Measurements of the ${}^2\mathrm{H}({}^{16}\mathrm{C},{}^{16}\mathrm{C}^{*}\to {}^4\mathrm{He}+{}^{12}\mathrm{Be}$ or ${}^6\mathrm{He}+{}^{10}\mathrm{Be}){}^2\mathrm{H}$ inelastic excitation and cluster-decay reactions have been carried out at a beam energy of about 23.5 MeV/u. A specially designed detection system, including one multilayer silicon-strip telescope at around zero degrees, has allowed the high-efficiency threefold coincident detection and therefore the event-by-event determination of the energy of the unstable nucleus beam. The decay paths from the ${}^{16}\mathrm{C}$ resonances to various states of the final ${}^{10}\mathrm{Be}$ or ${}^{12}\mathrm{Be}$ nucleus are recognized thanks to the well-resolved $Q$-value spectra. The reconstructed resonances at 16.5(1), 17.3(2), 19.4(1), and 21.6(2) MeV are assigned as the $0^{+}, 2^{+}, 4^{+}$, and $6^{+}$ members, respectively, of the positive-parity ${(3/2_{\pi }^{-})}^2{(1/2_{\sigma }^{-})}^2$-bond linear-chain molecular band in ${}^{16}\mathrm{C}$, based on the angular-correlation analysis for the 16.5 MeV state and the excellent agreement of decay patterns between the measurements and theoretical predictions. Moreover, another intriguing high-lying state was observed at 27.2(1) MeV which decays almost exclusively to the $\approx 6$ MeV states of ${}^{10}\mathrm{Be}$, in line with the newly predicted pure $\sigma$-bond linear-chain configuration.

We revisit a sudden increase of the isotope shift of the charge radius of Pb isotopes at $N>126$ based on a Skyrme Hartree-Fock-Bogoliubov theory. New parametrizations of the pairing interaction optimized for four selected Skyrme interactions greatly improve a description of this phenomenon. The density-dependent spin-orbit interaction is also investigated and further increases the charge radius. The pairing correlations significantly change the properties of the neutron orbits near the Fermi level and play a vital role in pulling out the well-bound protons in the Pb isotopes at $N>126$. Regarding ${}^{208}\mathrm{Pb}$ as a “core” nucleus, a novel pairing core swelling effect is proposed: The pairing interaction reduces the radius of “valence” neutron orbits by the shrinkage of the diffused $1g_{9/2}$ orbit and the mixing of the sharp $0i_{11/2}$ orbit. Simultaneously, the core nucleus swells, leading to the sudden enhancement of the charge radius at $N>126$. This characteristic behavior appears in the density profile near the nuclear surface and its measurement is highly desirable.

Lifetimes of a few negative parity levels and multipole mixing ratios ($\delta$) for a few dipole transitions in ${}^{49}\mathrm{V}$, populated through the ${}^{48}\mathrm{Ti}({}^4\mathrm{He},2np){}^{49}\mathrm{V}$ reaction with a 48 MeV ${}^4\mathrm{He}$ beam, were measured. The Indian National Gamma Array (INGA) facility was used to detect $\gamma$ rays at three different angles. Large basis shell model calculations were performed to understand the microscopic origin of these levels and to interpret the observations. $K$ mixing between different $K$ bands in ${}^{49}\mathrm{V}$ were established from one-nucleon-transfer spectroscopic factor calculations and total Routhian surface (TRS) calculations.

The fusion reactions induced by ${}^4\mathrm{He}$ projectiles on heavy target nuclei provide the reference to study the reaction dynamics of exotic halo nuclei. The present analysis aims to probe the effects of different nuclear density distributions and the effective nucleon-nucleon ($NN$) interaction potentials on the fusion cross section of ${}^4\mathrm{He}$-induced reactions for heavy target nuclei. The nuclear densities for the heavy nuclei are obtained within the well-known Skyrme-Hartree-Fock model and the relativistic mean-field (RMF) approach for the $\mathrm{NL}{3}^{*}$ parameter set. These densities are integrated with the density-dependent M3Y and the relativistic R3Y nucleon-nucleon ($NN$) potentials to obtain the nuclear interaction potential. The fusion cross section and the astrophysical $S$ factor are obtained for ${}^4\mathrm{He}+{}^{208}\mathrm{Pb}, {}^4\mathrm{He}+{}^{209}\mathrm{Bi}, {}^4\mathrm{He}+{}^{235}\mathrm{U}$, and ${}^4\mathrm{He}+{}^{238}\mathrm{U}$ systems within the $\ell$-summed Wong model. The relativistic R3Y $NN$ potential folded with RMF densities are observed to give a better fit to the available experimental data. Furthermore, a comparison is made for the results obtained using Hill-Wheeler and Wentzel-Kramers-Brillouin transmission coefficients for ${}^4\mathrm{He}+{}^{208}\mathrm{Pb}$ system. We found a reasonable fit in the cross section at around the Coulomb-barrier energies for both the approximations and also similar predictions can be drawn for all considered systems.

