In the present work, a $K$ isomeric state in ${}^{250}\mathrm{No}$, which is more stable against fission than the ground state, was experimentally studied. The aim was to measure the fission branch of this isomeric state. In total, 780 fission events attributed to the decay of ${}^{250}\mathrm{No}$ were detected. Among them 133 cases were attributed to the ground-state decay with a half-life of 4.0(4) $\mu \mathrm{s}$, which was populated by the deexcitation of the isomeric state via electromagnetic transitions with a half-life of 23(4) $\mu \mathrm{s}$. In addition, in two more cases, this long-lived isomeric state was populated in the deexcitation of a hitherto unknown, yet higher-lying and short-lived isomeric state with a half-life of $0.7_{-0.3}^{+1.4}\mu \mathrm{s}$. No direct fission from the long-lived isomeric state, i.e., with a lifetime of longer than 40 $\mu \mathrm{s}$, was identified. This results in an upper limit of 0.035 for the branching ratio for fission. This is a significantly more strict limit than the previously known value of 0.5. Nonobservation of fission branching of the long-lived isomer is discussed relative to theoretical predictions and within various semiempirical ways, which resulted in an attribution of a lower limit of ${10}^4$ for the fission-hindrance factor, caused by the $K$ quantum number. The presences of multiple high-$K$ isomeric states seemingly is a widespread phenomenon in deformed heavy nuclei.

The extremely neutron-deficient even-even uranium isotopes ${}^{216,218}\mathrm{U}$ were produced in the complete-fusion reactions induced by impinging ${}^{40}\mathrm{Ar}$ and ${}^{40}\mathrm{Ca}$ ions on ${}^{180,182,184}\mathrm{W}$ targets. Fusion evaporation residues were separated in flight by the gas-filled recoil separator SHANS (Spectrometer for Heavy Atoms and Nuclear Structure) and subsequently identified using the recoil-$\alpha$-correlation method. The improved ground-state to ground-state $\alpha$-decay properties of ${}^{216,218}\mathrm{U}$ were reported in [Z. Y. Zhang et al., Phys. Rev. Lett. 126, 152502 (2021)]. In this paper, we report on new $\alpha$-decay activities with $E_{\alpha }=10163\left(27\right)$ keV for ${}^{216}\mathrm{U}$ and $E_{\alpha }=10073\left(16\right)$ keV for ${}^{218}\mathrm{U}$, which decay from the $8^{+}$ isomeric states of ${}^{216,218}\mathrm{U}$ into the $2^{+}$ states of their daughter nuclei ${}^{212,214}\mathrm{Th}$, respectively. The new results extend the systematics of the $\alpha$-decay fine structure for the $N=124$ and 126 even-even isotones.

Background: For data on radioactive nuclei, $\beta$ decay provides some of the most important information, applicable to various fields. However, some $\beta$-decay data are not available due to experimental difficulties. For this reason, theoretically calculated results have been embedded in the data on radioactive nuclear $\beta$ decay to compensate for the missing information.

Purpose: It is necessary to treat various nuclear correlations as precisely as possible for theoretical $\beta$-decay calculations. In particular, the pairing correlation is one of the most important factors for reproducing $\beta$-decay half-lives correctly. Therefore, we first study the effect of zero- and finite-range isovector pairings on half-lives. Second, we investigate the isoscalar pairing strengths, which are determined through experimental data of half-lives. Finally, we predict the isoscalar pairing strengths and half-lives of neutron-rich nuclei.

Methods: To calculate the $\beta$-decay half-lives, a proton-neutron quasiparticle random-phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The half-lives are calculated by including the allowed and first-forbidden transitions. The isoscalar pairing strength is estimated by a Bayesian neural network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data.

Results: It was confirmed that the finite-range isovector pairing ensures that the $\beta$-decay half-lives are insensitive to the model space, while the zero-range one is largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of the experimental data, although those of highly deformed nuclei were underestimated. We also studied the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well.

Conclusions: Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data with the same accuracy as other theoretical works. To achieve a more precise prediction, the nuclear deformation is important.

