The influence of atomic and conductivity electrons in the metal matrices on the $\alpha$-decay rate is analyzed. The Coulomb interaction of inner atomic electrons and free electrons with the nuclei is treated in the adiabatic approximation and as a shake-off process, respectively. The role of conductivity electrons is analyzed in the framework of strict collision theory. Simple formulas are derived for the exponential tunneling probability $P$ in the approximation of a short tunneling path compared to characteristic electronic dimensions. It is shown that the pre-exponential factor in the decay rate depends on the energy absorbed by electrons during decay, whereas $P$ is independent of it. The half-life of the nucleus surrounded by electrons is a bit larger $(\sim 1\%)$ than that of the bare nucleus.

The time evolution of the medium created in heavy ion collisions can be described by hydrodynamical models. After expansion and cooling, the hadrons are created in a freeze-out. Their distribution describes the final state of this medium. In particular their azimuthal asymmetry, characterized by the elliptic flow coefficient $v_2$, is one of the most important observables in heavy ion physics. In recent years it has been revealed that, if measuring relative to higher order event planes ${\Psi }_n$, higher order flow coefficients $v_n$ for $n>2$ can be measured. This is due to initial state fluctuations, previously not described by analytic solutions of relativistic hydrodynamics. In this paper we show the first solutions that utilize higher order asymmetries and thus yield realistic $v_n$ flow coefficients. It is a clear consequence of this that different flow patterns may lead to the same observed flow coefficients. We also compare our results to PHENIX measurements and determine a possible parameter set corresponding to these data.

We analyze the transverse-momentum spectra of strange hadrons produced in Pb + Pb collisions at the collision energy $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for different centrality bins. Our approach combines the concept of chemical nonequilibrium with the single-freeze-out scenario. The two ideas are realized in the framework of the Cracow model, whose thermodynamic parameters have been established in earlier studies of the ratios of hadron multiplicities. The geometric parameters of the model are obtained from the fit to the spectra of pions and kaons, only. Using these parameters, we obtain an excellent description of the spectra of protons and the $K_S^0,K^{*}{\left(892\right)}^0$, and $\varphi \left(1020\right)$ mesons. A satisfactory description is obtained for the $\Lambda ,\Xi$, and $\Omega$ hyperons.

An experiment to measure single-spin asymmetries of semi-inclusive production of charged pions in deep-inelastic scattering on a transversely polarized ${}^3\mathrm{He}$ target was performed at Jefferson Laboratory in the kinematic region of $0.16<x<0.35$ and $1.4<Q^2<2.7$ ${\mathrm{GeV}}^2$. Pretzelosity asymmetries on ${}^3\mathrm{He}$, which are expressed as the convolution of the $h_{1T}^{\perp }$ transverse-momentum-dependent distribution functions and the Collins fragmentation functions in the leading order, were measured for the first time. Under the effective polarization approximation, we extracted the corresponding neutron asymmetries from the measured ${}^3\mathrm{He}$ asymmetries and cross-section ratios between the proton and ${}^3\mathrm{He}$. Our results show that both ${\pi }^{\pm }$ on ${}^3\mathrm{He}$ and on neutron pretzelosity asymmetries are consistent with zero within experimental uncertainties.

Background: The dense neutron-rich matter found in supernovae and inside neutron stars is expected to form complex nonuniform phases, often referred to as nuclear pasta. The pasta shapes depend on density, temperature and proton fraction and determine many transport properties in supernovae and neutron star crusts.

Purpose: To characterize the topology and compute two observables, the radial distribution function (RDF) $g\left(r\right)$ and the structure factor $S\left(q\right)$, for systems with proton fractions $Y_p=0.10,0.20,0.30$, and $0.40$ at about one-third of nuclear saturation density, $n=0.050{\mathrm{fm}}^{-3}$, and temperatures near $kT=1\mathrm{MeV}$.

Methods: We use two recently developed hybrid CPU/GPU codes to perform large scale molecular dynamics (MD) simulations with $51200$ and $409600$ nucleons. From the output of the MD simulations we obtain the two desired observables.

Results: We compute and discuss the differences in topology and observables for each simulation. We observe that the two lowest proton fraction systems simulated, $Y_p=0.10$ and $0.20$, equilibrate quickly and form liquidlike structures. Meanwhile, the two higher proton fraction systems, $Y_p=0.30$ and $0.40$, take a longer time to equilibrate and organize themselves in solidlike periodic structures. Furthermore, the $Y_p=0.40$ system is made up of slabs, lasagna phase, interconnected by defects while the $Y_p=0.30$ systems consist of a stack of perforated plates, the nuclear waffle phase.

