A comprehensive and detailed analysis of hadronic abundances measured in $\mathrm{Au}\text{−}\mathrm{Au}$ collisions at RHIC at $\sqrt{s_{\mathit{NN}}}=130$ and 200 GeV is presented. The rapidity densities measured in the central rapidity region have been fitted to the statistical hadronization model and the chemical freeze-out parameters determined as a function of centrality, using data from experiments BRAHMS, PHENIX, and STAR. The chemical freeze-out temperature turns out to be independent of centrality to accuracy of a few percentages, whereas the strangeness undersaturation parameter ${\gamma }_S$ decreases from almost unity in central collisions to a significantly lower value in peripheral collisions. Our results are in essential agreement with previous analyses, with the exception that fit quality at $\sqrt{s_{\mathit{NN}}}=200$ GeV is not as good as previously found. From the comparison of the two different energies, we conclude that the difference in fit quality, as described by ${\chi }^2$ values, is owing to the improved resolution of measurements that has probably exceeded the intrinsic accuracy of the simplified theoretical formula used in the fits.

We searched for a temperature dependence of the half-life ($T_{1/2}$) of ${}^{64}\mathrm{Cu}$ embedded in natural copper. We did not observe any change in $T_{1/2}$ between room temperature and 12 K on the level of 0.25%. Some earlier studies had suggested an increased $T_{1/2}$ (by a few percent) for electron-capture and ${\beta }^{-}$ decay dominated radioactive decays in a metallic environment at low temperature compared to measurements at room temperature. Our result is in excellent agreement with the recommended $T_{1/2}$ value for ${}^{64}\mathrm{Cu}$ and with very recent studies on ${}^{198}\mathrm{Au}$.

The results of two recent papers searching for the disappearance of collective enhancements with energy in nuclear level densities are examined. It is found that the effects of such enhancements are less than has been assumed. The reduction in the size of the effect only partially resolves the disagreement between theory and experiment. This effect also plays a role in explaining the results of an earlier experiment.

Semirealistic nucleon-nucleon interactions applicable to the self-consistent mean-field (both Hartree-Fock and Hartree-Fock-Bogolyubov) calculations are developed by modifying the M3Y interaction. The modification is made to reproduce binding energies and rms matter radii of doubly magic nuclei, single-particle levels in ${}^{208}\mathrm{Pb}$ and even-odd mass differences of the Sn isotopes. We find parameter sets with and without the tensor force. The new interactions are further checked by the saturation properties of the uniform nuclear matter, including the Landau-Migdal parameters. By the mean-field calculations, interaction dependence of the neutron drip line is investigated for the O, Ca, and Ni isotopes, and of the single-particle energies for the $N=16,32,50$, and 82 and $Z=50$ nuclei. Results of the semirealistic interactions including the tensor force are in fair agreement with available experimental data for all of these properties.

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell-model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed that improve and stabilize methods commonly used today.

The $g$-factor of the $4^{+}$ state in ${}^{134}\mathrm{Te}$ has been measured for the first time by using a new technique developed for measuring angular correlations with Gammasphere. Also reported is the first measurement of the $g$-factor of the $15/2^{+}$ state in ${}^{135}\mathrm{I}$ and the mixing ratios of several transitions. Furthermore, spins and parities are assigned to several levels in ${}^{134}\mathrm{Te}$ and ${}^{135}\mathrm{I}$. The $g$-factor measurements are compared to shell model predictions and good agreement is found between experiment and theory.

Results for elastic electron scattering by nuclei, calculated with charge densities of Skyrme forces and covariant effective Lagrangians that accurately describe nuclear ground states, are compared against experiment in stable isotopes. Dirac partial-wave calculations are performed with an adapted version of the ELSEPA package. Motivated by the fact that studies of electron scattering off exotic nuclei are intended in future facilities in the commissioned GSI and RIKEN upgrades, we survey the theoretical predictions from neutron-deficient to neutron-rich isotopes in the tin and calcium isotopic chains. The charge densities of a covariant interaction that describes the low-energy electromagnetic structure of the nucleon within the Lagrangian of the theory are used to this end. The study is restricted to medium- and heavy-mass nuclei because the charge densities are computed in mean-field approach. Because the experimental analysis of scattering data commonly involves parameterized charge densities, as a surrogate exercise for the yet unexplored exotic nuclei, we fit our calculated mean-field densities with Helm model distributions. This procedure turns out to be helpful to study the neutron-number variation of the scattering observables and allows us to identify correlations of potential interest among some of these observables within the isotopic chains.