Yanez et al. [Phys. Rev. Lett. 112, 152702 (2014)] measured unusually high neutron decay width for the hot fusion reaction ${}^{25,26}\mathrm{Mg}+{}^{248}\mathrm{Cm}$ compared to the theoretical estimations available till that date. Various theoretical models have been developed since then to upgrade our understanding of the phenomenon but good agreement is not yet achieved. We have made an attempt for the same, which is based on a modified back-shifted Fermi gas model that also includes the shell and pairing energy correction. Though it works well for the neutron decay, it needs a dissipative effect also to evaluate the fission decay width correctly. It predicts the neutron to total decay width ratio 0.82–0.89 for dissipation coefficients 15–22 and thus closed to the measured value $0.89\pm 0.13$.

A hybrid model that employs the hadron-string transport model UrQMD and the $(3+1)$-dimensional relativistic viscous hydrodynamic code vHLLE, is used to investigate the beam energy dependence of the correlation coefficient $\rho (v_2^2,\left[p_T\right])$ between the average transverse momentum $\left[p_T\right]$ of hadrons emitted in an event and the square of the anisotropic flow coefficient $v_2^2$. For $\mathrm{Au}+\mathrm{Au}$ collisions, the model predicts characteristic patterns for the energy and event-shape dependence of the variances for $\left[p_T\right]$ and $v_n^2$ [$\mathrm{Var}(\left[p_T\right]$ and $\mathrm{Var}\left(v_2^2\right)$], and the covariance of $v_n^2$ and $\left[p_T\right] \left[\mathrm{cov}(v_2^2,\left[p_T\right])\right]$, consistent with the attenuation effects of the specific shear viscosity $\eta /s$. In contrast, $\rho (v_2^2,\left[p_T\right])$ is predicted to be insensitive to the beam energy but sensitive to the initial-state geometry of the collisions. These observations suggest that a precise set of measurements for $\mathrm{Var}\left(\left[p_T\right]\right), \mathrm{Var}\left(v_2^2\right), \mathrm{cov}(v_2^2,\left[p_T\right])$ and $\rho (v_2^2,\left[p_T\right])$ as a function of beam energy and event shape, could serve to constrain better the eccentricities and their fluctuations over the entire span of beam energies, and consequently aid precision extraction of the temperature and baryon chemical-potential dependence of $\eta /s$ from the wealth of $\mathrm{Au}+\mathrm{Au}$ data obtained in the RHIC beam energy scan.

The quantum mechanical fragmentation theory–based three cluster model is employed to investigate the ground-state ternary fission of two Fm isotopes nuclei having atomic mass $A_P=242$ and 258. The mass asymmetry coordinate and the relative separation among the decaying fragments play a crucial role for the estimation of the fragmentation structure and related barrier penetration process. First, the choice of third fragment ($A_3$) is fixed by minimizing the probable $A_3$ fragments having different proton neutron configurations. Further, the fission fragment combinations ($A_1+A_2+A_3$) are identified for the fixed third fragments by selecting the channel of lower ternary fragmentation potential and higher relative fission yield. Two type of tripartition of radioactive nuclei are considered such as equatorial cluster tripartition (ECT) and collinear cluster tripartition (CCT). A comparative analysis of ternary fragmentation potential and relative fission yield within ECT and CCT geometrical arrangement is carried out for different choices of third fragment, i.e., $A_3=1$ to $A_P$/3. The choice of most probable fragments suggest that the proton and neutron magic shell closures play essential role in the ternary mass division. Finally, a relative analysis of binary and ternary fragmentation is worked out for better insight of dynamics involved.

We present the $\text{TDDFT}+\text{Langevin}$ model that incorporates microscopic time-dependent density function theory (TDDFT) with macroscopic Langevin model. By extracting the energy-dependent dissipation effect from the TDDFT dynamics, quantum effects are introduced to the Langevin-type stochastic fission analysis. In this paper, by means of Skyrme nuclear effective interactions, the energy-dependent friction coefficients to be used in Langevin calculations are provided individually for 25 fission nuclei chosen from uranium, plutonium, curium, californium, and fermium isotopes. The validity of the energy-dependent friction coefficients are confirmed by comparing to the existing experimental fission fragment yields. In conclusion, depending on the energy, the transition of energy dissipation mechanism from conventional viscous energy dissipation to inertial energy dissipation is shown.

