We report on a seven-dimensional generator coordinate calculation in the two deformation parameters $\beta$ and $\gamma$ together with projection on three-dimensional angular momentum and two particle numbers for the low-lying states in ${}^{76}\mathrm{Kr}$. These calculations are based on covariant density functional theory. Excellent agreement is found with the data for the spectrum and the electric multipole transition strengths. This answers the important question of dynamic correlations and triaxiality in a fully microscopic way. We find that triaxial configurations dominate both the ground state and the quasi $\gamma$ band. This yields a different picture from the simple interpretation in terms of “coexistence of a prolate ground state with an oblate low-lying excited state,” which is based on the measured sign of spectroscopic quadrupole moments. This study also provides for the first time a benchmark for the collective Hamiltonian in five dimensions. Moreover, we point out that the staggering phase of the $\gamma$ band is not a safe signature for rigid triaxiality of the low-energy structure.

Previous analytical formulas in the Glauber model for high-energy nucleus-nucleus collisions developed by Wong are utilized and extended to study antiproton-nucleus annihilations for both high and low energies, after taking into account the effects of Coulomb and nuclear interactions, and the change of the antiproton momentum inside a nucleus. The extended analytical formulas capture the main features of the experimental antiproton-nucleus annihilation cross sections for all energies and mass numbers. At high antiproton energies, they exhibit the granular property for the lightest nuclei and the black-disk limit for the heavy nuclei. At low antiproton energies, they display the effect of antiproton momentum increase due to the nuclear interaction for light nuclei, and the effect of magnification due to the attractive Coulomb interaction for heavy nuclei.

The experimental data of fusion cross sections for the different projectile and target nuclei systems are systematically analyzed. In order to explore the positive $Q$-value neutron transfer (PQNT) effect we systematically analyze their fusion functions F($x$) as a function of $x$, which reduces the barrier height, radius, and curvature of fusion systems. From the comparison of F($x$)s among them, it is found that after neutron transfer when the deformation of interacting nuclei increases largely, the enhancement of fusion cross sections can be observed at energies below the Coulomb barrier due to the PQNT effect. However, even if the fusion systems show the PQNT values, the fusion cross sections are almost the same due to the small deformation of interaction nuclei after neutron transfer. Many experiments need to be systematically done for this research.

For the ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ system, we find that the breakup process takes place from the forward angle or far distance region through the interaction distance which is obtained from ratios of elastic scattering cross sections to the Rutherford cross section. It is well known that the behavior of the ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ system is closely related to Coulomb dipole excitation effect. From the first ${\chi }^2$ analysis for the elastic cross section of the ${}^9\mathrm{Li}+{}^{208}\mathrm{Pb}$ system, we obtain the short-range potential of the ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ system by exploiting the optical model calculation for the Coulomb dipole excitation effect. To include the effect of the long-range interaction, we use a dynamic complex polarization potential including the Coulomb dipole potential and a long-range nuclear potential with Woods-Saxon form. Using the second ${\chi }^2$ analysis for the elastic cross section of the ${}^{11}\mathrm{Li}+{}^{208}\mathrm{Pb}$ system, we obtain the electric dipole transition probabilities $B\left(E1\right)$ which becomes 1.42 $e^2{\mathrm{fm}}^2$ and 1.41 $e^2{\mathrm{fm}}^2$ at $E_{\mathrm{c}.\mathrm{m}.}$ = 23.1 MeV and 28.3 MeV, respectively.

Motivated by new experimental spectra in transfermium mass region, we have investigated broken-pair high-$K$ multiparticle excited states and their rotational bands for the $N=150$ isotones around $Z=100$, by using the configuration-constrained pairing-deformation-frequency self-consistent total-Routhian-surface (TRS) model. In order to avoid the spurious phase transition encountered in the Bardeen-Copper-Schrieffer (BCS) pairing, the particle-number-conserving method has been employed for pairing calculations. Pairing correlations are remarkably reduced for the rotations of broken-pair multiparticle states. The present configuration-constrained TRS calculations reproduce reasonably existing experimental data. The abnormal feature in the recently observed $K^{\pi }=8^{-}$ bands of ${}^{252}\mathrm{No}$ and ${}^{250}\mathrm{Fm}$ would be associated with configuration mixing.

