Nuclear pairing gaps of normally deformed and superdeformed nuclei are investigated using the particle-number-conserving (PNC) formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency $\omega$ dependence and seniority (number of unpaired particles) $\nu$ dependence of the pairing gap $\mathrm{\Delta ̃}$ are investigated. For the ground-state bands of even-even nuclei, PNC calculations show that, in general, $\mathrm{\Delta ̃}$ decreases with increasing $\omega$, but the $\omega$ dependence is much weaker than that calculated by the number-projected Hartree-Fock-Bogolyubov approach. For the multiquasiparticle bands (seniority $\nu >2$), the pairing gaps stay almost $\omega$ independent. As a function of the seniority $\nu$, the bandhead pairing gaps $\mathrm{\Delta ̃}(\nu ,\omega =0)$ decrease slowly with increasing $\nu$. Even for the highest seniority $\nu$ bands identified so far, $\mathrm{\Delta ̃}(\nu ,\omega =0)$ remains greater than $70\%$ of $\mathrm{\Delta ̃}(\nu =0,\omega =0)$.

We present a systematic analysis of the effects induced by tensor correlations on low-lying collective states of magic nuclei, by using the fully self-consistent random phase approximation (RPA) model with Skyrme interactions. The role of the tensor correlations is analyzed in detail in the case of quadrupole (2${}^{+}$) and octupole (3${}^{-}$) low-lying collective states in ${}^{208}\mathrm{Pb}$. The example of ${}^{40}\mathrm{Ca}$ is also discussed, as well as the case of magnetic dipole states (1${}^{+}$).

We have analyzed a large set of $\alpha +\alpha$ elastic scattering data for bombarding energies ranging from 0.6 to 29.5 MeV. Because of the complete lack of open reaction channels, the optical interaction at these energies must have a vanishing imaginary part. Thus, this system is particularly important because the corresponding elastic scattering cross sections are very sensitive to the real part of the interaction. The data were analyzed in the context of the velocity-dependent São Paulo potential, which is a successful theoretical model for the description of heavy-ion reactions from sub-barrier to intermediate energies. We have verified that, even in this low-energy region, the velocity dependence of the model is quite important for describing the data of the $\alpha +\alpha$ system.

Combining data on unpolarized and polarized inclusive proton structure functions, we perform the first detailed study of quark-hadron duality in individual helicity-1/2 and 3/2 virtual photoproduction cross sections. We find that duality is realized more clearly in the helicity-1/2 channel, with duality-violating corrections $\lesssim$$10\%$ over the entire nucleon resonance region, while larger, $\lesssim$$20\%$ corrections are found in the helicity-3/2 sector. The results are in general agreement with quark model expectations, and suggest that data above the $\Delta$ resonance region may be used to constrain both spin-averaged and spin-dependent parton distributions.

By exploiting the SAGE spectrometer a simultaneous measurement of conversion electrons and $\gamma$ rays emitted in the de-excitation of excited levels in the neutron-deficient nuclei ${}^{184,186}\mathrm{Hg}$ was performed. The light Hg isotopes under investigation were produced using the $4n$ channels of the fusion-evaporation reactions of ${}^{40}\mathrm{Ar}$ and ${}^{148,150}\mathrm{Sm}$. The measured K- and L-conversion electron ratios confirmed the stretched $E2$ nature of several transitions of the yrast bands in ${}^{184,186}\mathrm{Hg}$. Additional information on the $E0$ component of the $2_2^{+}\to 2_1^{+}$ transition in ${}^{186}\mathrm{Hg}$ was obtained.

