mathrm{stat}}+0.{17}_{\mathrm{syst}}})$ fm and $r_{\omega p}=(+2.{78}_{-0.{54}_{\mathrm{stat}}-0.{12}_{\mathrm{syst}}}^{+0.{67}_{\mathrm{stat}}+0.{11}_{\mathrm{syst}}})+i(-0.{01}_{-0.{50}_{\mathrm{stat}}-0.{00}_{\mathrm{syst}}}^{+0.{46}_{\mathrm{stat}}+0.{06}_{\mathrm{syst}}})$ fm, resulting in a repulsive force. The real and imaginary parts for $a_{\omega p}$ and $r_{\omega p}$ are determined separately for the first time. A small $P$-wave contribution does not affect the obtained values.

We present mass excesses (ME) of neutron-rich isotopes of Ar through Fe, obtained via time of flight $B\rho$ mass spectrometry at the National Superconducting Cyclotron Laboratory. Our new results have significantly reduced systematic uncertainties relative to a prior analysis, enabling the first determination of ME for ${}^{58,59}\mathrm{Ti},{}^{62}\mathrm{V},{}^{65}\mathrm{Cr},{}^{67,68}\mathrm{Mn}$, and ${}^{69,70}\mathrm{Fe}$. Our results show the $N=34$ subshell weaken at Sc and vanish at Ti, along with the absence of an $N=40$ subshell at Mn. This leads to a cooler accreted neutron star crust, highlighting the connection between the structure of nuclei and neutron stars.

A process of the decay of the anomalously low-lying nuclear isomer ${}^{229m}\mathrm{Th}(3/2^{+},8.28\pm 0.17$ eV) in the thorium anion $\left({\mathrm{Th}}^{-}\right)$ via the internal conversion (IC) channel is studied. We show that the half-life of the nuclear isomer in the $6d_{3/2}^{3}7s_{1/2}^2$ ground state and in the $6d_{3/2}^{2}7s_{1/2}^{2}7p_{1/2}^1$ excited state of ${\mathrm{Th}}^{-}$ is $\approx 1.5$ and $\approx 1.1$ times bigger than in the $6d_{3/2}^{2}7s_{1/2}^2$ ground state of the Th atom. The IC probabilities in the anion decreases despite the decay via the additional $6d_{3/2}$ or $7p_{1/2}$ electrons. This counterintuitive result is a consequence (a) of a decrease in the amplitudes of the $6d_{3/2}$ and $7s_{1/2}$ wave functions near the nucleus due to an increase in their diffuseness of upon the addition of extra electron and (b) of mutual compensation in the IC probability due to a kinematic factor, which depends on the energy of the conversion electron in the continuum as $E_c^{-1/2}$, and the $E_c^{1/4}$ growth of the amplitudes of the electron wave functions.

The optical model potential, which reflects an overall feature of the nuclear property and reaction dynamics, has been widely adopted to describe the nucleus-nucleus interaction phenomenologically. Experimentally, knowledge of the optical potential can only be learned in the vicinity of a sensitive radius. In this study, the notch technique was applied to extract the radial sensitive regions of the tightly bound system ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ and weakly bound systems ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ and ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ at energies around the Coulomb barrier. It is the first time that we observed two distinct sensitive regions, corresponding to the inner volume absorption and the outer surface absorption processes. Strong energy dependence of the sensitive regions was found as well. Based on this result, we further investigated the interaction property of ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ and found that the threshold anomaly was observed in the volume interaction, whereas the abnormal near-threshold behavior was presented in the surface part.