The ${}^{65}\mathrm{Cu}$ nucleus was populated by the ${}^{64}\mathrm{Ni}$(${}^7\mathrm{Li}$,$\alpha 2\mathrm{n}$)${}^{65}\mathrm{Cu}$ reaction and the lifetime of the 9/2${}^{+}$ state at 2.5 MeV was measured by electronic fast-timing technique, providing the value $\tau =$ 37(3) ps. The reduced transition probability $B\left(E3\right)=8.82\left(165\right)$ W.u. is deduced and compared to theoretical predictions in the framework of a particle-vibration (weak) coupling model. The results indicate that the 9/2${}^{+}$ state is a member of the 3${}^{-}\otimes \pi p$3/2 multiplet, built by coupling the octupole 3${}^{-}$ phonon of ${}^{64}\mathrm{Ni}$ to an unpaired proton in the $p_{3/2}$ level, confirming the robustness of core excitations in the medium mass nucleus ${}^{64}\mathrm{Ni}$.

We study the heavy-quark scattering on partons of the quark-gluon plasma (QGP), being especially interested in the collisional (elastic) scattering processes of heavy quarks $Q$ on light quarks $q$ and gluons $g$. We calculate the different cross sections for perturbative partons (massless on-shell particles in the vacuum) and for dynamical quasiparticles (off-shell particles in the QGP medium as described by the dynamical quasiparticles model “DQPM”) using the leading-order Born diagrams. Our results show clearly the effect of a finite parton mass and width on the perturbative elastic $\left[q\right(g)Q\to q(g\left)Q\right]$ cross sections which depend on temperature $T$, energy density $\varepsilon$, the invariant energy $\sqrt{s}$, and the scattering angle $\theta$. Our detailed comparisons demonstrate that the finite width of the quasiparticles in the DQPM—which encodes the multiple partonic scattering—has little influence on the cross section for $qQ\to qQ$ as well as $gQ\to gQ$ scattering, except close to thresholds. Thus, when studying the dynamics of energetic heavy quarks in a QGP medium the spectral width of the degrees-of-freedom may be discarded. We have, furthermore, compared the cross sections from the DQPM with corresponding results from hard-thermal-loop (HTL) approaches. The HTL-inspired models—essentially fixing the regulators by elementary vacuum cross sections and decay amplitudes instead of properties of the QGP at finite temperature—provide quite different results, especially with respect to the temperature dependence of the $qQ$ and $gQ$ cross sections (in all settings). Accordingly, the transport properties of heavy quarks will be very different as a function of temperature when compared to DQPM results.

Light neutron-rich even-even nuclei, of which the ground state is oblately deformed, are looked for, examining the Nilsson diagram based on realistic Woods-Saxon potentials. One-particle energies of the Nilsson diagram are calculated by solving the coupled differential equations obtained from the Schrödinger equation in coordinate space with the proper asymptotic behavior for $r\to \infty$ for both one-particle bound and resonant levels. The eigenphase formalism is used in the calculation of one-particle resonant energies. Large energy gaps on the oblate side of the Nilsson diagrams are found to be related to the magic numbers for the oblate deformation of the harmonic-oscillator potential where the frequency ratios (${\omega }_{\perp }:{\omega }_z$) are simple rational numbers. In contrast, for the prolate deformation the magic numbers obtained from simple rational ratios of (${\omega }_{\perp }:{\omega }_z$) of the harmonic-oscillator potential are hardly related to the particle numbers, at which large energy gaps appear in the Nilsson diagrams based on realistic Woods-Saxon potentials. The argument for an oblate shape of ${}_{14}^{42}$Si${}_{28}$ is given. Among light nuclei the nucleus ${}_6^{20}$C${}_{14}$ is found to be a good candidate for having the oblate ground state. In the region of the mass number $A\approx 70$ the oblate ground state may be found in the nuclei around ${}_{28}^{76}$Ni${}_{48}$ in addition to ${}_{28}^{64}$Ni${}_{36}$.

