Background: Nonyrast states in neutron-rich nuclei are being investigated experimentally. These states reveal various aspects and details of the nuclear structure, such as the fluctuation around the axially symmetric shape.

Purpose: The beyond-mean-field effects in neutron-rich nuclei with $N\simeq 28$ are investigated. We focus on the role of collective mass in triaxial-shape dynamics.

Method: We employ the five-dimensional quadrupole collective Hamiltonian method with the potential obtained in a constrained Hartree-Fock-Bogoliubov approach with a Skyrme energy-density functional and the collective-mass functions obtained by the cranking approximation. The method includes triaxial deformations.

Results: We find that ${}^{42}\mathrm{Mg}, {}^{40}\mathrm{Si}, {}^{44}\mathrm{S}$, and ${}^{46}\mathrm{S}$ show $\gamma$-soft: A flat behavior in the potential energy surface along the triaxial deformation. Their low-lying spectra show a strong nucleus dependence, while those obtained with a collective mass assumed as constant are similar to each other. The energy ratio $E\left(0_2^{+}\right)/E\left(2_1^{+}\right)$ and the $B\left(E2\right)$ ratio $B(E2;0_2^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ show a unique property of the $0_2^{+}$ state, while the energy and $B\left(E2\right)$ ratios in neutron-deficient $\gamma$-soft nuclei with $N=78$ do not depend on nucleus so much.

Conclusions: Low-lying spectra are determined by not only the potential energy but also the collective mass. We clarify the important role of the collective mass in low-energy dynamics in the neutron-rich $N\approx 28$ nuclei.

For the electromagnetic-induced fission of even ${}^{222–230}\mathrm{Th}$ isotopes, the effect of the transition from a symmetric fission mode to an asymmetric one on the charge/mass, total kinetic energy, neutron multiplicity distributions, and probability for a given neutron multiplicity per fission event is explored within an improved scission-point model. The simultaneous description all these observables and correlations between them are presented.

The possibility of new short distance physics applicable inside the cores of neutron stars is incorporated into the equation of state generated by the quark-meson coupling model. The contribution of this new physics to the energy density is taken to be proportional to the amount of overlap between the quark cores of the baryons involved. With no change to the properties of symmetric nuclear matter at saturation density, including an incompressibility compatible with data on giant monopole resonances, one can sustain neutron stars with a maximum mass $M_{\max }>2.1M_{\odot }$, even when hyperons are included.

We have calculated ${\beta }^{-}$ decay rates to the continuum and bound states of some fully ionized atoms in the stellar $s$-process environment having free electron density and temperature in the range $n_e={10}^{26}-{10}^{27}{\mathrm{cm}}^{-3}$ and $T=1\times {10}^8$ to $5\times {10}^8$ K, respectively. The presence of bare atoms in these particular situations has been confirmed by solving the Saha ionization equation taking into account the ionization potential depression (IPD). At these temperatures, low lying excited energy levels of parent nuclei may have thermal equilibrium population and those excited levels may also decay via ${\beta }^{-}$ emission. The nuclear matrix element (NME) of all the transitions of the set of 15 nuclei is calculated using nuclear shell model. These NMEs are then used to calculate the comparative half-life ($f{t}_{1/2}$) of the transitions. Calculated terrestrial half-lives of the ${\beta }^{-}$ decays are in good agreement with the experimental results in most of the cases. Decay to bound and continuum states of bare atoms from ground and/or isomeric levels and excited nuclear levels are calculated separately. The ratio of bound state to continuum state decay rates as a function of IPD modified $Q$ value reveals that the bound state ${\beta }^{-}$ decay rate may compete and even dominate for $Q$ value $<100$ keV. The importance of the bound state ${\beta }^{-}$ decay in stellar situations has been shown explicitly. We have calculated total ${\beta }^{-}$ decay rates (bound state plus continuum state) taking into account the IPD corrected neutral atom $Q$ value as a function of density and temperature. We have also presented results for the stellar ${\beta }^{-}$ half-lives and compared the ratio of neutral atom to bare atom half-lives for different density and temperature combinations. These results may be useful for $s$-process nucleosynthesis calculations.

