The process of electron-positron annihilation into $\eta \left({\eta }^{\prime }\right)2\pi$ is described within the extended Nambu–Jona-Lasinio model in the energy range up to about 2 GeV. Contributions of intermediate vector mesons $\rho \left(770\right)$ and $\rho \left(1450\right)$ are taken into account. Results for the $\eta 2\pi$ channel are found to be in a reasonable agreement with experimental data. Predictions for production of ${\eta }^{\prime }2\pi$ are given. The corresponding estimations for decays $\tau \to \eta \left({\eta }^{\prime }\right)2\pi \nu$ are given in the Appendix.

Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the shell model language or equivalently to nuclear shapes with different deformation.

Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it.

Method: We study in detail a long chain of mercury isotopes, ${}^{172--200}$Hg, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least-squares fit to the known energies and absolute $B\left(E2\right)$ transition rates of states up to 3 MeV.

Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, $B\left(E2\right)$'s, quadrupole shape invariants, wave functions, isotopic shifts, and mean-field energy surfaces.

Conclusions: We obtain a fairly good agreement with the experimental data for all the studied observables and we conclude that the Hamiltonian and the states we obtain constitute a good approximation to the Hg isotopes.

The ${}^{58}$Ni($n,\gamma$) cross section has been measured at the neutron time of flight facility n_TOF at CERN, in the energy range from 27 meV up to 400 keV. In total, 51 resonances have been analyzed up to 122 keV. Maxwellian averaged cross sections (MACS) have been calculated for stellar temperatures of $kT=5–100$ keV with uncertainties of less than 6%, showing fair agreement with recent experimental and evaluated data up to $kT$ = 50 keV. The MACS extracted in the present work at 30 keV is $34.2\pm 0.6_{\mathrm{stat}}\pm 1.8_{\mathrm{sys}}$ mb, in agreement with latest results and evaluations, but 12% lower relative to the recent KADoNIS compilation of astrophysical cross sections. When included in models of the $s$-process nucleosynthesis in massive stars, this change results in a 60% increase of the abundance of ${}^{58}$Ni, with a negligible propagation on heavier isotopes. The reason is that, using both the old or the new MACS, ${}^{58}$Ni is efficiently depleted by neutron captures.

Total radiative thermal neutron-capture $\gamma$-ray cross sections for the ${}^{182,183,184,186}$W isotopes were measured using guided neutron beams from the Budapest Research Reactor to induce prompt and delayed $\gamma$ rays from natural and isotopically-enriched tungsten targets. These cross sections were determined from the sum of measured $\gamma$-ray cross sections feeding the ground state from low-lying levels below a cutoff energy, $E_{\mathrm{crit}}$, where the level scheme is completely known, and continuum $\gamma$ rays from levels above $E_{\mathrm{crit}}$, calculated using the Monte Carlo statistical-decay code dicebox. The new cross sections determined in this work for the tungsten nuclides are ${\sigma }_0{(}^{182}\mathrm{W})=20.5\left(14\right)$ b and ${\sigma }_{11/2^{+}}{(}^{183}{\mathrm{W}}^m,5.2\mathrm{s})=0.177\left(18\right)$ b; ${\sigma }_0{(}^{183}\mathrm{W})=9.37\left(38\right)$ b and ${\sigma }_{5^{-}}{(}^{184}{\mathrm{W}}^m,8.33\mu \mathrm{s})=0.0247\left(55\right)$ b; ${\sigma }_0{(}^{184}\mathrm{W})=1.43\left(10\right)$ b and ${\sigma }_{11/2^{+}}{(}^{185}{\mathrm{W}}^m,1.67\min )=0.0062\left(16\right)$ b; and, ${\sigma }_0{(}^{186}\mathrm{W})=33.33\left(62\right)$ b and ${\sigma }_{9/2^{+}}{(}^{187}{\mathrm{W}}^m,1.38\mu \mathrm{s})=0.400\left(16\right)$ b. These results are consistent with earlier measurements in the literature. The ${}^{186}$W cross section was also independently confirmed from an activation measurement, following the decay of ${}^{187}$W, yielding values for ${\sigma }_0{(}^{186}\mathrm{W})$ that are consistent with our prompt $\gamma$-ray measurement. The cross-section measurements were found to be insensitive to choice of level density or photon strength model and only weakly dependent on $E_{\mathrm{crit}}$. Total radiative-capture widths calculated with dicebox showed much greater model dependence; however, the recommended values could be reproduced with selected model choices. The decay schemes for all tungsten isotopes were improved in these analyses. We were also able to determine new neutron-separation energies from our primary $\gamma$-ray measurements for the respective ($n,\gamma$) compounds: ${}^{183}$W [$S_n=6190.88\left(6\right)$ keV]; ${}^{184}$W [$S_n=7411.11\left(13\right)$ keV]; ${}^{185}$W [$S_n=5753.74\left(5\right)$ keV]; and, ${}^{187}$W [$S_n=5466.62\left(7\right)$ keV].