Conclusions: The periodic configurations observed in our MD simulations for proton fractions $Y_p\ge 0.30$ have important consequences for the structure factors $S\left(q\right)$ of protons and neutrons, which relate to many transport properties of supernovae and neutron star crust. A detailed study of the waffle phase and how its structure depends on temperature, size of the simulation, and the screening length showed that finite-size effects appear to be under control and, also, that the plates in the waffle phase merge at temperatures slightly above $1.0\mathrm{MeV}$ and the holes in the plates form a hexagonal lattice at temperatures slightly lower than $1.0\mathrm{MeV}$.

Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for the quasiparticle random-phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probing collective excitations of weakly bound nuclei embedded in the continuum. The monopole excitation modes in magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated.

Excited states in the neutron-deficient nucleus ${}_{72}{}^{161}\mathrm{Hf}_{89}$ have been populated using the ${}^{118}\mathrm{Sn}\left({}^{48}\mathrm{Ti},5n\right){}^{161}\mathrm{Hf}$ and ${}^{110}\mathrm{Pd}\left({}^{56}\mathrm{Fe},5n\right){}^{161}\mathrm{Hf}$ fusion-evaporation reactions at 240 and 270 MeV, respectively. The level scheme for ${}^{161}\mathrm{Hf}$ has been extended with the observation of new band structures and an $I^{\pi }=(13/2^{+})$ isomeric state with a half-life of 4.8(2) $\mu \mathrm{s}$ has been identified. The decay path from this isomer to the $(7/2^{-})$ ground state is established. The yrast band, based on the $(13/2^{+})$ isomeric state, is extended up to $(73/2^{+})$ and side band structures are identified up to $(69/2^{-})$ and $(55/2^{-})$. Quasiparticle assignments for these rotational structures are made on the basis of their alignment properties and Woods-Saxon cranked shell-model calculations.

We investigate the structure of ${}^{18}\mathrm{F}$ with the microscopic wave function based on the three-body ${}^{16}\mathrm{O}+p+n$ model. In the calculation of the generator coordinate method of the three-body model, $T=0$ energy spectra of $J^{\pi }=1^{+},3^{+}$, and $5^{+}$ states and $T=1$ spectra of $J^{\pi }=0^{+},2^{+}$ states in ${}^{18}\mathrm{F}$ are described reasonably. Based on the dinucleon picture, the effect of the spin-orbit force on the $T=0$ and $T=1 pn$ pairs around the ${}^{16}\mathrm{O}$ core is discussed. The $T=1$ pair in the $J^{\pi }=0^{+}$ state gains the spin-orbit potential energy involving the odd-parity mixing in the pair. The spin-orbit potential energy gain with the parity mixing is not so efficient for the $T=0$ pair in the $J^{\pi }=1^{+}$ state. The parity mixing in the pair is regarded as the internal symmetry breaking of the pair in the spin-orbit potential at the nuclear surface.

New reaction mechanisms occurring in heavy ion collisions at low energy (10–30 MeV/nucleon) are investigated within the stochastic mean field model. We concentrate on the analysis of ternary breakup events, of dynamical origin, occurring in semicentral reactions, where the formation of excited systems in various conditions of shape and angular momentum is observed. We show how this fragmentation mode may emerge from the combined action of surface (neck) instabilities and angular momentum effects. Interesting perspectives on this mechanism in neutron-rich (or exotic) systems are developing, with the possibility of accessing information on the low-density behavior of the nuclear symmetry energy.

We present a complete formulation of second-order $(2+1)$-dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

Globally neutral neutron stars, obtained from the solution of the called Einstein-Maxwell-Thomas-Fermi equations that account for all the fundamental interactions, have been recently introduced. These configurations have a more general character than the ones obtained with the traditional Tolman-Oppenheimer-Volkoff equations, which impose the condition of local charge neutrality. The resulting configurations have a less massive and thinner crust, leading to a new mass-radius relation. Signatures of this new structure of the neutron star on the thermal evolution might be a potential test for this theory. We compute the cooling curves by integrating numerically the energy balance and transport equations in general relativity, for globally neutral neutron stars with crusts of different masses and sizes, according to this theory for different core-crust transition interfaces. We compare and contrast our study with known results for local charge neutrality. We found a new behavior for the relaxation time, depending upon the density at the base of the crust, ${\rho }_{\mathrm{crust}}$. In particular, we find that the traditional increase of the relaxation time with the crust thickness holds only for configurations whose density of the base of the crust is greater than $\approx 5\times {10}^{13} \mathrm{g} \mathrm{cm}{}^{-3}$. The reason for this is that neutron star crusts with very thin or absent inner crust have some neutrino emission processes blocked, which keeps the crust hotter for longer times. Therefore, accurate observations of the thermal relaxation phase of neutron stars might give crucial information on the core-crust transition which may aid us in probing the inner composition and structure of these objects.