The recently measured reaction cross sections for the neutron-rich carbon isotopes (${}^{19}\mathrm{C}$, ${}^{20}\mathrm{C}$, and ${}^{22}\mathrm{C}$) on a proton target at 40 A MeV are analyzed using the finite range Glauber model (FRGM) and the microscopic optical potential calculated within the Brueckner-Hartree-Fock formalism (BHF). In FRGM nucleon-nucleon cross sections are used, while in the latter (BHF), Hamada-Johnston, Urbana v-14, and the Argonne v-18 internucleon potentials are employed to calculate the microscopic optical potential. The required nucleon density distributions are calculated within the relativistic mean-field (RMF) framework. To test the halo structure, the extended neutron density distribution for ${}^{22}\mathrm{C}$ is also used. The analysis reveals that the BHF results of all three internucleon potentials are very close to each other, and also agree with the corresponding results of the FRGM. Our results, using RMF densities, are in agreement with the experimental data for all isotopes of carbon except ${}^{22}\mathrm{C}$, for which we require extended neutron density distribution, indicating a halo structure.

Low-lying states for even-even, odd-mass, and doubly odd nuclei in the mass $A~130$ region are systematically investigated using a pair-truncated shell model. In this model the collective nucleon pairs with angular momenta zero and two are the basic ingredients for even-even nuclei. Additional unpaired nucleons are added to the even-even core for a description of odd-mass and doubly odd nuclei. The effective interactions consist of single-particle energies and monopole and quadrupole pairing plus quadrupole-quadrupole interactions, whose strengths are assumed to be linearly changed as functions of the number of nucleons so as to describe the level schemes of the even-even and odd-mass nuclei. Energy levels of the low-lying collective states for even-even Xe, Ba, Ce, and Nd isotopes are reproduced very well along with intraband and interband $B(E2)$ values, which simulate the typical features of the O(6) limit of the interacting boson model. For odd-mass and doubly odd nuclei, complicated level schemes and electromagnetic moments are in excellent agreement with the experimental data.

The ${}^{160}\mathrm{Gd}$(${}^9\mathrm{Be}$,$\alpha 3$n)${}^{162}\mathrm{Dy}$ reaction has been used to study high-spin states in ${}^{162}\mathrm{Dy}$. Pulsed beam conditions were utilized for enhanced isomer sensitivity. An isomer at 2188.1(3) keV with a half-life of 8.3(3) $\mu \text{s}$ has been discovered and assigned $K$${}^{\pi }$$=$ $8^{+}$ with a two-quasineutron configuration. Among 11 $\gamma$-ray decay branches, an E2, $\Delta K=8$ transition to the ground-state band was observed with a reduced hindrance of $f_{\nu }=35$, agreeing well with systematics correlating $f_{\nu }$ with the product of the valence neutron and proton numbers ($N_p{N}_n$) over an extended $N,Z$ range. Small deviations from $N_p{N}_n$ dependence are analyzed for a range of two-quasiparticle isomer decays and interpreted as arising from a weak dependence on the isomer excitation energy relative to the yrast line.

The elastic, inelastic, and transfer cross sections are measured for the ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ reaction at energies around the Coulomb barrier. The optical model analysis of elastic scattering shows a breakup threshold anomaly in the energy dependence of the real and imaginary potentials. The observed energy dependence is found to be consistent with the dynamic polarization potential obtained from the coupled-channels calculations that explain the above measured reaction channels simultaneously. A comparison of different reaction probabilities reveals that the relative contribution of breakup starts increasing at energies below the Coulomb barrier, in contrast to the behavior of other reaction channels, which get closed as energy is lowered. The large probability of projectile breakup at sub-Coulomb energies leads to the observation of a nonzero imaginary potential even at $E_{\text{lab}}⩽0.8V_B$.

Identified charged pion, kaon, and proton spectra are used to explore the system size dependence of bulk freeze-out properties in $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ and 62.4 GeV. The data are studied with hydrodynamically motivated blast-wave and statistical model frameworks in order to characterize the freeze-out properties of the system. The dependence of freeze-out parameters on beam energy and collision centrality is discussed. Using the existing results from Au $+$ Au and $\mathit{pp}$ collisions, the dependence of freeze-out parameters on the system size is also explored. This multidimensional systematic study furthers our understanding of the QCD phase diagram revealing the importance of the initial geometrical overlap of the colliding ions. The analysis of $\mathrm{Cu}+\mathrm{Cu}$ collisions expands the system size dependence studies from $\mathrm{Au}+\mathrm{Au}$ data with detailed measurements in the smaller system. The systematic trends of the bulk freeze-out properties of charged particles is studied with respect to the total charged particle multiplicity at midrapidity, exploring the influence of initial state effects.