In the framework of the modified statistical model there have been simulated fission process of the excited compound nuclei ${}^{210}\mathrm{Rn}$ and ${}^{215}\mathrm{Fr}$ produced in ${}^{16}\mathrm{O}+{}^{194}\mathrm{Pt}$ and ${}^{19}\mathrm{F}+{}^{196}\mathrm{Pt}$ reactions and calculated the evaporation residue cross section, the fission cross section, the fission probability, the average prescission neutron multiplicity, the mean fission time, and the anisotropy of fission fragments angular distribution as a function of excitation energy. The classical collective motion of the excited compound nuclei about the ground state, the temperature dependence of the location, the height of fission transition points, and the projection of the total spin of the compound nucleus onto the symmetry axis $K$ have been considered in the statistical calculations. A constant nuclear dissipation was applied in the statistical calculations. In the statistical calculations, the temperature coefficient of the effective potential $k$ and the scaling factor of the fission-barrier height $r_s$ were considered as a free parameter and their magnitudes inferred by fitting measured data on the evaporation residue cross section and the fission cross section for the excited compound nuclei ${}^{210}\mathrm{Rn}$ and ${}^{215}\mathrm{Fr}$. It was shown that the results of calculations are in good agreement with the experimental data by using appropriate values for these parameters equal to $k=0.0160\pm 0.0050\mathrm{Me}{\mathrm{V}}^{-2}$ and $r_s=1.0030\pm 0.0020$ for ${}^{210}\mathrm{Rn}$ and $k=0.0065\pm 0.0040\mathrm{Me}{\mathrm{V}}^{-2}$ and $r_s=1.0040\pm 0.0015$ for ${}^{215}\mathrm{Fr}$. Furthermore, by using appropriate values of parameters $k$ and $r_s$ have been calculated the average prescission neutron multiplicity, the fission probability, the mean fission time, and the anisotropy of fission fragments angular distribution for the nuclei ${}^{210}\mathrm{Rn}$ and ${}^{215}\mathrm{Fr}$. Comparison of the theoretical data with the experimental data were shown that the modified statistical model is well able to reproduce different experimental data. Although, at high excitation energies the results of calculations for the anisotropy of fission fragments angular distribution and fission probability are slightly lower than the experimental data.

A calculation of two-neutrino double-$\beta$ $\left(2\nu \beta \beta \right)$ decay matrix elements within the interacting boson model (IBM) that is based on the nuclear density functional theory is presented. The constrained self-consistent mean-field (SCMF) calculation using a universal energy density functional (EDF) and a pairing interaction provides potential energy surfaces with triaxial quadrupole degrees of freedom for even-even nuclei corresponding to the initial and final states of the $2\nu \beta \beta$ decays of interest. The SCMF energy surface is then mapped onto the bosonic one, and this procedure determines the IBM Hamiltonian for the even-even nuclei. The same SCMF calculation provides the essential ingredients of the interacting boson fermion-fermion model (IBFFM) for the intermediate odd-odd nuclei and the Gamow-Teller and Fermi transition operators. The EDF-based IBM and IBFFM provide a simultaneous description of excitation spectra and electromagnetic transition rates for each nucleus, and single-$\beta$ and $\beta \beta$ decay properties. The calculated $2\nu \beta \beta$-decay nuclear matrix elements are compared with experiment and with those from earlier theoretical calculations.

Time-dependent density-functional theory is mathematically formulated through nonlinear coupled time-dependent three-dimensional partial differential equations, and it is natural to expect a strong sensitivity of its solutions to variations of the initial conditions, akin to the butterfly effect ubiquitous in classical dynamics. Since the Schrödinger equation for an interacting many-body system is, however, linear and mathematically the exact equations of the density-functional theory reproduce the corresponding one-body properties, it would follow that the Lyapunov exponents are also vanishing within a density-functional theory framework. Whether for realistic implementations of the time-dependent density-functional theory the question of the absence of the butterfly effect and whether the dynamics provided is indeed a predictable theory was never discussed. At the same time, since the time-dependent density-functional theory is a unique tool allowing us to study the nonequilibrium dynamics of strongly interacting many-fermion systems, the question of predictability of this theoretical framework is of paramount importance. Our analysis, for a number of quantum superfluid many-body systems (unitary Fermi gas, nuclear fission, and heavy-ion collisions) with a classical equivalent number of degrees of freedom $O\left({10}^{10}\right)$ and larger, suggests that its maximum Lyapunov exponents are negligible for all practical purposes.