The yield ratios of neutron-proton $\left[R\right(n/p\left)\right]$ and ${}^3\mathrm{H}\text{−}{}^3\mathrm{He}$ $\left[R\right(t/{}^3\mathrm{He}\left)\right]$ with reduced rapidity from 0 to 0.5 are simulated for 50 MeV/u ${}^{48,50,52,54,56,58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ neutron-deficient systems at all reduced impact parameters by using the isospin-dependent quantum molecular dynamics (IQMD) model. Neutron and proton density distributions (used for the phase-space initialization of the reaction system in IQMD) and the proton skin thickness $\mathrm{\Delta }{R}_{pn}$ of different neutron-deficient Ni isotopes are given by the Skyrme-Hartree-Fock model. The results show that both $R(n/p)$ and $R(t/{}^3\mathrm{He})$ from different centralities are strongly linear with $N/Z$ of different Ni projectiles, but are exponentially dependent on $\mathrm{\Delta }{R}_{pn}$ with better fitting. It is therefore suggested that $R(n/p)$ and $R(t/{}^3\mathrm{He})$ from any same centrality (peripheral collisions are much better, with bigger yield ratios and curve slopes) could be treated as possible experimental probes to extract the proton skin thickness of neutron-deficient isotopes from isotopes near the $\beta$-stability line.

In this work, the two-photon-exchange (TPE) effects in $ep\to en{\pi }^{+}$ at small $-t$ are discussed within a hadronic model. Under the pion dominance approximation the TPE contribution to the amplitude can be described by a scalar function in the limit $m_e\to 0$. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated when only the elastic intermediate state is considered. We find that the TPE corrections to the unpolarized differential cross section are about from $-4\%$ to $-20\%$ at $Q^2=1$–1.6 ${\mathrm{GeV}}^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections ${\sigma }_{\mathrm{L},\mathrm{T},\mathrm{LT},\mathrm{TT}}$. We find that the TPE corrections (at $Q^2=1$–1.6 ${\mathrm{GeV}}^2$) to ${\sigma }_{\mathrm{L}}$ are about from $-10\%$ to $-30\%$, to ${\sigma }_{\mathrm{T}}$ are about $20\%$, and to ${\sigma }_{\mathrm{LT},\mathrm{TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $ep\to en{\pi }^{+}$ at small $-t$ are important to extract the separated cross sections ${\sigma }_{\mathrm{L},\mathrm{T},\mathrm{LT},\mathrm{TT}}$ and the electromagnetic magnetic form factor of ${\pi }^{+}$ in the experimental analysis.

Background: $\alpha$ decay is one of the most important decay modes of atomic nuclei. The half-life of $\alpha$ decay provides valuable information for nuclear structure study. Many theoretical models and empirical formulas have been suggested to describe the half-life of $\alpha$ decay as a function of decay energy ($Q_{\alpha }$), atomic number ($Z$), nucleon number ($A$), and other related variables. However, the analysis of theoretical uncertainty is rarely done for those $\alpha$ decay models.

Purpose: We aim to perform a systematic and detailed study on the theoretical uncertainty of existing $\alpha$ decay formulas based on statistical methods.

Methods: The nonparametric bootstrap method is used to evaluate the uncertainties of two $\alpha$ decay formulas, the universal decay law (UDL) and the new Geiger-Nuttall law (NGNL). Such a method can simultaneously obtain the uncertainty of each parameter, the correlation between each pair of parameters, and the total, statistical, and systematic uncertainties of each formula. Both even-even (ee) nuclei and odd-$A$ ($\mathrm{o}A$) nuclei are used in the analysis. The collected data are separated into three parts: ee nuclei, $\mathrm{o}A$ nuclei without spin or parity change ($\mathrm{o}A\mathrm{\_nc}$), and $\mathrm{o}A$ nuclei with spin and/or parity change ($\mathrm{o}A\mathrm{\_c}$). Based on the residues between observed data and corresponding calculations, the statistical and systematic uncertainties are decomposed from the total uncertainty, from which one can clarify the effects from the shell structure, pairing, and angular momentum change on describing $\alpha$ decay half-life.