An implementation of the generalized time-dependent generator coordinated method (TD-GCM) is developed, that can be applied to the dynamics of small- and large-amplitude collective motion of atomic nuclei. Both the generator states and weight functions of the GCM correlated wave function depend on time. The initial generator states are obtained as solutions of deformation-constrained self-consistent mean-field equations, and are evolved in time by the standard mean-field equations of nuclear density functional theory (TD-DFT). The TD-DFT trajectories are used as a generally nonorthogonal and overcomplete basis in which the TD-GCM wave function is expanded. The weights, expressed in terms of a collective wave function, obey a TD-GCM (integral) equation. In this explorative paper, the generalized TD-GCM is applied to the excitation energies and spreading width of giant resonances, and to the dynamics of induced fission. The necessity of including pairing correlations in the basis of TD-DFT trajectories is demonstrated in the latter example.

We explore the structure of the ground state of ${}^{20}\mathrm{Ne}$ by investigating various density profiles. Four candidates for the ground state configurations, (a) $j\text{−}j$ coupling and (b) SU(3) shell model and (c) $5\alpha$ and (d) ${}^{16}\mathrm{O}+\alpha$ cluster model configurations, are generated by utilizing the antisymmetrized quasicluster model. A high-energy reaction theory, the Glauber model, relates these one-body density distributions and reaction observables. The angular distributions of the elastic scattering cross sections clearly distinguish these configurations and tell which is the most plausible one: The ground state of ${}^{20}\mathrm{Ne}$ favors a $16+4$ nucleon bicluster structure. A comprehensive investigation of other electric observables also supports this conclusion.

Neutrino-induced reactions on ${}^{40}\mathrm{Ar}$ are investigated by the shell model for Gamow-Teller transitions and the random-phase approximation (RPA) for forbidden transitions. For the $1^{+}$ multipole, an effective interaction in the $sd\text{−}pf$ shell obtained by the extended Kuo-Krenciglowa (EKK) method from chiral interactions is used to study $B\left(\text{GT}\right)$, the charged-current reaction ${}^{40}\mathrm{Ar}({\nu }_e,e^{-}){}^{40}\mathrm{K}$, $B\left(M1\right)$ in ${}^{40}\mathrm{Ar}$, and the neutral-current reaction ${}^{40}\mathrm{Ar}(\nu ,{\nu }^{\prime }){}^{40}\mathrm{Ar}$. A considerable quenching for spin modes is found in the analysis of $B\left(M1\right)$, and this quenching is taken into account for the evaluation of the cross sections of the neutral-current reaction. The sensitive dependence of the reaction cross sections on the quenching of the axial-vector coupling constant, $g_A$, is pointed out.

Background: In the fusion process, the investigation of the reaction dynamics in the time evolution of the nuclear configuration is necessary. The neck parameter $\epsilon$ which is one of the parameters representing the nuclear configuration in the two center shell model is important in fusion owing to the nucleons transferring through the neck. The time evolution of the neck has not been discussed in detail, but is crucial for fusion cross section in the assessment of new elements synthesis.

Purpose: The dynamical analysis for the fusion hindrance under the neck formation on the nuclear deformation space has been done. The fusion probability $P_{\text{CN}}$ considering the different denecking motion and the fusion hindrance are discussed.

Method: The calculations were performed using the dynamical model of nucleus-nucleus collisions based on the multidimensional Langevin equations.

Results: The formation of the neck bridge at the approaching stage is found to be crucial to the fusion hindrance. It is clarified that the inner barrier appears owing to the change in the degree of mass asymmetry $\alpha$ with the relaxation of $\epsilon$.

Conclusions: The fusion hindrance occurs because the inner barrier is formed by the early neck formation. The role of the neck parameter $\epsilon$ is critically important for the fusion dynamics.