A measurement of the direct two-proton removal from ${}^{42}\mathrm{Si}$ has provided the first structural information on the $N=28$ isotone ${}^{40}\mathrm{Mg}$. The value for the inclusive cross section for two-proton removal from ${}^{42}\mathrm{Si}$ of 40${}_{-17}^{+27}$ $\mu$b is significantly lower than that predicted by structure calculations using the recent SDPF-MU shell-model effective interaction combined with eikonal reaction theory. This observed discrepancy is consistent with the interpretation that only one of the predicted low-lying 0${}^{+}$ states in ${}^{40}\mathrm{Mg}$ is bound. A two-state mixing analysis describing two-proton knockout cross sections along $N=28$ provides support for the interpretation of a prolate-deformed ${}^{40}\mathrm{Mg}$ ground state.

A rotational band was observed for the first time in ${}^{106}\mathrm{Nb}$ by means of γ-γ-γ and γ-γ-γ-γ measurements of prompt fission γ rays from ${}^{252}\mathrm{Cf}$ by using the Gammasphere multidetector array. Projected shell model and potential-energy surface calculations were performed and were compared to the experimental data of ${}^{106}\mathrm{Nb}$ and the previously reported ${}^{104}\mathrm{Nb}$. Configurations and spin-parity were assigned to the ground level, low-lying levels, and rotational bandheads of the two Nb isotopes. The new rotational band in ${}^{106}\mathrm{Nb}$ was interpreted as a $K^{\pi }=2^{-}$ band with a configuration π1/2${}^{+}$[431] × ν5/2${}^{-}$[532]. The same spin-parity and configuration were assigned to the analogous band in ${}^{104}\mathrm{Nb}$. π1/2${}^{+}$[431] × ν5/2${}^{+}$[413], $K^{\pi }=3^{+}$ were assigned to the 0.66-μs isomer and explained the $M$2 isomeric decay to the ground in ${}^{106}\mathrm{Nb}$. The proton intruder orbital π1/2${}^{+}$[431] plays an important role in shape evolution with regard to triaxial deformation in these neutron-rich Nb isotopes.

The properties of loosely bound proton-rich nuclei around $A=20$ are investigated within the framework of the nuclear shell model. In these nuclei, the strength of the effective interactions involving the loosely bound proton $s_{1/2}$ orbit is significantly reduced in comparison with that of those in their mirror nuclei. We evaluate the reduction of the effective interaction by calculating the monopole-based-universal interaction ($V_{\mathrm{MU}}$) in the Woods-Saxon basis. The shell-model Hamiltonian in the $sd$ shell, such as USD, can thus be modified to reproduce the binding energies and energy levels of the weakly bound proton-rich nuclei around $A=20$. The effect of the reduction of the effective interaction on the structure and decay properties of these nuclei is also discussed.

Background: The ${}^{12}\mathrm{C}{(}^6\mathrm{Li},d)$ reaction has been used as an indirect method to calculate the astrophysical $S$ factor for the ${}^{12}\mathrm{C}$($\alpha ,\gamma )$ reaction at Gamow energy (300 keV).

Purpose: The ${}^{12}\mathrm{C}{(}^6\mathrm{Li},d)$ reaction is usually interpreted in terms of direct transfer. In this work we investigate the reaction mechanism and determine the effects of breakup on transfer and therefore on the extracted spectroscopic amplitudes.

Method: The deuteron angular distributions for the ${}^{12}\mathrm{C}{{(}^6\mathrm{Li},d)}^{16}{\mathrm{O}}^{*}$has been measured at 20 MeV, populating discrete states of ${}^{16}\mathrm{O}$. continuum discretized coupled channel-coupled reaction channel (CDCC-CRC) calculations have been used to analyze the data.

Results: Results show a new reaction mechanism, where transfer occurs after the breakup of the loosely bound ${}^6\mathrm{Li}$ in the population of some bound states of ${}^{16}\mathrm{O}$. A comparison of the CDCC-CRC calculations with respect to the measured data were used to determine the $\alpha$ spectroscopic amplitudes and factors for the different states of ${}^{16}\mathrm{O}$. Using the spectroscopic amplitudes obtained in this work, the $E2$ $S$ factor for the ${}^{12}\mathrm{C}$($\alpha$,$\gamma$) reaction has been calculated in the framework of a two-body potential model and compared to measurements.