The asymmetric fission dynamics of ${}^{180}\mathrm{Hg}$ has been analyzed in the framework of the time-dependent generator coordinate method (TDGCM) based on covariant density functional theory (CDFT) with the relativistic PC-PK1 functional. Three-dimensional $({\beta }_2,{\beta }_3,q_N)$ constrained CDFT calculations have been performed to determine the scission configurations. Remarkably, an asymmetric fission valley is observed in the potential energy surface in the ${\beta }_2\text{−}{\beta }_3$ plane and the heavy/light fragments at scission are ${}^{101}\mathrm{Rh}/{}^{79}\mathrm{Br}$, in good agreement with the data. Furthermore, we find that the heavy fragments of lowest-energy scission configurations, compared to those of other scission points, have rather small quadrupole deformations (${\beta }_2\sim 0.4$) and certain octupole deformations (${\beta }_3\sim 0.3–0.4$), which are driven by the extended neutron octupole shell gap with $N=56$. Based on the scission configurations, the estimated total kinetic energy distribution is consistent with the trend of experimental data. Finally, the dynamical TDGCM calculation reproduces the asymmetric yield distribution of the low-energy fission of ${}^{180}\mathrm{Hg}$, especially for the peak positions.

The existence of states with angular momenta $I=4$ and 6 of four fermions in an angular momentum $j=9/2$ shell that are stationary for any rotationally invariant two-body interaction despite the presence of other states with the same angular momentum, the Escuderos-Zamick states, is shown to be equivalent to the invariance to any such interaction of the span of states generated from $I=0$ states by one-body operators. This invariance is verified by exact calculation independently of previous verifications of the equivalent statement. It explains the occurrence of the Escuderos-Zamick states for just $I=4$ and 6. The action of an arbitrary interaction on the invariant space and its orthogonal complement is analyzed, leading to a relation of the Escuderos-Zamick energy levels to levels with $I=10$ and 12. Aspects of the observed spectra of ${}^{94}\mathrm{Ru}$, ${}^{96}\mathrm{Pd}$, and ${}^{74}\mathrm{Ni}$ are discussed in the light of this relation.

Background: Experimental and theoretical investigation of breakup coupling effects due to different cluster structures (${}^8\mathrm{Be}+n$ and ${}^5\mathrm{He}+\alpha$), relative importance of neutron or ${}^5\mathrm{He}/\alpha$ transfer, and their contribution to $\alpha$ production are important to understand reaction mechanism in a weakly bound projectile (${}^9\mathrm{Be}$) near the Coulomb barrier.

Purpose: Breakup coupling effect on elastic scattering and measurement of angular distributions and energy spectra of $\alpha$ particles produced through breakup, transfer, and complete fusion processes to disentangle their relative contributions and to investigate the relative importance of breakup followed by fusion (breakup-fusion) are compared to transfer.

Methods: Elastic scattering, inclusive $\alpha$ production, lithium, and boron production cross sections have been measured for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system above Coulomb barrier energies. Continuum-discretized-coupled-channels (CDCC) breakup coupling effect using ${}^8\mathrm{Be}+n$ and ${}^5\mathrm{He}+\alpha$ cluster configurations have been investigated. Coupled reaction channels (CRC) calculations for $1\mathit{p}, 1\mathit{d}$, and $1\mathit{n}$ stripping and $1\mathit{p}, 1\mathit{d}$ pickup leading to ${}^8\mathrm{Li}+{}^{52}\mathrm{Cr}, {}^7\mathrm{Li}+{}^{53}\mathrm{Cr}, {}^8\mathrm{Be}+{}^{52}\mathrm{V}$, and ${}^{10}\mathrm{B}+{}^{50}\mathrm{Ti}, {}^{11}\mathrm{B}+{}^{49}\mathrm{Ti}$, respectively, were performed and compared with the experimental data. Theoretical calculations for the estimation of various reaction channels contributing to $\alpha$ production have been performed with CDCC and CRC methods using the fresco code.

Results: Global optical model parameters for the ${}^9\mathrm{Be}$ projectile describe the elastic scattering data very well and the optical model fit improves the ${\chi }^2$ slightly. CRC calculations show a major contribution in the production of lithium through $1\mathit{p}, 1\mathit{d}$ stripping and boron through $1\mathit{p}, 1\mathit{d}$ pickup reactions. $\alpha$ production angular and energy distributions are obtained, and direct $\alpha$ production is described with contributions from noncapture breakup, breakup-fusion, and transfer reactions.