Coherent photoproduction of the neutral-pion and $\eta$-meson on the deuteron, $\gamma d\to {\pi }^0\eta d$, was experimentally studied at incident photon energies ranging from the reaction threshold to 1.15 GeV. The total cross section demonstrates a rapid rise below 1 GeV. The data are underestimated by the existing theoretical calculations based on quasifree ${\pi }^0\eta$ photoproduction on the nucleon followed by deuteron coalescence. At the same time, the data are rather well reproduced by the calculations taking into account the final-state interaction. We also measured for the first time the differential cross sections: the ${\pi }^0\eta$ invariant-mass distribution $d\sigma /d{M}_{\pi \eta }$, the ${\pi }^{0}d$ invariant-mass distribution $d\sigma /d{M}_{\pi d}$, the $\eta d$ invariant-mass distribution $d\sigma /d{M}_{\eta d}$, and the distribution over the deuteron emission angle $d\sigma /d{\mathrm{\Omega }}_d$ in the overall center-of-mass frame. The measured cross section $d\sigma /d{\mathrm{\Omega }}_d$ does not exhibit strongly backward-peaking behavior predicted by the calculations. At all incident energies, an increase in $d\sigma /d{M}_{\eta d}$ near the $\eta d$ threshold is observed, which indicates a bound or virtual $\eta d$ state resulting from a strong attraction between $\eta$ and a deuteron. The possibilities of using coherent ${\pi }^0\eta$ photoproduction on a nucleus to study the $\eta$-nuclear interaction are also discussed.

The $\gamma$-ray emissions from a radiopure cerium-bromide crystal with a mass of 4381 g were measured for a total of 497.4 d by means of high-resolution $\gamma$-ray spectrometry in the HADES underground laboratory at a depth of 500 m.w.e. A search for $0/2\nu \epsilon \epsilon$ and $0/2\nu \epsilon {\beta }^{+}$ double beta decay transitions of ${}^{136}\mathrm{Ce}$ and ${}^{138}\mathrm{Ce}$ was performed using Bayesian analysis techniques. No signals were observed for a total of 35 investigated decay modes. 90% credibility limits were set in the order of ${10}^{18}$–${10}^{19}$ yr. Existing constraints from a cerium oxide powder measurement were tested with a different cerium compound and half-life limits could be improved for most of the decay modes. The most likely accessible decay mode of the ${}^{136}\mathrm{Ce}$ $2\nu \epsilon \epsilon$ transition into the $0_1^{+}$ state of ${}^{136}\mathrm{Ba}$ results in a new best 90% credibility limit of $5.0\times {10}^{18}$ yr.

The phase transition of hadronic matter to deconfined quark matter in the interior of the neutron star is studied. A relativistic quark model is used to describe the hadronic matter whereas the MIT bag model is used to represent the quark matter. The coexistence of hadron-quark mixed phase in equilibrium is also investigated. The equation of state with nucleon $+$ quark (NP-hybrid) and nucleon $+$ hyperon $+$ quark (NP $+$ hyp-hybrid) matter is developed and stellar properties, such as the maximum mass, radii, tidal deformability, and gravitational redshift are determined. The behavior of the speed of sound and the adiabatic index in the hybrid matter are also studied. It is found that within the conformal limits of the speed of sound, stars below the $2\text{−}{M}_{\odot }$ limit lack a sizable quark core but exhibit mixed phase of hadrons and quarks.

The $\gamma$-decay properties of an excited state in ${}^{26}\mathrm{Al}$ at 6398.3(8) keV have been reexamined using the ${}^{11}\mathrm{B}+{}^{16}\mathrm{O}$ fusion-evaporation reaction. This level represents a key 93.1(8)-keV resonance in the ${}^{25}\mathrm{Mg}+p$ system and its relative branching to the ${}^{26}\mathrm{Al}$ ground state, $f_0$, has been determined to be $0.76\pm 0.03$ (stat.) $\pm 0.10$ (syst.). This is a significantly higher value than the most recent evaluation and implies a considerable increase in the production of cosmic $\gamma$ rays from ${}^{26}\mathrm{Al}$ radioactivity.