Conclusions: The present study very clearly shows that the breakup and transfer coupling effects are strong in the ${}^{12}\mathrm{C}{(}^6\mathrm{Li},d)$ reaction. The present work extracts, in the framework of a coupled reaction channel theory, the spectroscopic amplitudes of the bound and unbound states of ${}^{16}\mathrm{O}$. All previous analysis and new measurements should therefore be reexamined from this viewpoint to extract the astrophysical observables correctly.

Background: The motivation for this study is the experimental evidence for rigid triaxial deformation at low energy in ${}^{76}\mathrm{Ge}$ that was recently observed.

Purpose: Quadrupole shapes and low-energy spectra of the isotopes ${}^{72–82}\mathrm{Ge}$ are analyzed using a theoretical framework based on nuclear density functional theory.

Method: The relativistic functional DD-PC1, supplemented by a finite-range pairing force, is used to perform constrained triaxial mean-field calculations of energy surfaces as functions of quadrupole deformation parameters. The corresponding collective Hamiltonian, based on DD-PC1, is employed in the calculation of excitation spectra and transition rates.

Results: Model calculations reproduce the empirical trend of collective observables and predict the evolution of shapes from weakly triaxial in ${}^{74}\mathrm{Ge}$ to $\gamma$ soft in ${}^{78,80}\mathrm{Ge}$. For ${}^{76}\mathrm{Ge}$, in particular, the theoretical excitation spectrum is in good agreement with available data, the experimental ratio $E\left(2_2^{+}\right)/E\left(2_1^{+}\right)$ is reproduced, as well as the pattern and amplitude of the staggering in energy between odd- and even-spin states in the $\gamma$ band.

Conclusions: The mean-field potential of ${}^{76}\mathrm{Ge}$ appears to be $\gamma$ soft. Collective correlations drive the nucleus toward triaxiality but do not stabilize a rigid triaxial shape. Both the experimental and theoretical staggering of levels in the $\gamma$ band display a pattern consistent with triaxial shapes but the amplitudes are negligible and do not present evidence for rigid triaxiality.

The role of baryon-antibaryon annihilation during the hadronic stage of a relativistic heavy ion collision is explored by simulating the chemical evolution of a hadron gas. Beginning with a chemically equilibrated gas at an initial temperature of 170 MeV, the chemical composition of a representative hydrodynamic cell is followed throughout the hadronic stage. The cell's volume changes with time according to a parametrization that mimics a three-dimensional hydrodynamic expansion. The chemical evolution includes both annihilation and regeneration of baryons, consistent with detailed balance. During the hadronic stage, the number of baryons drops by approximately 40% for the case in which there is no net baryonic charge. When the calculations are performed without the baryon regenerating processes, e.g., $5\pi \to p\overline{p}$, the loss of baryons was found to be closer to 50%. After accounting for annihilation, yields are consistent with measurements from the ALICE Collaboration at the Large Hadron Collider (LHC). Baryon annihilation is shown to alter the extracted chemical breakup temperature by significantly changing the $p/\pi$ ratio. Assuming that annihilation cross sections are independent of the strangeness and isospin of the annihilating baryon and antibaryon, the loss of strange baryons from annihilation is found to be similar.