Conclusions: Breakup coupling for ${}^5\mathrm{He}+\alpha$ and ${}^8\mathrm{Be}+n$ cluster structures shows a repulsive and attractive coupling effect on elastic scattering, respectively. The ${}^8\mathrm{Be}+n$ cluster structure also shows a dipole polarization effect by suppressing the Coulomb rainbow compared to the ${}^5\mathrm{He}+\alpha$ cluster structure. Kinematic analysis of the $\alpha$ particles energy spectra suggest that $\alpha$ production is dominated by breakup-fusion over cluster transfer. CRC calculations suggest that $1\mathit{p}, 1\mathit{d}$ stripping and pickup reactions are a major contributor to lithium and boron production cross sections.

Background: In quantum mechanics, entanglement is the most striking phenomenon which has no counterpart in classical systems. Although different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics.

Purpose: We aim to study mode entanglement in the seniority model, derive analytic formulas for the one-body reduced density matrix of states with seniority $\nu =0,1,2$, and 3, and also determine the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, we compare the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states.

Methods: In the seniority model the analytic results are calculated using the quasispin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the $G$-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies.

Results: In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states is revealed. Numerical results are presented for the lightest stable calcium isotopes and for ${}^{94}\mathrm{Ru}$ nucleus.

Conclusions: For ${}^{94}\mathrm{Ru}$, the seniority model accounts for the $0g_{9/2}$ mode entropies, but seniority mixing is important for certain yrast states. Interaction induced quantum fluctuations decrease the occupation of the $0f_{5/2}$, $1p_{3/2}$, and $1p_{1/2}$ shells, and result in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple ${\left(0g_{9/2}\right)}^4$ seniority model. The $0f_{7/2}$ shell based seniority model is more accurate for the $\mathrm{Ca}$ isotopes, but seniority mixing is substantial for some ${}^{44}\mathrm{Ca}$ yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.

Neutron-rich carbon isotopes have been investigated within the Gamow shell model (GSM) based on a realistic nuclear force. ${}^{14}\mathrm{C}$ was chosen as the core in the shell-model calculations of the neutron-rich carbon isotopes. The effect from the coupling to the continuum is well considered by using the complex-momentum Berggren representation which treats bound, resonant, and continuum states on an equal footing. Using the many-body perturbation theory named the $\widehat{Q}$-box folded-diagram method, the complex GSM effective interaction was derived from the CD-Bonn interaction. We find that the inclusion of the continuum coupling in the calculation is important in the description of neutron-rich carbon isotopes, especially in reproducing the experimental $1/2^{+}$ ground states of ${}^{19}\mathrm{C}$ and ${}^{21}\mathrm{C}$. Our calculation indicates a shell closure at $N=16$ in the carbon chain, while the $N=14$ shell, which exists in the next even-$Z$ chain of oxygen isotopes, disappears. The calculation suggests that ${}^{22}\mathrm{C}$ is the heaviest bound carbon isotope, i.e., the neutron drip line.

The beam energy scan program at RHIC provides data on net-proton number fluctuations with the goal to detect the QCD critical end point and first-order phase transition. Interpreting these experimental signals requires a vital understanding of the interplay of critical phenomena and the nonequilibrium dynamics of the rapidly expanding fireball. We study these aspects with a fluid dynamic expansion coupled to the explicit propagation of the chiral order parameter sigma via a Langevin equation. Assuming a sigma-proton coupling through an effective proton mass, we relate cumulants of the order parameter and the net-proton number at freeze-out and obtain observable cumulant ratios as a function of beam energy. We emphasize the role of the nonequilibrium first-order phase transition where a mixed phase with gradual freeze-out can significantly alter the cumulants. We find that the presence of a critical end point is clearly visible in the cumulant ratios for a relatively wide range of center-of-mass energies.

A microscopic nuclear equation of state compatible with all current astrophysical constraints constructed within the Brueckner-Hartree-Fock formalism is presented and extended in a consistent way to finite temperature. The effects of finite temperature on the properties of neutron stars are studied in detail and a universal relation regarding stellar stability is proposed.

Background: Approximately half of all atomic nuclei heavier than iron are synthesized by the slow neutron-capture process. The weak component of this process is not well understood and the reaction rates of each isotope in the s-process path affect nucleosynthesis abundances downstream.