A new resonance having a relative decay energy of $~0.6$ MeV has been observed above the two-neutron separation energy in ${}^{24}\mathrm{O}$ at an excitation energy of $~7.5$ MeV. The new level was found to directly feed the first excited state in ${}^{23}\mathrm{O}$, an $E=0.045(2)$-MeV resonance, through the measurement of neutron-neutron correlations. Energy level comparisons with ${}^{23}\mathrm{O}$ suggest that this new level in ${}^{24}\mathrm{O}$ is dominated by an unpaired neutron in the $\nu 0d_{3/2}$ single-particle orbital coupled to a single hole in the $\nu 0d_{5/2}$ single-particle orbital. Establishment of this two-neutron discrimination technique provides a means for investigating high-lying excited states in neutron-rich nuclei.

Results from first measurements of charged-particle differential elliptic flow, obtained in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV with the ALICE detector at CERN’s Large Hadron Collider (LHC), are compared to those obtained for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=0.2$ TeV with the PHENIX detector at BNL’s Relativistic Heavy Ion Collider (RHIC). The comparisons, made as a function of centrality (cent) or the number of participant pairs ($N_{\text{part}}$) and particle transverse momentum $p_T$, indicate an excellent agreement between the magnitude and trends for the flow coefficients $v_2(p_T,\text{cent})$. Analysis indicates that the averaged specific viscosity of the quark gluon plasma (QGP) produced in LHC collisions is similar to that for the strongly coupled QGP produced in RHIC collisions.

In this paper a microscopic approach to calculation of the nuclear matrix element $M^{0\nu }$ for neutrinoless double-$\beta$ decay with an account for nuclear deformation is presented in length and applied for ${}^{76}\mathrm{Ge}$, ${}^{150}\mathrm{Nd}$, and ${}^{160}\mathrm{Gd}$. The proton-neutron quasiparticle random-phase approximation with a realistic residual interaction (the Brueckner $G$ matrix derived from the charge-depending Bonn nucleon-nucleon potential) is used as the underlying nuclear structure model. The effects of the short-range correlations and the quenching of the axial vector coupling constant $g_A$ are analyzed. The results suggest that neutrinoless double-$\beta$ decay of ${}^{150}\mathrm{Nd}$, to be measured soon by the SNO$+$ Collaboration, may provide one of the best probes of the Majorana neutrino mass. This confirms our preliminary conclusion in Fang et al. [Phys. Rev. C 82, 051301(R) (2010)].

Fragmentation of light charged particles is studied for various systems at different incident energies between 50 and 1000 MeV/nucleon. We analyze fragment production at the incident energies below, at, and above the transition energies using the isospin-dependent quantum molecular dynamics model. The trends observed for the fragment production and rapidity distributions depend upon the incident energy, size of the fragments, and composite mass of the reacting system, as well as on the impact parameter of the reaction. The free nucleons and light charged particles show continuous homogeneous changes, irrespective of the transition energies, indicating that there is no relation between the transition energy and production of the free as well as light charged particles.