Charge-current quasielastic (anti)neutrino scattering cross sections on a ${}^{12}$C target are analyzed using a spectral function $S(p,\mathcal{E})$ that gives a scaling function in accordance with the ($e,e^{\prime }$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations, it has a realistic energy dependence, and natural orbitals (NOs) from the Jastrow correlation method are used in its construction. In all calculations the standard value of the axial mass $M_A=1.032$ GeV/$c$${}^2$ is used. The results are compared with those when NN correlations are not included, as in the relativistic Fermi gas model, or when harmonic-oscillator single-particle wave functions are used instead of NOs. The role of the final-state interactions (FSIs) on the theoretical spectral and scaling functions, as well as on the cross sections, is accounted for. A comparison of the results for the cases with and without FSI, as well as to results from the phenomenological scaling function obtained from the superscaling analysis, is carried out. Our calculations based on the impulse approximation underpredict the MiniBooNE data but agree with the data from the NOMAD experiment. The possible missing ingredients in the considered theoretical models are discussed.

We investigate the possibilities of observing the decay mode for ${}^{124}$Xe in which two electrons are captured, two neutrinos are emitted, and the final daughter nucleus is in its ground state, using dark matter experiments with liquid xenon. The first upper limit of the decay half-life is calculated to be 1.66 $\times$ 10${}^{21}$ years at a 90% confidence level (C.L.) obtained with the published background data from the XENON100 experiment. Employing a known background model from the large underground xenon (LUX) experiment, we predict that the detection of double-electron capture of ${}^{124}$Xe to the ground state of ${}^{124}$Te with LUX will have approximately 115 events, assuming a half-life of 2.9 $\times$ 10${}^{21}$ years. We conclude that measuring ${}^{124}$Xe 2$\nu$ double-electron capture to the ground state of ${}^{124}$Te can be performed more precisely with the proposed LUX-Zeplin (LZ) experiment.

We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. In the model we assume fusion in a potential that is screened by an effective electron cloud around colliding nuclei (extended Salpeter ion-sphere model). We calculate the mean-field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical $S$ factors, and enhancement factors of reaction rates. As a byproduct, we study the analytic behavior of the screening potential at small separations between the reactants. In this model, astrophysical $S$ factors depend not only on nuclear physics but on plasma screening as well. The enhancement factors are in good agreement with calculations by other methods. This allows us to formulate a combined, pure analytic model of strong plasma screening in thermonuclear reactions. The results can be useful for simulating nuclear burning in white dwarfs and neutron stars.