Purpose: To measure the neutron-capture cross sections of two weak s-process nuclei, ${}^{70,72}\mathrm{Ge}$, using the neutron time-of-flight technique. Measuring the capture cross sections for isotopes in this region of the chart of nuclides has proven challenging due to dominant scattering cross sections.

Method: Samples consisted of pellets made of pressed enriched metallic powders. The ${}^{70,72}\mathrm{Ge}$ neutron-capture cross sections were measured as a function of neutron energy using the Detector for Advanced Neutron Capture Experiments at Los Alamos National Laboratory.

Results: Neutron-capture cross sections were measured from 10 eV to 1 MeV. These are the first measurements for ${}^{70,72}\mathrm{Ge}$ between 300 keV and 1 MeV neutron energy. Maxwellian-averaged cross sections were calculated in the astrophysically relevant neutron energy range (5 keV $\le kT\le$ 100 keV). Their value at $kT=30$ keV was found to be $89\pm 11$ mb for ${}^{70}\mathrm{Ge}$ and $58\pm 5$ mb for ${}^{72}\mathrm{Ge}$. Both values are in agreement with recent time-of-flight measurements at n_TOF (neutron Time-Of-Flight facility at the European Organization for Nuclear Research).

Conclusions: The average cross section results from this work for ${}^{70}\mathrm{Ge}$ show minor ($<1\sigma$) disagreement with a recent measurement by the n_TOF collaboration at higher neutron energies. This corresponds to the neutron energy region that had previously never been measured ($>300$ keV). Two reaction library databases underestimate the ${}^{72}\mathrm{Ge}$ average cross section below 30 keV according to n_TOF and DANCE. This is likely due to capture resonances that are missing from the theoretical cross sections in the databases that were identified in both time-of-flight measurements. Additionally, a rudimentary analysis of the impact of both cross section measurements on stellar nucleosynthesis abundances using the NETZ nucleosynthesis tool is presented.

The production of Fl isotopes in proton evaporation channels is investigated systematically within the dinuclear system model. Because the proton evaporation is the easiest for Mc isotopes among the isotopes around $Z=114$, one can synthesize Fl isotopes in the proton evaporation channel. The calculated ER cross sections by the DNS model reproduce the experimental data very well. The dependence of the production cross sections on projectile isospin in capture, fusion, and survival processes in ${}^{32,34,36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions is studied. The capture cross sections and survival probability in the ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reaction are the largest, while the fusion probability in the ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$ reaction is the highest. The reaction ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Am}$ is a promising candidate to synthesize the unknown isotope ${}^{290}\mathrm{Fl}$ with the maximum ER cross section of 4.07 pb in the $p1n$ evaporation channel. Another new isotope ${}^{291}\mathrm{Fl}$ can be produced in the ${}^{54}\mathrm{Cr}+{}^{239}\mathrm{Pa}$ reaction and the production cross section is estimated to be 0.11 pb.

We investigate the multineutron excitations of neutron-rich ${}^8\mathrm{He}$ in the electric dipole strength using a ${}^4\mathrm{He}+n+n+n+n$ five-body model. Many-body unbound states of ${}^8\mathrm{He}$ are obtained in the complex scaling method. We found that the different excitation modes coexist in the dipole strength below the excitation energy of 20 MeV. The strength below 10 MeV comes from the ${}^7\mathrm{He}+n$ channel, indicating the sequential breakup of ${}^8\mathrm{He}$ via the ${}^7\mathrm{He}$ resonance to ${}^6\mathrm{He}+n+n$. Above 10 MeV, the strength is obtained from many-body continuum states with strong configuration mixings, suggesting a new collective motion of four neutrons with the dipole oscillation against ${}^4\mathrm{He}$.

The dominance of prolate over oblate deformations in the ground states of deformed even-even nuclei has long been known empirically. Although various theoretical approaches have been applied, the underlying mechanism is not yet considered as being adequately understood. One of those theoretical approaches has found an interesting interference effect between the spin-orbit coupling and the surface diffuseness in the single-particle potential. Recently the proxy-SU(3) model claimed that the prolate dominance would emerge naturally from the SU(3) symmetry assuming the highest-weight irreducible representations as ground-state configurations. This article presents a possible interpretation of the interference effect in the former approach in the context of the latter approach, more specifically invoking the dual-shell mechanism that includes both the three-dimensional harmonic-oscillator shells and the spin-orbit-like shells.