Global polarizations ($P$) of $\mathrm{\Lambda } \left(\overline{\mathrm{\Lambda }}\right)$ hyperons have been observed in noncentral heavy-ion collisions. The strong magnetic field primarily created by the spectator protons in such collisions would split the $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ global polarizations ($\mathrm{\Delta }P=P_{\mathrm{\Lambda }}-P_{\overline{\mathrm{\Lambda }}}<0$). Additionally, quantum chromodynamics predicts topological charge fluctuations in vacuum, resulting in a chirality imbalance or parity violation in a local domain. This would give rise to an imbalance ($\mathrm{\Delta }n=\frac{N_{\text{L}}-N_{\text{R}}}{\langle N_{\text{L}}+N_{\text{R}}\rangle }\ne 0$) between left- and right-handed $\mathrm{\Lambda }$ ($\overline{\mathrm{\Lambda }}$) as well as a charge separation along the magnetic field, referred to as the chiral magnetic effect (CME). This charge separation can be characterized by the parity-even azimuthal correlator ($\mathrm{\Delta }\gamma$) and parity-odd azimuthal harmonic observable ($\mathrm{\Delta }{a}_1$). Measurements of $\mathrm{\Delta }P, \mathrm{\Delta }\gamma$, and $\mathrm{\Delta }{a}_1$ have not led to definitive conclusions concerning the CME or the magnetic field, and $\mathrm{\Delta }n$ has not been measured previously. Correlations among these observables may reveal new insights. This paper reports measurements of correlation between $\mathrm{\Delta }n$ and $\mathrm{\Delta }{a}_1$, which is sensitive to chirality fluctuations, and correlation between $\mathrm{\Delta }P$ and $\mathrm{\Delta }\gamma$ sensitive to magnetic field in $\mathrm{Au}+\mathrm{Au}$ collisions at 27 GeV. For both measurements, no correlations have been observed beyond statistical fluctuations.

Background: Intrinsic charm, nonperturbative charm in the hadron wavefunction, has long been speculated but has never been satisfactorily proven. Open charm and $J/\psi$ measurements in a fixed-target configuration at the LHCb searched for this contribution but reported no evidence.

Purpose: $\overline{D}$ meson and $J/\psi$ production is calculated for the SMOG fixed-target configuration in the LHCb experiment using a combination of perturbative QCD and intrinsic charm to see whether intrinsic charm would indeed be observable in the SMOG kinematics.

Methods: Open charm and $J/\psi$ production is calculated to next-to-leading order in perturbative QCD. Because a gas jet nuclear target is used, cold nuclear matter effects are included in the perturbative calculations. The intrinsic charm is calculated assuming production from a $|uudc\overline{c}\rangle$ Fock state.

Results: The differential rapidity and transverse momentum distributions in $p+\mathrm{Ne}$, $p+\mathrm{He}$, and $p+\mathrm{Ar}$ fixed-target interactions are calculated in the SMOG acceptance and compared to data. The predicted asymmetries between $\overline{D}$ (leading charm) and $D$ (nonleading charm) are also shown.

Conclusions: The contribution from intrinsic charm is small and decreases with center-of-mass energy. The calculations agree well with the current SMOG data, with or without intrinsic charm.

Nuclei in the $Z\approx 40,N\approx 60$ region have one of the most complicated structural evolutions across the nuclear chart, with coexisting shapes arising from different mixed configurations. In such a region, it is difficult to investigate odd-mass nuclei. In this paper a new algebraic framework is introduced: the interacting boson-fermion model with configuration mixing. Using this framework, with a boson core and a proton in the $1f_{5/2},2p_{3/2},2p_{1/2},1g_{9/2}$ orbits, a calculation is carried out to understand the structural evolution of the odd-mass niobium isotopes ($Z=41$) with neutron number 52–62. The calculated results are compared to energy levels, two-neutron separation energies, $E2$ and $M1$ transition rates, and quadrupole and magnetic moments. The detailed analysis discloses the effects of an abrupt crossing of states between normal and intruder configurations [Type II quantum phase transition (QPT)], which is accompanied by a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type I QPT), where both types of QPTs occur around the critical point of neutron number 60. The identification of both types of QPTs in the same chain of isotopes provides an empirical manifestation of intertwined quantum phase transitions (IQPTs) in odd-mass nuclei and the relevance of IQPTs to the niobium chain.