The framework of nuclear energy density functionals is applied to a study of the formation and evolution of cluster states in nuclei. The relativistic functional DD-ME2 is used in triaxial and reflection-asymmetric relativistic Hartree-Bogoliubov calculations of relatively light $N=Z$ and neutron-rich nuclei. The role of deformation and degeneracy of single-nucleon states in the formation of clusters is analyzed, and interesting cluster structures are predicted in excited configurations of Be, C, O, Ne, Mg, Si, S, Ar, and Ca $N=Z$ nuclei. Cluster phenomena in neutron-rich nuclei are discussed, and it is shown that in neutron-rich Be and C nuclei cluster states occur that are characterized by molecular bonding of $\alpha$ particles by the excess neutrons.

The nuclear level densities of ${}^{194\text{–}196}\mathrm{Pt}$ and ${}^{197,198}\mathrm{Au}$ below the neutron separation energy have been measured using transfer and scattering reactions. All the level density distributions follow the constant-temperature description. Each group of isotopes is characterized by the same temperature above the energy threshold corresponding to the breaking of the first Cooper pair. A constant entropy excess $\Delta S=1.9k_B$ and $1.1k_B$ is observed in ${}^{195}\mathrm{Pt}$ and ${}^{198}\mathrm{Au}$ with respect to ${}^{196}\mathrm{Pt}$ and ${}^{197}\mathrm{Au}$, respectively, giving information on the available single-particle level space for the last unpaired valence neutron. The breaking of nucleon Cooper pairs is revealed by sequential peaks in the microcanonical caloric curve.

The predictions on the $\alpha$-decay chains of the isotopes of the superheavy nuclei with $Z=120$ in the range $272\le A\le 319$ have been done within the Coulomb and proximity potential model for deformed nuclei. A comparison of our calculated $\alpha$ half-lives with the values computed using the Viola-Seaborg [J. Inorg. Nucl. Chem. 28, 741 (1966)] systematic, the universal curve of Poenaru et al. [Phys. Rev. C 74, 014312 (2006)], and the analytical formulas of Royer [J. Phys. G: Nucl. Part. Phys. 26, 1149 (2000)] show good agreement with each other. An extensive study on the spontaneous fission half-lives of all the isotopes under study has been performed to identify the mode of decay of these isotopes. The study reveals that the $\alpha$-decay half-lives and the mode of decay of the isotopes of ${}^{298,299}120$, which are evaluated by using our formalisms, agree well with the experimental observations of Oganessian et al. [Phys. Rev. C 79, 024603 (2009)]. Our study on the isotopes of $Z=120$ predicts that the $\alpha$ decay restricts within the range $277\le A\le 308$ as those isotopes with $A\le 276$ and those nuclei with $A \ge$ 309 do not survive fission. We have also forecasted the mode of decay of ${}^{288-302}120$ superheavy nuclei as six consistent $\alpha$ chains from the nuclei of ${}^{288,289,291-295}120$, seven consistent $\alpha$ chains from the nuclei of ${}^{290}120$, five consistent $\alpha$ chains from the nuclei of ${}^{296,297}120$, and three consistent $\alpha$ chains from the nuclei of ${}^{300-302}120$, which could be of great interest to the experimentalists. The one-proton and two-proton separation energy calculations on ${}^{272-319}120$ superheavy nuclei have revealed that the isotopes spanning the range $273\le A\le 291$ may be considered to be the probable proton emitters.

We investigate the effects of long-range dynamic polarization on elastic cross sections for heavy-ion collisions which comprise the Coulomb dipole excitation (CDE) potential and the long-range nuclear (LRN) potential. To study these effects, we perform a ${\chi }^2$ analysis for the elastic cross sections of ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ and ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ systems using the long-range dynamic polarization potentials. For the CDE we formulate some empirical models to reproduce the experimental Coulomb dipole strength $B\left(E1\right)$ distribution and apply to the collision of ${}^{11}\mathrm{Li}$ and ${}^6\mathrm{He}$. But the CDE potential turns out to be not enough to explain the experimental data relevant to the nuclei. It leads us to additionally take the LRN potential peculiar to these halo nuclei into account. Our model, which was constructed by adding the CDE and LRN potentials to the conventional short-range nuclear potential corrected by the Coulomb interaction, provides a good description of the experimental data. In particular, the surface type is shown to be more reasonable rather than the volume type in the LRN potential.