The Woods-Saxon basis has achieved great success in both nonrelativistic and covariant density functional theories in recent years. Due to its nonanalytical nature, however, applications of the Woods-Saxon basis are numerically complicated and computationally time consuming. In this paper, based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we check in detail the convergence with respect to the basis space in the Dirac sea. An optimized Dirac Woods-Saxon basis is proposed, whose corresponding potential is close to the nuclear mean field. It is shown that the basis space of the optimized Dirac Woods-Saxon basis required for convergence is substantially reduced compared with the original one. In particular, it does not need to contain the bases from continuum in the Dirac sea. The application of the optimized Woods-Saxon basis would greatly reduce computing resource for large-scale density functional calculations.

We present an approach to modeling the ground-state mass of atomic nuclei based directly on a probabilistic neural network constrained by relevant physics. Our physically interpretable machine learning (PIML) approach incorporates knowledge of physics by using a physically motivated feature space in addition to a soft physics constraint that is implemented as a penalty to the loss function. We train our PIML model on a random set of approximately 20% of the atomic mass evaluation (AME) and predict the remaining 80%. The success of our methodology is exhibited by a ${\sigma }_{\mathrm{rms}}\approx 186$ keV match to data for the training set and ${\sigma }_{\mathrm{rms}}\approx 316$ keV for the entire AME with $Z\ge 20$. We show that our general methodology can be interpreted using feature importance.

The structure of ${}^{83}\mathrm{As}$, ${}^{85}\mathrm{As}$, and ${}^{87}\mathrm{As}$ have been studied in fusion-fission reaction ${}^{238}\mathrm{U}+{}^9\mathrm{Be}$. Fission fragments were identified in mass and atomic number using the VAMOS$++$ spectrometer and the coincident $\gamma$ rays were detected in the $\gamma$-ray tracking array AGATA. New transitions in ${}^{83}\mathrm{As}$ and ${}^{85}\mathrm{As}$ are reported and placed in the level schemes. A level scheme of the excited states in ${}^{87}\mathrm{As}$ is proposed for the first time. The data are interpreted in frame of large-scale shell-model calculations, SU3 symmetries, and beyond mean-field frameworks. A spherical regime at magic number $N=50$ is predicted and the location of the proton $g_{9/2}$ orbital is proposed for the first time. Development of collectivity in a prolate deformed, $\gamma$-soft regime in the open shell cases ${}^{85}\mathrm{As}$ and ${}^{87}\mathrm{As}$, most neutron-rich isotopes beyond $N=50$, is concluded. Data and theoretical calculations give confidence to a relatively high extrapolated excitation energy about 4 MeV of the $9/2^{+}$ state in ${}^{79}\mathrm{Cu}$, one proton above ${}^{78}\mathrm{Ni}$.

The production of ${}^{243–254}\mathrm{No}$ is investigated within the framework of the improved quantum molecular dynamical model incorporated with a statistical model. The calculated results of the ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ fusion reaction can reproduce the experimental data well. The impact parameter and the incident energy influence the fusion probability and the lifetime of the neck in fusion reaction process. Furthermore, the evaporation residue cross sections of ${}^{40,44,48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, ${}^{20}\mathrm{Ne}+{}^{233,235,238}\mathrm{U}$, ${}^{16}\mathrm{O}+{}^{242}\mathrm{Pu}$, and ${}^{26}\mathrm{Mg}+{}^{232}\mathrm{Th}$ reactions are calculated. From investigation, the more neutrons there are in the projectile or target for the same projectile-target combination, the larger evaporation residue cross sections will be. Six unknown isotopes ${}^{243–248}\mathrm{No}$ are predicted with maximum evaporation residue cross sections 0.061 pb, 2.250 pb, 0.005 nb, 0.530 nb, 0.432 nb, and 3.518 nb, respectively. The corresponding fusion reactions are ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},5n){}^{243}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},4n){}^{244}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},3n){}^{245}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},2n){}^{246}\mathrm{No}$, ${}^{233}\mathrm{U}({}^{20}\mathrm{Ne},6n){}^{247}\mathrm{No}$, and ${}^{233}\mathrm{U}({}^{20}\mathrm{Ne},5n){}^{248}\mathrm{No}$, respectively.