Three three-quasiparticle isomers, one at an excitation energy of 2.3 MeV with $T_{1/2}=0.48\left(4\right)\mu \mathrm{s}$, and two shorter-lived with unknown half-lives at slightly lower energies have been identified in ${}^{129}\mathrm{Nd}$ using the MARA $+$ JUROGAM 3 setup and the recoil tagging technique. All three isomers present decay patterns characteristic of high-$K$ isomers. The known 6.7 s $\beta$-decaying isomer previously assigned to the $5/2^{+}$ level is now assigned to the new $7/2^{-}$ ground state. A new low-spin $5/2^{+}$ isomeric state with a half-life of a few tens of nanoseconds has been identified, while a previously known 2.6 s $\beta$-decay activity was assigned to the band head of the $\nu 1/2^{+}\left[411\right]$ band. The transitions depopulating the high-$K$ isomers to low-lying states also establish the relative energies of three low-lying one-quasiparticle bands, leading to a new spin-parity assignment of $7/2^{-}$ to the ground state of ${}^{129}\mathrm{Nd}$. The partial half-lives of the depopulating transitions suggest spin-parities $21/2^{+}, 19/2^{+}$, and $17/2^{+}$ for the three high-$K$ isomers. The properties of the band built on the $21/2^{+}$ isomeric state suggest a one neutron-two proton configuration. Based on the results of extensive calculations with different models, we also assign one neutron–two proton configurations to the $19/2^{+}$ and $17/2^{+}$ isomeric states. The assigned configurations of the $17/2^{+}$ and $21/2^{+}$ isomeric states involve the $\pi 9/2^{+}\left[404\right]$ orbital, which is identified in three-quasiparticle bands of proton-rich $A\approx 130$ nuclei.

Background: The $\alpha$ cluster is a prominent feature, not only in light nuclei but also in heavy nuclei. To study the $\alpha$-particle formation in the mean-field calculation, the localization function has been extensively utilized. However, the localization function does not guarantee the proximity of four different nucleons which is required by the $\alpha$-particle formation. A simple indicator of the proximity is desired. Recently, experimental measurement of the quasifree $\alpha$-knockout reaction for Sn isotopes reveals the cross sections with a monotonic decrease with increasing neutron number. [Science 371, 260 (2021)]. This is interpreted as evidence of the surface $\alpha$ formation.

Purpose: We propose a simple and comprehensible quantity to assess the proximity of four nucleons with different spins and isospins. Using this, we examine the recent measurement of $\alpha$-knockout cross sections in Sn isotopes.

Methods: The local $\alpha$-removal strength is proposed to quantify the possibility to form an $\alpha$ particle at a specific location inside the nucleus. In addition, it provides the strength of ground and excited states in the residual nuclei after the removal of the $\alpha$ particle. To make the calculation feasible, we introduce several approximations, such as point-$\alpha$, mean-field, and no rearrangement approximations. We use the Hartree-Fock-plus-BCS method for the mean-field calculation for Sn isotopes. We also propose another measure, the local $\alpha$ probability, which should provide a better correlation with the $\alpha$-knockout cross sections.

Results: The calculation of the local $\alpha$-removal strength is extremely easy in the mean-field model with no rearrangement. For even-even Sn isotopes, the local $\alpha$-removal strengths to the ground state of residual nuclei are almost universal in the nuclear surface region. In contrast, the local $\alpha$ probability produces strong neutron number dependence consistent with the experiment.

Conclusions: The local $\alpha$-removal strength and the local $\alpha$ probability are easily calculable in the mean-field models. Recent experimental data for Sn isotopes may be explained by a simple model without explicit consideration of $\alpha$ correlation.