The heavy-ion radiative capture ${}^{12}\mathrm{C}$$({}^{16}\mathrm{O}$$,\gamma {}^{28}\mathrm{Si})$ was measured at the sub-Coulomb barrier bombarding energy $E_{\mathrm{lab}}=15.7$ MeV, which corresponds to the lowest important resonance observed in the ${}^{12}\mathrm{C}+$ ${}^{16}\mathrm{O}$ fusion excitation function. Thanks to combination of the bismuth germanate (BGO) $\gamma$-ray array and the $0^{\circ }$ DRAGON electromagnetic spectrometer at TRIUMF, the $\gamma$-decay spectrum from the entrance channel down to the ground state of ${}^{28}$Si was measured. Comparisons of the experimental spectrum to $\gamma$ spectrum extracted from Monte Carlo simulations of the complete setup suggest a $J^{\pi }=2^{+}$ spin-parity assignment to the entrance channel and yield the radiative capture cross section ${\sigma }_{RC}=0.22\pm 0.04\mu$b. Combining this present spin assignment with previous data on radiative capture, a $J(J+1)$ systematics was constructed, and it indicated a moment of inertia commensurate with the ${}^{12}\mathrm{C}+$${}^{16}\mathrm{O}$ grazing angular momentum. Strong dipole transitions are observed from the entrance channel to $T=1$ states around 11.5 MeV and are found to result from enhanced $M{1}_{IV}$ transitions to states exhausting a large part of the $M1$ sum rule built on the ground state of ${}^{28}$Si. This specific decay was also reported at bombarding energies close to the Coulomb barrier in our previous study of the ${}^{12}\mathrm{C}$$({}^{12}\mathrm{C}$$,{\gamma }^{24}$Mg) heavy-ion radiative capture reaction. Similarities between both systems are investigated.

We carry out a combined analysis of elliptic and triangular flow data using viscous relativistic hydrodynamics. We show that these data allow us to put tight constraints on models of the early dynamics of a nucleus-nucleus collision. Specifically, the rms values of the initial ellipticity ${\varepsilon }_2$ and the initial triangularity ${\varepsilon }_3$ are constrained to lie within a narrow band for each centrality. We use these constraints as a filter for existing Monte Carlo models of initial state, and provide a simple test that can be performed on any candidate model to determine its compatibility with data.

Nuclear structure (energy levels, elastic and inelastic electron-nucleus scattering, and transition probability) of ${}^{23}\mathrm{Na}$, ${}^{25}\mathrm{Mg}$, ${}^{27}\mathrm{Al}$, and ${}^{41}\mathrm{Ca}$ nuclei have been studied using shell-model calculations. A set of two-body interactions are used in this paper. The universal $sd$ of the Wildenthal interaction in the proton-neutron formalism, universal $sd$-shell interaction A, universal $sd$-shell interaction B, and GXFP1 interaction for the $fp$ shell is used with the nucleon-nucleon realistic interaction Michigan three-range Yakawa as a two-body interaction for core-polarization calculations. Two shell-model codes, cpm3y and nushell for Windows, have been used to calculate the results. The wave functions of radial single-particle matrix elements have been calculated with harmonic-oscillator and Woods-Saxon potentials. The level schemes are compared with the experimental data up to 5.776, 5.251, and 4.51 MeV for ${}^{23}\mathrm{Na}$, ${}^{25}\mathrm{Mg}$, and ${}^{27}\mathrm{Mg}$, respectively. Very good agreements are obtained for all nuclei in this study. Results from electron scattering form-factor calculations have shown that the core-polarization effects are essential to obtain a reasonable description of the data with no adjustable parameters.

By using the activation technique, the cross section for the reaction Ho($n$,2$n$) Ho was measured at two neutron energies of 13.5 and 14.8 MeV to resolve inconsistencies in the existing database. The 94- and 91.39-keV γ rays from the decay of the Ho${}^m$ isomeric state and Ho${}^g$ ground state, respectively, were recorded with a high-resolution high-purity germanium detector. The monoenergetic neutron beam was produced via the H($d$,$n$) He reaction. The cross sections also were estimated with the talys-1.4 nuclear model code that uses different level-density options at neutron energies that vary from the reaction threshold to 20 MeV. Results are also discussed and are compared with some corresponding values found in the literature.