When the time-dependent Hartree-Fock-Bogoliubov intrinsic equations of motion are solved in the case of seniority-one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility to skip from one orbital to another. This unpleasant feature is by-passed with a new set of pairing time-dependent equations that allows the possibility that the unpaired nucleon changes its single-particle level. These equations generalize the time-dependent Hartree-Fock-Bogoliubov equations of motion by including the Landau-Zener effect. The derivation of these new equations is presented in detail. These equations are applied to the case of a superasymmetric fission process, that is, to explain the fine structure the ${}^{14}\mathrm{C}$ emission from ${}^{233}\mathrm{Ra}$. In this context, a new version of the Woods-Saxon model extended for two-center potentials is used.

We show that the measurement of dileptons might provide only a restricted view into the most dense stages of heavy-ion reactions. Thus, possible studies of meson and baryon properties at high baryon densities, as, e.g., done at the GSI High Acceptance DiElectron Spectrometer (HADES) and envisioned for the Facility for Antiproton and Ion Research (FAIR) compressed baryonic matter experiments, might observe weaker effects than currently expected in certain approaches. We argue that the strong absorption of resonances in the high-baryon-density region of the heavy-ion collision masks information from the early hot and dense phase due to a strong increase of the total decay width because of collisional broadening. To obtain additional information, we also compare the currently used approaches to extract dileptons from transport simulations, i.e., shining, only vector mesons from final baryon resonance decays and instant emission of dileptons and find a strong sensitivity on the method employed in particular at FAIR and the CERN Super Proton Synchrotron energies. It is shown explicitly that a restriction to ρ meson (and therefore dilepton) production only in final-state baryon resonance decays provide a strong bias toward rather low baryon densities. The results presented are obtained from ultrarelativistic quantum molecular dynamics v2.3 calculations using the standard setup.

The reaction mechanism for the correlated ${\pi }^0\gamma$ emission in the photon-induced reaction on a proton target is studied. Since this reaction is studied in the GeV region, one can assume that it proceeds through the formation of the vector meson in the intermediate state. The vector meson, being an unstable particle, decays into ${\pi }^0\gamma$ bosons after propagating a certain distance. The analysis shows that the ${\pi }^0\gamma$ event seen in coincidence in the final state dominantly arises owing to the decay of ω meson. The calculated results reproduce the measured ${\pi }^0\gamma$ invariant mass distribution spectra very well.

There has been a recent flurry of interest in the possibility of condensates of $\alpha$ particles in nuclei. In this Rapid Communication we discuss occurrence conditions for such states. Using the quantality condition of Mottelson we show that condensates are only marginally expected in $\alpha$-particle states. We proceed to demonstrate that few-body nuclear condensates are ill defined and emphasize the conflict between $\alpha$-localization and $\alpha$-condensate formation. We also explore the connection between Ikeda diagrams, linear chains, and Tonks-Girardeau gases. Our findings show that no new information is contained in the approximations of nuclear states as $\alpha$-cluster condensates. Furthermore, condensates of more than three $\alpha$ particles are very unlikely to exist due to couplings to other degrees of freedom.

The nuclear structure of ${}^{67}\mathrm{Co}$ has been investigated through ${}^{67}\mathrm{Fe}$ $\beta$ decay. The ${}^{67}\mathrm{Fe}$ isotopes were produced at the LISOL facility in proton-induced fission of ${}^{238}\mathrm{U}$ and selected using resonant laser ionization combined with mass separation. The application of a new correlation technique unambiguously revealed a $496(33)$ ms isomeric state in ${}^{67}\mathrm{Co}$ at an unexpected low energy of 492 keV. A ${}^{67}\mathrm{Co}$ level scheme was deduced. Proposed spin and parities suggest a spherical $(7/2^{-})$ ${}^{67}\mathrm{Co}$ ground state and a deformed first excited $(1/2^{-})$ state at 492 keV, interpreted as a proton 1p-2h prolate intruder state.

We systematically investigate the $\alpha$-decay and spontaneous fission half-lives for heavy and superheavy nuclei with proton number $Z⩾90$. The $\alpha$-decay half-lives are obtained by the deformed version of the density-dependent cluster model (DDCM). In the DDCM, the microscopic potential between the $\alpha$ particle and the daughter nucleus is evaluated numerically from the double-folding model with the M3Y interaction. The influence of the core deformation on the double-folding potential is also properly taken into account by the multipole expansion method. The spontaneous fission half-lives of nuclei from ${}^{232}\mathrm{Th}$ to ${}^{286}114$ are calculated with the parabolic potential approximation by taking nuclear structure effects into account. The agreement between theoretical results and the newly observed data is satisfactory for both $\alpha$ emitters and spontaneous fission nuclei. The competition between $\alpha$ decay and spontaneous fission is analyzed in detail and the branching ratios of these two decay modes are predicted for the unknown cases.