We have analyzed the data on $J/\psi$-to-Drell-Yan production cross-section ratios in proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions, measured by the NA50 Collaboration in the CERN Super Proton Synchrotron energy domain. The adapted version of the two-component QVZ model [J. Qiu, J. P. Vary, and X. Zhang, Nucl. Phys. A 698, 571 (2002); J. Qiu, J. P. Vary, and X. Zhang, Phys. Rev. Lett. 88, 232301 (2002)] has been employed to calculate $J/\psi$ production cross sections. For both $J/\psi$ and Drell-Yan production, nuclear modifications to the free nucleon structure functions are taken into account. In heavy-ion collisions, such modifications are assumed to be proportional to the local nuclear density resulting in centrality-dependent initial state effects. Differences in quark and gluon shadowing lead to a new source of impact parameter dependence of the $J/\psi$-to-Drell-Yan production ratio. For $J/\psi$, the final state interaction of the produced $c\overline{c}$ pairs with the nuclear medium is also taken into account. A satisfactory description of the data in both $p+A$ and $A+A$ collisions is obtained. The role of the shadowing corrections is investigated in detail. Model calculations are extrapolated to predict the centrality dependence of the $J/\psi$-to-Drell-Yan ratio in the GSI Facility for Antiproton and Ion Research energy regime.

The level density and $\gamma$-ray strength function in the quasicontinuum of ${}^{238}\mathrm{Np}$ have been measured using the Oslo method. The level-density function follows closely the constant-temperature level-density formula and reaches $43\times {10}^6$ levels per MeV at $S_n=5.488$ MeV of excitation energy. The $\gamma$-ray strength function displays a two-humped resonance at low-energy as also seen in previous investigations of Th, Pa, and U isotopes. The structure is interpreted as the scissors resonance and has an average centroid of ${\omega }_{\mathrm{SR}}=2.26\left(5\right)$ MeV and a total strength of $B_{\mathrm{SR}}=10.8\left(12\right){\mu }_N^2$, which is in excellent agreement with sum-rule estimates. The scissors resonance is shown to have an impact on the ${}^{237}\mathrm{Np}$${(n,\gamma )}^{238}$Np cross section.

Excited states above the seniority $\nu =2$ isomers have been investigated in even neutron-rich ${}^{118–128}$Sn isotopes produced by fusion-fission of 6.9 MeV/$A$ ${}^{48}\mathrm{Ca}$ beams with ${}^{208}\mathrm{Pb}$ and ${}^{238}\mathrm{U}$ targets and by fission of 6.7 MeV/$A$ ${}^{64}\mathrm{Ni}$ beams on a ${}^{238}\mathrm{U}$ target. Level schemes up to excitation energies in excess of 8 MeV have been established based on multifold $\gamma$-ray coincidence relationships measured with the Gammasphere array. Isotopic identification of crucial transitions was achieved through a number of techniques, including prompt and delayed cross-coincidence methods. As a result, seniority $\nu =4$, 15${}^{-}$, and 13${}^{-}$ isomers were observed and their half-lives determined. These long-lived states in turn served as steppingstones to delineate the isomeric decays and to locate higher-lying states with good sensitivity. As the observed isomeric decays feed down to 10${}^{+}$ and 7${}^{-}$ isomers, firm spin-parity assignments could be proposed for most of the seniority $\nu =4$ states. Higher-lying, seniority $\nu =6$ levels were assigned tentatively on the basis of the observed deexcitation paths as well as of general yrast population arguments. Shell-model calculations were carried out down to ${}^{122}\mathrm{Sn}$ in the $g_{7/2}$, $d_{5/2}$, $d_{3/2}$, $s_{1/2}$, and $h_{11/2}$ model space of neutron holes with respect to a ${}^{132}\mathrm{Sn}$ core. Effective two-body interactions were adjusted such that satisfactory agreement with data was achieved for ${}^{130}\mathrm{Sn}$. The results reproduce the experimental level energies and spin-parity assignments rather well. The intrinsic structure of the states is discussed on the basis of the calculated wave functions which, in many instances, point to complex configurations. In a few cases, the proposed assignments lead to unresolved issues. The smooth, systematic decrease of the level energies with mass $A$ is accompanied by the similarly regular behavior with $A$ of the reduced transition probabilities extracted from the isomeric half-lives. This $A$ dependence is discussed for the $E1$ and $E2$ transitions in the decay of the seniority $\nu =4$ isomers and is compared to that determined in earlier work for the $E2$ transition rates from the $\nu =2,3$ isomers.