We calculate the second-order viscous correction to the kinetic distribution, $\delta f_{\left(2\right)}$, and use this result in a hydrodynamic simulation of heavy-ion collisions to determine the complete second-order correction to the harmonic spectrum, $v_n$. At leading order in a conformal fluid, the first viscous correction is determined by one scalar function, ${\chi }_{0p}$. One moment of this scalar function is constrained by the shear viscosity. At second order in a conformal fluid, we find that $\delta f\left(\mathit{p}\right)$ can be characterized by two scalar functions of momentum, ${\chi }_{1p}$ and ${\chi }_{2p}$. The momentum dependence of these functions is largely determined by the kinematics of the streaming operator. Again, one moment of these functions is constrained by the parameters of second-order hydrodynamics, ${\tau }_{\pi }$ and ${\lambda }_1$. The effect of $\delta f_{\left(2\right)}$ on the integrated flow is small (up to $v_4$) but is quite important for the higher harmonics at modestly large $p_T$. Generally, $\delta f_{\left(2\right)}$ increases the value of $v_n$ at a given $p_T$ and is most important in small systems.

The simplicity in the nuclear quadrupole moments reported recently in ${}^{107-129}$Cd, i.e., a linear increase of the ${11/2}^{-}$ quadrupole moments, is investigated microscopically with the covariant density functional theory. Using the newly developed functional PC-PK1, the quadrupole moments as well as their linear increase tendency with the neutron number are excellently reproduced without any ad hoc parameters. The core polarization is found to be very important and contributes almost half of the quadrupole moments. The simplicity of the linear increase is revealed to be due to the pairing correlation which smears out the abrupt changes induced by the single-particle shell structure.

We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka et al. [Phys. Rev. Lett. 104, 012501 (2010)]. It is demonstrated that our proposed model can consistently describe a large amount of spectroscopic data as well as binding energies in the $pf$ and $p{f}_{5/2}{g}_{9/2}$ shell spaces and could serve as a practical shell model for even heavier mass regions.

The standard procedure of extracting the proton root-mean-square radii from models for the Sachs form factors $G_e\left(q\right)$ and $G_m\left(q\right)$ fitted to elastic electron-proton scattering data is more uncertain than traditionally assumed. The extrapolation of $G\left(q\right)$, from the region $q_{\min }<q<q_{\max }$ covered by data to momentum transfer $q=0$ where the rms radius is obtained, often depends on uncontrolled properties of the parametrization used. Only when ensuring that the corresponding densities have a physical behavior at large radii $r$ can reliable rms radii be determined.

The $\gamma$-ray strength function in the quasicontinuum has been measured for ${}^{231–233}$Th, ${}^{232,233}$Pa, and ${}^{237–239}$U using the Oslo method. All eight nuclei show a pronounced increase in $\gamma$ strength at ${\omega }_{\mathrm{SR}}\approx 2.4$ MeV, which is interpreted as the low-energy $M1$ scissors resonance (SR). The total strength is found to be $B_{\mathrm{SR}}=9–11{\mu }_N^2$ when integrated over the 1–4 MeV $\gamma$-energy region. The SR displays a double-hump structure that is theoretically not understood. Our results are compared with data from ($\gamma$, ${\gamma }^{\prime }$) experiments and theoretical sum-rule estimates for a nuclear rigid-body moment of inertia.

We have measured the $K$-shell internal conversion coefficient, ${\alpha }_K$, for the 65.7-keV $M$4 transition in ${}^{119}$Sn to be 1621(25). This result agrees well with Dirac-Fock calculations in which the effect of the $K$-shell atomic vacancy is accounted for and disagrees with calculations in which the vacancy is ignored. This extends our precision tests of theory to $Z$ = 50, the lowest $Z$ yet measured.