The dominance of prolate over oblate ground-state deformations has been a well-known empirical fact. With the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and taking Te, Xe, and Ba isotopes with neutron number $82⩽N⩽126$ as examples, a self-consistent and microscopic study of the prolate-shape dominance is given. According to the calculated potential-energy curves, most of these isotopes have both prolate and oblate minima and prefer prolate in the ground state, while the small amount of oblate ground-state shapes mainly appear after the major shell is half filled. It is also found that the prolate-shape dominance enhances with the proton number increasing from 52 to 56. The dominance and its enhancement can be well understood by the microscopic canonical single-particle energies obtained in the DRHBc theory, in good agreement with the schematic interpretation based on the Nilsson diagram. Finally, pairing correlations are found to bring more energy displacements to oblate minima on average but do not play a decisive role in prolate-shape dominance.

The neutron-induced capture-to-fission cross section ratio of ${}^{233}\mathrm{U}$ has been measured at the Los Alamos Neutron Science Center at Los Alamos National Laboratory in the energy range from 0.7 eV to 250 keV. The detector setup combines the Detector for Advanced Neutron Capture Experiments (DANCE) to measure $\gamma$ rays generated from both capture and fission reactions, and the neutron detector array at DANCE to measure fission neutrons. This is the first measurement of the capture-to-fission ratio between 2 and 30 keV. The evaluations are in good agreement with the results in the resolved resonance region. In both the unresolved resonance region and the fast neutron region, a lower capture-to-fission ratio is obtained in this work from 10 to 150 keV compared to current evaluations, while good agreement with the experimental data and the evaluations is found above 150 keV. Statistical model calculations were performed to compare with the experimental data. Significantly reduced $\langle {\mathrm{\Gamma }}_{\gamma }\rangle$ was required to reproduce the measured data.

The influences of $\alpha$-clustering configurations on the giant dipole resonance (GDR) in hot compound systems are discussed under the framework of an extended quantum molecular dynamics (EQMD) model. The computed GDR spectra in the hot nucleus ${}^{28}\mathrm{Si}$ are split into two peaks which are very consistent with the experimental measurement and are remarkably sensitive to the configurations of projectile ${}^{16}\mathrm{O}$, including the linear chain, kite, square, and tetrahedron configurations. Meanwhile, the sensitivity of the GDR lineshapes to the configurations of ${}^{16}\mathrm{O}$ gradually increases with angular momentum. However, for the fusion system induced by ${}^{20}\mathrm{Ne}$, their GDR lineshapes in ${}^{47}\mathrm{V}$ and ${}^{32}\mathrm{S}$ are mostly independent of the $\alpha$-clustering configurations compared with those in the hot compound systems induced by the projectile ${}^{16}\mathrm{O}$, which may be attributed to their much more similar geometric structures between the square pyramid and trigonal bipyramid configurations in ${}^{20}\mathrm{Ne}$. Additionally, we find that the GDR lineshapes in hot compound systems are sensitive to the geometric distributions of the projectile in phase space when it is compared to those with Woods-Saxon distribution and polarization in projectiles. These results demonstrate that the GDR can be taken as an experimental observable to extract information about the configurations of reaction systems.

The average number of neutrons emitted in neutron-induced nuclear fission has been measured for major actinides from thermal to relativistic incident energy ranges. On the other hand, the complete probability distributions could not be reconstructed from experimental data beyond a few MeV because the unfolding of the neutron-counter response is an ill-conditioned inverse problem. In order to obtain the complete neutron-multiplicity distributions without simplifying assumption on their shapes, this paper submits a robust Tikhonov-inspired regularization procedure. A revaluation, with this method, of the only available dataset, provides precise neutron-multiplicity distributions for uranium-235 and plutonium-239 up to 12 MeV. Their exact shapes are exploited to extract, for the first time from experimental data, the second-chance fission partial probability.