Results: If $N>126$ and $N⩽126$ nuclei are considered together, the systematic uncertainty of residues between observed and predicted half-lives are larger than if those groups are considered separately. Without a shell correction term, a much larger systematic uncertainty is found if parameters obtained for $N⩽126$ nuclei are used to describe the half-lives of $N>126$ nuclei. Based on the Bohr-Sommerfeld quantization condition and simple assumptions, a detailed shell correction term is obtained for $N>126$ nuclei, for which the value is similar to that in NGNL. A global hindrance on the $\alpha$ decay process is found in $\mathrm{o}A\mathrm{\_nc}$ ($\mathrm{o}A\mathrm{\_c}$) nuclei compared with ee ($\mathrm{o}A\mathrm{\_nc}$) nuclei. If parameters obtained from ee ($\mathrm{o}A\mathrm{\_nc}$) nuclei are used, the half-lives of $\mathrm{o}A\mathrm{\_nc}$ ($\mathrm{o}A\mathrm{\_c}$) nuclei are generally underestimated with large systematic uncertainties, which can be related to the contribution of pairing effect and angular momentum. The parameter of angular momentum term in NGNL is obtained with large uncertainty and very sensitive to the selections of the dataset. The recently observed superallowed decay from ${}^{104}\mathrm{Te}$ to ${}^{100}\mathrm{Sn}$ is also discussed based on uncertainty analysis.

Conclusions: The theoretical uncertainty of existing $\alpha$ decay formulas is successfully evaluated by the nonparametric bootstrap method, which simultaneously indicates the important effect in $\alpha$ decay, such as the shell effect and the pairing effect. In addition, statistical results show strong correlations between the parameters of the second and third terms in both UDL and NGNL, which demands further investigations.

The shell-model-like approach (SLAP) based on cranking covariant density functional theory (CDFT) with a separable pairing force is developed. The developed cranking CDFT-SLAP with separable pairing force is applied to investigate the rotational spectra in ${}^{60}\mathrm{Fe}$, including the positive-parity yrast band and two negative-parity signature partner bands, in comparison with the cranking CDFT-SLAP with monopole pairing force calculations, which is a good test of its performance on ${}^{60}\mathrm{Fe}$. Reasonable agreement with the available data is achieved.

Background: The semimicroscopic algebraic quartet model (SAQM) generates the excitation spectra of shell-like quartets, formed by two protons and two neutrons in a well-defined shell configuration. It is based on the SU(3) symmetry, which is valid only in light nuclei. Algebraic quartet models have been proposed for heavy nuclei, too, but their shell model background is not known.

Purpose: I wish to construct an algebraic approach for the description of shell-like quarteting in heavy nuclei.

Methods: The SAQM is extended based on the pseudo- and proxy-SU(3) symmetries.

Results: The procedure of the generalization is presented. The new models are applied for the description of the energy spectrum and electromagnetic transitions of the low-lying bands of ${}^{224}\mathrm{Th}$.

Conclusions: In the present case the performance of the two approximate symmetries is fairly similar due to the alike nature of the relevant shell orbits. The possibly similar or different results of the two symmetries are discussed.

We resum the nonequilibrium gradient corrections to a single-particle distribution function evolved by the Boltzmann equation in the relaxation time approximation (RTA). We first study a system undergoing Bjorken expansion and show that, for a constant relaxation time, the exact solution of the RTA Boltzmann equation at late times (i.e., after the decay of nonhydrodynamic modes) generates the Borel resummed Chapman-Enskog series. Extending this correspondence to systems without Bjorken symmetry, we construct a ($3+1$)-dimensional hydrodynamic generator for RTA kinetic theory, which is an integral representation of the Chapman-Enskog series in the limit of vanishing nonhydrodynamic modes. Relaxing this limit, we find at earlier times a set of nonhydrodynamic modes coupled to the RTA Chapman-Enskog expansion. Including the dynamics of these nonhydrodynamic modes is shown to control the emergence of hydrodynamics as an effective field theory description of nonequilibrium fluids, which works well even for far-off-equilibrium situations where the Knudsen number is initially large.

Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory [Phys. Rev. C 93, 015501 (2016); Phys. Rev. C 93, 049902(E) (2016); Phys. Rev. C 95, 059901(E) (2017)]. In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at the Fock-space level. We adjust the unitary phases by matching the corresponding two-pion exchange nucleon-nucleon potentials and rederive the box diagram contribution to the axial current operator following the approach of the JLab-Pisa group, thereby reproducing our original result. We provide a detailed information on the calculation of the box diagram including the relevant intermediate steps in order to facilitate a clarification of this disagreement.

A fully quantal algebraic version of the Bohr-Mottelson unified model is presented with the important property that its quantization is defined by the fully antisymmetric many-nucleon unitary irreps (irreducible representations), which span the many-nucleon Hilbert space of a nucleus. The spatial component of this model, with added spin $\mathrm{SU}{\left(2\right)}_S$ and isospin $\mathrm{SU}{\left(2\right)}_T$ degrees of freedom, is uniquely defined by the requirement that its Lie algebra of observables includes the nuclear quadrupole moments, its angular momenta, and kinetic energy. Thus, it is determined to be an $\mathrm{Sp}(3,\mathbb{R})$ Lie algebra, which is then combined with the spin and isospin algebras of a Lie algebra for an $\mathrm{Sp}(3,\mathbb{R})\times {\mathrm{SU}\left(2\right)}_S\times {\mathrm{SU}\left(2\right)}_T$ dynamical group of the desired algebraic unified model. The irreps of this model are uniquely defined by their $\mathrm{Sp}(3,\mathbb{R})$ lowest weights, spins, and isospins, and have the property that observed transitions between rotational states of nuclei can be expressed in terms of these irreps and their mixtures. The algebraic unified model parallels the Bohr-Mottelson version in almost all respects, including the possibility of taking into account the effects of Coriolis and centrifugal forces as subsequent perturbations. In addition, it defines the admissible fully antisymmetric many-nucleon irreps and puts a new perspective on the phenomenon of shape coexistence. It avoids use of an overcomplete set of coordinates and corrects the phenomenological unified model treatment of angular momentum quantization. These changes have significant implications for the dynamics of nuclear rotations, which are hidden when its moments of inertia are considered as adjustable parameters in the standard expression of rotational kinetic energies.

Isomers in ${}^{66}\mathrm{Ga}$, ${}^{67}\mathrm{Ge}$, and ${}^{69}\mathrm{Ge}$ were recoil implanted into ferromagnetic hosts of iron and gadolinium at $\approx 6$ K, and the hyperfine magnetic fields were determined by time differential perturbed angular distribution (TDPAD) measurements. The hyperfine field strengths at $\approx 6$ K are compared to the results of previous higher-temperature measurements and the amplitudes of the $R\left(t\right)$ functions are compared to empirical expectations. The results show that gadolinium can be a suitable host for high-precision in-beam $g$-factor measurements. The results of new $g$-factor measurements for isomers in ${}^{66}\mathrm{Ga}$ and ${}^{67}\mathrm{Ge}$ are $g({}^{66}\mathrm{Ga}, 7^{-})=+0.126\left(4\right)$, supporting a ${[{\pi }_{f5/2}\otimes \nu g_{9/2}]}_{7^{-}}$ configuration assignment, and $g({}^{67}\mathrm{Ge}, 9/2^{+})=-0.1932\left(22\right)$, derived from a new measurement of the ratio $g{(}^{67}\mathrm{Ge})/g{(}^{69}\mathrm{Ge})=0.869\left(9\right)$. These values are in agreement with previous results. The $R\left(t\right)$ amplitudes indicate that the nuclear alignment produced in the isomeric states was significantly lower than the empirically expected $\sigma /I\approx 0.35$.

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$), and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so-called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground-state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, and equilibrium deformations and pairing energies of the even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of the time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground-state and excited-state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in ${}^{165,167,169,171}\mathrm{Tm}$ are reproduced reasonably well. The appearance of backbendings or upbendings in these nuclei is well understood from the analysis of the variations of the occupation probabilities of the single-particle states and their contributions to total angular momentum alignment with rotational frequency.