We extend to odd-odd core hypernuclei our independent particle shell model (IPSM) formalism developed previously for the evaluation of the ${\Gamma }_{\mathrm{NM}},{\Gamma }_{n/p}$, and $a_{\Lambda }$ hypernuclear weak decay observables. The present procedure reproduces the even-odd and even-even core results as particular cases. Adopting the standard strangeness-changing weak $\Lambda N\to \mathit{NN}$ transition potential with exchange of the complete pseudoscalar and vector meson octets ($\pi ,\eta ,K,\rho ,\omega ,K^{*}$) we get simple analytical expressions for all observables. Numerical values for ${}_{\Lambda }^4\mathrm{He},{}_{\Lambda }^5\mathrm{He},{}_{\hspace{0.5em}\Lambda }^{11}\mathrm{B},{}_{\hspace{0.5em}\Lambda }^{12}\mathrm{C},{}_{\hspace{0.5em}\Lambda }^{16}\mathrm{O},{}_{\hspace{0.5em}\Lambda }^{17}\mathrm{O}$, and ${}_{\Lambda }^{28}\mathrm{Si}$ hypernuclei are obtained and compared with available experimental data, putting special attention on the asymmetry parameter. We remark that, in the present form, the IPSM gives roughly the same value of $a_{\Lambda }$ for all hypernuclei in contradiction with experiments. We stress the necessity of introducing configuration mixing to go beyond the IPSM taking into account, in a more realistic way, nuclear structure effects. Moreover, one could to include more relevant degrees of freedom, even within the IPSM framework, like: (i) modifications of the exchange potential (two-pion, $a_1$ meson, $\Delta T=3/2$ terms of vector mesons, etc.), (ii) final state interactions accounting for the distortion of the plane waves of emitted nucleons, and (iii) two-nucleon induced decay, as possible ways to solve the puzzle.

A pairing interaction fitted to be applied in nuclei with active particles moving close to the continuum threshold or even immersed in the continuum itself is introduced. It is found that the effects of the nonresonant continuum upon physically meaningful quantities is unimportant. We applied the theory to heavy tin isotopes and good agreement between theory and the very few available experimental data is found.

We construct nuclear energy density functionals in terms of derivatives of densities up to sixth, next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$). A phenomenological functional built in this way conforms to the ideas of the density matrix expansion and is rooted in the expansions characteristic to effective theories. It builds on the standard functionals related to the contact and Skyrme forces, which constitute the zero-order (LO) and second-order (NLO) expansions, respectively. At ${\mathrm{N}}^3\mathrm{LO}$, the full functional with density-independent coupling constants, and with the isospin degree of freedom taken into account, contains 376 terms, whereas the functionals restricted by Galilean and gauge symmetries contain 100 and 42 terms, respectively. For functionals additionally restricted by the spherical, space-inversion, and time-reversal symmetries, the corresponding numbers of terms are equal to 100, 60, and 22, respectively.

We present new results concerning the properties of solvable states of four particles in a $j=9/2$ shell which have seniority $v=4$ and angular momentum $I=4$ or 6. In particular, based on properties of certain coefficients of fractional parentage, we show that the number of pairs coupled to angular momentum $I$ is equal to one for these states. Similar results can be derived entirely analytically for four particles in a $j=7/2$ shell.

Excited states of the extremely neutron-deficient nucleus ${}^{197}\mathrm{At}$ have been studied in an in-beam experiment using the fusion-evaporation reaction ${}^{118}\mathrm{Sn}$(${}^{82}\mathrm{Kr}$,$p2n$)${}^{197}\mathrm{At}$. $\gamma$ rays belonging to ${}^{197}\mathrm{At}$ feeding the $I^{\pi }=(9/2^{-})$ ground state, as well as γ rays feeding the 311-keV $I^{\pi }=(13/2^{+})$ isomer, decaying via the emission of γ rays, and the 52-keV $I^{\pi }=(1/2^{+})$ α-decaying isomer have been identified using the recoil-α-decay tagging technique. Total Routhian surface calculations predict a near-spherical shape for the ($9/2^{-}$) ground state and oblate shapes with ${\beta }_2$ around −0.2 for the ($1/2^{+}$) and the ($13/2^{+}$) states. These predictions agree with our experimental findings.

Measurements of elastic scattering for the ${}^6\mathrm{Li}+{}^{90}\mathrm{Zr}$ system has been performed at various energies, namely, 11, 12, 13, 15, 17, 19, 21, 25, and 30 MeV, to study the energy dependence of the interaction potential. Angular distributions have been measured in a wide angular range to extract the behavior of the potential reliably. The data have been analyzed using the phenomenological Woods-Saxon shaped optical potential and the double folding potential. The potential behavior shows the characteristics of the breakup threshold anomaly, namely, the increase in the imaginary potential near the barrier with a small reduction in the real part. Continuum-discretized-coupled-channel (CDCC) calculations give a good description of the measured elastic scattering data and predict large breakup coupling effects. The polarization potentials extracted from the CDCC calculations have been studied for the present system along with those for the ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$, and ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ systems, and a similar energy dependence has been obtained for all the cases considered.