The effect of deformation in the scattering and reaction of a ${}^9\mathrm{C}$ radioactive beam by protons and ${}^{12}\mathrm{C}$ is investigated within the relativistic impulse approximation and a modified Glauber model whose amplitude involved the combined effects of phase variation, higher momentum transfer components, Pauli blocking, and finite range. Spherical and deformed relativistic mean field densities are used. Using the proton scattering experiment by ${}^9\mathrm{C}$ as well as interaction cross section data, the proton and neutron root mean square (rms) radii and deformations are extracted. It is found that deformation strongly affects the scattering cross section and polarization at medium and large angles, where the second and third peaks are reproduced by a deformed density. The polarization is inverted at the peaks by deformation. The measured angular distribution of the proton by a ${}^9\mathrm{C}$ beam at $277–300$ MeV/u as well as the reaction cross section data of ${}^9\mathrm{C}+{}^{12}\mathrm{C}$ at 680 and 720 MeV/u are satisfactorily reproduced by an extracted deformed Woods-Saxon density of ${}^9\mathrm{C}$ with matter rms radius and deformation parameter of the order $R_m\approx 2.33$ fm and ${\beta }_m\approx 0.36$.

Background: The four-neutron correlation has been attracting much attention for decades. In addition to the study on the tetraneutron system, it is worthwhile to investigate the correlation in bound systems.

Purpose: The ${}^8\mathrm{He}$ nucleus is a system where four neutrons are weakly bound around the ${}^4\mathrm{He}$ core. The dineutron ($2n$) correlation has been long discussed in various weakly bound neutron-rich nuclei such as ${}^6\mathrm{He}$ and ${}^{11}\mathrm{Li}$, whereas the ${}^8\mathrm{He}$ nucleus gives us an opportunity to investigate the $2n\text{−}2n$ type four-neutron correlation.

Methods: We introduce a microscopic ${}^4\mathrm{He}+4n$ model and describe the ground-state structure of ${}^8\mathrm{He}$. The mixing of the two-$2n$ component in the ground state is examined. The ground-state wave function is verified by investigating various observables including high-energy scattering cross sections.

Results: Our model reasonably reproduces the available experimental data, the binding energy, charge radius, total reaction cross section, and proton-nucleus elastic scattering cross section data. We find that the significant mixing of the two-$2n$ cluster configurations around ${}^4\mathrm{He}$ in the ground state of ${}^8\mathrm{He}$: The ground state has a squared overlap of about 45% with a $2n\text{−}{}^4\mathrm{He}\text{−}2n$ configuration with the ${}^4\mathrm{He}\text{−}2n$ distance of 3 fm and opening angle of ${80}^{\circ }$.

Conclusions: The ground state of ${}^8\mathrm{He}$ contains a certain amount of the two-$2n$ cluster component, indicating the strong nuclear deformation, which was experimentally observed recently.

Low-lying states in ${}^{206}\mathrm{Po}$ were investigated using the fast-timing technique with ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ and high-purity germanium detectors. The excited states in this nucleus were populated via two consecutive electron capture decays from ${}^{206}\mathrm{Rn}$. The parent isotope was produced in the ${}^{194}\mathrm{Pt}({}^{16}\mathrm{O},4n){}^{206}\mathrm{Rn}$ fusion-evaporation reaction at the FN-Tandem facility at the Institute for Nuclear Physics, University of Cologne. The previously known value for the lifetime of the $4_1^{+}$ state in ${}^{206}\mathrm{Po}$ was confirmed using the generalized centroid difference (GCD) method. The lifetime of the $6_1^{+}$ state was determined from $\beta$ decay in the first application of the GCD method for x-ray–$\gamma$ coincidences. A Monte Carlo based approach was applied to address the indirect population of the $6_1^{+}$ state by the decay of ${}^{206}\mathrm{At}$. The experimental results were examined in the context of the transition of single-particle excitations to collective behavior in the neutron-deficient Po isotopes. The obtained $B(E2;6_1^{+}\to 4_1^{+})$ value suggests that for the $6_1^{+}$ states in even-even Po isotopes the transition from a noncollective regime at $N=126$ to a collective regime occurs at $N\le 120$.