Properties of low-energy dipole states in ${}^{232}\mathrm{Th}$ have been investigated with the nuclear resonance fluorescence technique. The present work used monoenergetic $\gamma$-ray beams at energies of 2–4 MeV from the high-intensity $\gamma$-ray source at Triangle Universities Nuclear Laboratory. Over 40 transitions corresponding to deexcitation to the ground state and first excited state were observed for the first time. Excitation energies, integrated cross sections, decay widths, branching ratios, and transition strengths for those states in ${}^{232}\mathrm{Th}$ were determined and compared with quasiparticle random-phase-approximation calculations. A large number of $E1$ transitions were observed for the first time in actinide nuclei with summed strength of $3.28(69)\times {10}^{-3}\hspace{0.5em}{e}^2{\mathrm{fm}}^2$. The observed summed $M1$ strength of 4.26(63)${\mu }_N^2$ is in good agreement with the other actinides and with the systematics of the scissors mode in deformed rare-earth nuclei.

In this paper, we calculate the diffusion coefficients that are related to the neutrino opacities considering the formation of nuclear pasta and homogeneous matter at low densities. Our results show that the mean-free paths are significantly altered by the presence of nuclear pasta in stellar matter when compared with the results obtained with homogeneous matter. These differences in neutrino opacities certainly influence the Kelvin-Helmholtz phase of protoneutron stars and consequently the results of supernova explosion simulations.

We investigate the binding energy per nucleon and hadron properties in infinite and homogeneous nuclear matter within the framework of the in-medium modified Skyrme model. We first consider the medium modifications of the single hadron properties by introducing the optical potential for pion fields into the original Lagrangian of the Skyrme model. The parameters of the optical potential are well fitted to the low-energy phenomenology of pion-nucleus scattering. Furthermore, the Skyrme term is also modified in such a way that the model reproduces the bulk properties of nuclear matter, in particular, the binding energy per nucleon.

In a study motivated by a recent experiment, the distribution of electric dipole strength in the neutron-rich ${}^{68}\mathrm{Ni}$ isotope was computed using a relativistic random-phase approximation with a set of effective interactions that—although well calibrated—predict significantly different values for the neutron-skin thickness in ${}^{208}\mathrm{Pb}$. The emergence of low-energy “pygmy” strength that exhausts about $5\%$–$8\%$ of the energy-weighted sum rule (EWSR) is clearly identified. In addition to the EWSR, special emphasis is placed on the dipole polarizability. In particular, our results suggest a strong correlation between the dipole polarizability of ${}^{68}\mathrm{Ni}$ and the neutron-skin thickness of ${}^{208}\mathrm{Pb}$. Yet we find a correlation just as strong, and an even larger sensitivity, between the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ and the fraction of the dipole polarizability exhausted by the pygmy resonance. These findings suggest that dipole polarizability may be used as a proxy for the neutron skin.

Cross sections for ($p,t$) two-neutron transfer reactions are calculated in the one-step zero-range distorted-wave Born approximation for the tin isotopes ${}^{124}\mathrm{Sn}$ and ${}^{136}\mathrm{Sn}$ and for incident proton energies from 15 to 35 MeV. Microscopic quasiparticle random-phase approximation form factors are provided for the reaction calculation and phenomenological optical potentials are used in both the entrance and the exit channels. Three different surface/volume mixings of a zero-range density-dependent pairing interaction are employed in the microscopic calculations and the sensitivity of the cross sections to the different mixings is analyzed. Since absolute cross sections cannot be obtained within our model, we compare the positions of the diffraction minima and the shapes of the angular distributions. No differences are found in the position of the diffraction minima for the reaction ${}^{124}\mathrm{Sn}$($p,t$)${}^{122}\mathrm{Sn}$. On the other side, the angular distributions obtained for the reaction ${}^{136}\mathrm{Sn}$($p,t$)${}^{134}\mathrm{Sn}$ with surface and mixed interactions differ at large angles for some values of the incident proton energy. For this reaction, we compare the ratios of the cross sections associated to the ground state and the first excited state transitions. Differences among the three different theoretical predictions are found and they are more important at the incident proton energy of 15 MeV. As a conclusion, we indicate ($p,t$) two-neutron transfer reactions with very neutron-rich Sn isotopes and at proton energies around 15 MeV as good experimental cases where the surface/volume mixing of the pairing interaction may be probed.