Materials selection for rare event physics requires high performance detectors and customized analyses. In this context a novel $\beta \text{−}\gamma$ detection system, composed of a liquid scintillator in coincidence with a high-purity germanium (HPGe) detector, was developed with the main purpose of studying ultratrace contamination of uranium, thorium, and potassium in liquid samples. In the search for ${}^{238}\mathrm{U}$ contaminations through neutron activation analysis, since the activation product ${}^{239}\mathrm{Np}$ decays to a relatively long-lived isomeric state of ${}^{239}\mathrm{Pu}$, it is possible to perform a time selection of these events, obtaining a strong background suppression. Investigating the time distribution of the coincidences between the ${\beta }^{-}$ decay of ${}^{239}\mathrm{Np}$ and the delayed events following the deexcitation of the ${}^{239}\mathrm{Pu}$ isomeric level at 391.6 keV, a precision measurement of the half-life of this level was conducted. The resulting half-life of the 391.6 keV ${}^{239}\mathrm{Pu}$ level is $190.2\pm 0.2$ ns, thus increasing the precision by about a factor of 20 over previous measurements.

The ground-state shape of the ${}^{80}\mathrm{Ge}$ nucleus and its evolution for the lowest collective excited states have been investigated in the framework of the Bohr model in order to clarify if the shape coexistence phenomenon is present. The obtained results, which are largely in agreement with the most recent experimental data, indicate a prolate shape for the ground state, respectively a sudden switch to a more deformed prolate one for certain excited states. Also, the first-excited $0_2^{+}$ state is found to be very high in energy, namely, at 2208 keV, being close to recent predictions made with shell-model calculations. Additionally, using the parameters fit for the few available experimental data for the ground band, the structure of the $\beta$ and $\gamma$ bands has been built to support future experiments.

We employ a realistic nuclear mean-field theory using the phenomenological, Woods-Saxon Hamiltonian with newly adjusted parameters containing no parametric correlations; originally present correlations are removed employing the Monte Carlo approach. We find very large neutron shell gaps at $N=136$ for all the four octupole deformations ${\alpha }_{3\mu =0,1,2,3}$. These shell gaps generate well-pronounced double potential-energy minima in the standard multipole $({\alpha }_{20},{\alpha }_{22},{\alpha }_{3\mu },{\alpha }_{40})$ representation, often at ${\alpha }_{20}=0$, which in turn generate exotic symmetries $C_{2v}$, $D_{2d}$, $T_d$, and $D_{3h}$, discussed in detail. The main goal of the article is to formulate spectroscopic criteria for experimental identification. Calculations employing macroscopic-microscopic method are performed for nuclei with $Z\ge 82$ and $N\ge 126$ in multidimensional deformation spaces to analyze the expected exotic symmetries and octupole shape instabilities in the mass table “northeast” of the doubly magic ${}^{208}\mathrm{Pb}$ nucleus. Whereas the proton-unperturbed properties of neutron-generated octupole shell effects are illustrated in detail for exotic ${}_{Z=82}{\mathrm{Pb}}_{N>126}$ nuclei, our discussion is extended into even-even $Z>82$ nuclei approaching the less exotic $Z/N$ ratios, to encourage experiments which could identify the predicted exotic symmetries. In addition to the tetrahedral point group symmetry, $T_d$, of which experimental evidence has recently been published, we present $D_{2d}$ symmetry resulting from a superposition of axially symmetric quadrupole and tetrahedral symmetries and two new point group symmetries, $D_{3h}$ and $C_{2v}$, associated with the octupole ${\alpha }_{33}$ and ${\alpha }_{31}$ energy minima, respectively. The multidimensional $n>2$ deformation spaces are treated as usual by projecting the total potential energies onto the $n=2$ subspace. Using the representation theory of point groups we formulate quantum mechanical criteria for experimental identification of exotic symmetries through analysis of the specific properties of the collective rotational bands generated by the symmetries. The resulting band structures happen to be markedly distinct from the structure of the bands generated by ellipsoidal symmetry quantum rotors; those various rotational properties are discussed in detail.

In light and medium-mass nuclei, two-body weak currents from chiral effective field theory account for a significant portion of the phenomenological quenching of Gamow-Teller transition matrix elements. Here we examine the systematic effects of two-body axial currents on Gamow-Teller strength and $\beta$-decay rates in heavy nuclei within energy-density functional theory. Using a Skyrme functional and the charge-changing finite amplitude method, we add the contributions of two-body currents to the usual one-body linear response in the Gamow-Teller channel, both exactly and though a density-matrix expansion. The two-body currents, as expected, usually quench both summed Gamow-Teller strength and decay rates, but by an amount that decreases as the neutron excess grows. In addition, they can enhance individual low-lying transitions, leading to decay rates that are quite different from those that an energy-independent quenching would produce, particularly in neutron-rich nuclei. We show that both these unexpected effects are related to changes in the total nucleon density as the number of neutrons increases.