A semiclassical model based on quantum time concepts is presented for the evaluation of bremsstrahlung emission probabilities in $\alpha$ decay of nuclei. The contribution to the bremsstrahlung emission from the different regions in tunneling is investigated using realistic double-folded nuclear and Coulomb potentials. Within this model, the contribution from the radiation emitted in front of the barrier before tunneling is much larger than that while leaving the barrier. A comparison with the data on ${}^{210}$Po shows that the results are sensitive to the nuclear potential, and the rectangular well used in many of the quantum mechanical approaches can even give qualitatively different results.

Quantum mechanical fragmentation theory (QMFT) is used to look for all possible target-projectile (t,p) combinations forming the “cold” compound nucleus (CN) ${}^{274}$Hs${}^{*}$ at the CN excitation energy $E^{*}$ of “hot, compact” configuration. The predicted reactions, referring to potential energy minima, include all the three reactions ${}^{248}$Cm + ${}^{26}$Mg, ${}^{238}$U + ${}^{36}$S, and ${}^{226}$Ra + ${}^{48}$Ca already used in experiments, and a few more. The optimum “cold” and “compact” (t,p) combination, corresponding to lowest interaction barrier and smallest interaction radius, is one with largest mass asymmetry, but because of the doubly magic ${}^{48}$Ca nucleus, the evaporation residue cross sections for the ${}^{226}$Ra + ${}^{48}$Ca reaction are shown to be further enhanced. For the decay of CN ${}^{274}$Hs${}^{*}$, synthesizing ${}^{269–271}$Hs via 3$n$–5$n$ emission, we use the dynamical cluster-decay model (DCM) with effects of quadrupole deformations and “hot” compact orientations included in it, which support symmetric fission, in agreement with experiments. The fusion evaporation residue cross sections ${\sigma }_{xn}$, for $x=3$, 4, and 5 neutrons emission from the above-mentioned three entrance channels, are calculated within one parameter fitting, namely, the neck length. For best fitted neck-length parameter, the roles of entrance channel and that of magic shells are analyzed. In spite of different entrance channels resulting in different evaporation residue cross sections, the neck-length parameter at a given $E^{*}$ is shown to be independent of the entrance channel. The role of magic shells is shown in enhancing evaporation residue cross sections, not only for the entrance channel ${}^{226}$Ra + ${}^{48}$Ca, but also for the residue ${}^{270}$Hs, compared to its neighboring isotopes ${}^{269,271}$Hs. The fusion evaporation residue cross sections for the proposed new reactions, in synthesizing CN ${}^{274}$Hs${}^{*}$, are also estimated for future new experiments.

The Feynman-Metropolis-Teller treatment of compressed atoms has been recently generalized to relativistic regimes and applied to the description of static and rotating white dwarfs in general relativity. We present here the extension of this treatment to the case of finite temperatures and construct the corresponding equation of state (EOS) of the system; applicable in a wide regime of densities that includes both white dwarfs and neutron star outer crusts. We construct the mass-radius relation of white dwarfs at finite temperatures obeying this new EOS and apply it to the analysis of ultra-low-mass white dwarfs with $M\lesssim 0.2M_{\odot }$. In particular, we analyze the case of the white dwarf companion of PSR J1738 + 0333. The formulation is then extrapolated to compressed nuclear matter cores of stellar dimensions, systems with mass numbers $A\approx {(m_{\mathrm{Planck}}/m_n)}^3$ or mass $M_{\mathrm{core}}\approx M_{\odot }$, where $m_{\mathrm{Planck}}$ and $m_n$ are the Planck and the nucleon mass. For $T\ll m_e{c}^2/k_B\approx 5.9\times {10}^9$ K, a family of equilibrium configurations can be obtained with analytic solutions of the ultrarelativistic Thomas-Fermi equation at finite temperatures. Such configurations fulfill global but not local charge neutrality and have strong electric fields on the core surface. We find that the maximum electric field at the core surface is enhanced at finite temperatures with respect to the degenerate case.