The fragmentation of thermalized sources is studied using a version of the Statistical Multifragmentation Model which employs state densities that take the pairing gap in the nuclear levels into account. Attention is focused on the properties of the charge distributions observed in the breakup of the source. Since the microcanonical version of the model used in this study provides the primary fragment excitation energy distribution, one may correlate the reduction of the odd-even staggering in the charge distribution with the increasing occupation of high-energy states. Thus, in the framework of this model, such staggering tends to disappear as a function of the total excitation energy of the source, although the energy per particle may be small for large systems. We also find that, although the deexcitation of the primary fragments should, in principle, blur these odd-even effects as the fragments follow their decay chains, the consistent treatment of pairing may significantly enhance these staggering effects on the final yields. In the framework of this model, we find that odd-even effects in the charge distributions should be observed in the fragmentation of relatively light systems at very low excitation energies. Our results also suggest that the odd-even staggering may provide useful information on the nuclear state density.

In the stochastic mean-field (SMF) approach, an ensemble of initial values for a selected set of one-body observables is formed by stochastic sampling from a phase-space distribution that reproduces the initial quantum fluctuations. Independent mean-field evolutions are performed with each set of initial values followed by averaging over the resulting ensemble. This approach has been recently shown to be rather versatile and accurate in describing the correlated dynamics beyond the independent particle picture. In the original formulation of SMF, it was proposed to use a Gaussian assumption for the phase-space distribution. This assumption turns out to be rather effective when the dynamics of an initially uncorrelated state is considered, which was the case in all applications of this approach up to now. Using the Lipkin-Meshkov-Glick (LMG) model, we show that such an assumption might not be adequate if the quantum system under interest is initially correlated and presents configuration mixing between several Slater determinants. In this case, a more realistic description of the initial phase-space is necessary. We show that the SMF approach can be advantageously combined with standard methods to describe phase-space in quantum mechanics. As an illustration, the Husimi distribution function is used here to obtain a realistic representation of the phase-space of a quantum many-body system. This method greatly improves the description of initially correlated fermionic many-body states. In the LMG model, while the Gaussian approximation failed to describe these systems in all interaction strength range, the novel approach gives a perfect agreement with the exact evolution in the weak coupling regime and significantly improves the description of correlated systems in the strong coupling regime.

The $\alpha ({}^{10}\mathrm{Be},\alpha ){}^{10}\mathrm{Be}$ resonant scattering reaction has been measured at nine ${}^{10}\mathrm{Be}$ beam energies from 25 to 48 MeV, scanning out resonances in ${}^{14}\mathrm{C}$ from excitation energies of 13 to 24 MeV. Angular distribution measurements were used to assign the spin and parity of $5^{-}$ to resonances at $E_x=18.82\left(2\right)$ and 19.67(2) MeV and $6^{+}$ at $E_x=20.80\left(2\right)$ MeV. The data also strongly indicate a $3^{-}$ resonance at 17.32(2) MeV. The systematic uncertainty on the excitation energies is 175 keV. An $R$-matrix analysis has been performed for the excitation energy range 16.5 to 22 MeV. The data are discussed in terms of cluster bands in ${}^{14}\mathrm{C}$.

Excited states of ${}^{163}\mathrm{Hf}$ were populated using the ${}^{94}\mathrm{Zr}({}^{74}\mathrm{Ge},5n)$ reaction and the decay $\gamma$ rays were measured with the Gammasphere spectrometer. Two previously known bands were extended to higher spins, and nine new bands were identified. In addition to bands associated with three- and five-quasiparticle configurations, two $\gamma \text{−}$vibrational bands coupled to the $i_{13/2}$ excitation were also observed. The lowest level of a newly identified, negative-parity band is proposed to be the ground state of the nucleus. A systematic delay of the high-spin proton crossing frequency with increasing quadrupole deformation from ${}^{162}\mathrm{Hf}$ to ${}^{172}\mathrm{Hf}$ was established. Extensive band searches failed to reveal a triaxial, strongly deformed structure in ${}^{163}\mathrm{Hf}$ similar to the one observed in several nuclei around $A\sim 165$.

Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei but also indicates the prediction power of the present approach to calculate the half-lives and in turn to extract the structural information of proton emitters.