Angular distributions of the ${}^{208}\mathrm{Pb}$(${}^7\mathrm{Li}$,${}^6\mathrm{He}$)${}^{209}\mathrm{Bi}$ reactions with one-proton transferred to the ground, first-excited, and second-excited states of ${}^{209}\mathrm{Bi}$ were measured at $E_{\mathrm{lab}}=25.67$, 28.55, 32.55, 37.55, and 42.55 MeV. The experimental data and the data available in the literature at $E_{\mathrm{lab}}=52$ MeV were analyzed within the theoretical framework of the distorted wave Born approximation and coupled reaction channels, respectively. The optical model potentials for the exotic system ${}^6\text{He}+{}^{209}$Bi, which is the exit channel of the reaction studied, have been extracted by means of fitting the angular distributions of transfer reactions. In the analyses, interaction potentials of the entrance channel ${}^7\text{Li}+{}^{208}\text{Pb}$ were derived from the elastic scattering data. For the ${}^6\text{He}+{}^{209}$Bi system, the phenomenon of the so-called breakup threshold anomaly was observed. Furthermore, the angular distributions of elastic scattering and total reaction cross sections by direct measurement for the ${}^6\text{He}+{}^{209}$Bi system in the energy region near and above the Coulomb barrier can be satisfactorily reproduced by employing the potentials extracted through the transfer reactions.

Fusion data for ${}^{48}\mathrm{Ca}+{}^{90,96}\mathrm{Zr}$ are analyzed by coupled-channels calculations that are based on the $\mathrm{M}3\mathrm{Y}+\mathrm{repulsion}$, double-folding potential. By applying a previously determined nuclear density of ${}^{48}\mathrm{Ca}$, the neutron densities of the zirconium isotopes are adjusted to optimize the fit to the fusion data, whereas the proton densities are determined by electron-scattering experiments. It is shown that the fusion data can be explained fairly well by including couplings to one- and two-phonon excitations of the reacting nuclei and to one- and two-nucleon transfer reactions but there is also some sensitivity to multiphonon excitations. The neutron skin thicknesses extracted for the two zirconium isotopes are consistent with antiproton measurements. The densities of the zirconium isotopes are used together with the previously determined nuclear density of ${}^{40}\mathrm{Ca}$ to calculate the $\mathrm{M}3\mathrm{Y}+\mathrm{repulsion}$ potentials and predict the fusion cross sections of ${}^{40}\mathrm{Ca}+{}^{90,96}\mathrm{Zr}$. The predicted cross sections for ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$ are in reasonable agreement with the data when the influence of multiphonon excitations and a modest transfer is considered. The prediction of the ${}^{40}\mathrm{Ca}+{}^{96}\mathrm{Zr}$ fusion cross section, on the other hand, is poor and underpredicts the data by 30% to 40%. Although couplings to transfer channels with positive $Q$ values were expected to play an important role, they are not able to explain the data, primarily because the predicted Coulomb barrier is about 1.5 MeV too high. Possible reasons for this failure are discussed.

The quantum molecular dynamics model has been improved to investigate the reaction dynamics induced by antiprotons. The reaction channels of elastic scattering, annihilation, charge exchange, and inelastic collisions have been included in the model. Dynamics on particle production, in particular pions, kaons, antikaons, and hyperons, is investigated in collisions of $\overline{p}$ on ${}^{12}\mathrm{C}$, ${}^{20}\mathrm{Ne}$, ${}^{40}\mathrm{Ca}$, ${}^{112}\mathrm{Sn}$, ${}^{181}\mathrm{Ta}$, ${}^{197}\mathrm{Au}$, and ${}^{238}\mathrm{U}$ from a low to high incident momentum. The rapidity and momentum distributions of ${\pi }^{+}$ and protons from the LEAR measurements can be well reproduced. The impacts of system size and incident momentum on particle emissions are investigated from the inclusive spectra, transverse momentum, and rapidity distributions. It is found that the annihilations of $\overline{p}$ on nucleons are of importance on the particle production. Hyperons are mainly produced via meson induced reactions on nucleons and strangeness exchange collisions when the incident momentum is below the threshold value of annihilation reaction. A higher nuclear temperature is obtained from the kaon emission, but it has a lower value for hyperon production.