We compute the nuclear matrix elements (NMEs) corresponding to the neutrinoless double beta ($0\nu \beta \beta$) decays of nuclei which attract current experimental interest. We concentrate on ground-state-to-ground-state decay transitions mediated by light (l-NMEs) or heavy (h-NMEs) Majorana neutrinos. The computations are done in realistic single-particle model spaces using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the l-NMEs and the h-NMEs include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak currents. In addition, both types of NMEs are corrected for the isospin symmetry by the recently proposed method in which the particle-particle proton-neutron interaction parameter ($g_{\mathrm{pp}}$) is decomposed into isoscalar ($g_{\mathrm{pp}}^{T=0}$) and isovector ($g_{\mathrm{pp}}^{T=1}$) parts. A detailed analysis of the l-NMEs and the h-NMEs is performed to benchmark our computer code and to compare with other recent calculations which produce h-NMEs that are in tension with each other.

Excited states in ${}^{135}\mathrm{Sb}$, populated in spontaneous fission of ${}^{248}\mathrm{Cm}$, are studied by means of prompt $\gamma$ spectroscopy, using the EUROGAM2 detector array. New excited states containing the neutron $i_{13/2}$ orbital in their wave functions are proposed. A more accurate value of the $i_{13/2}$ neutron single-particle energy in the ${}^{132}\mathrm{Sn}$ core potential is determined.

The neutron-drip-line nucleus ${}^{23}\mathrm{N}$ is investigated in a three-body model consisting of a ${}^{21}\mathrm{N}$ core and two valence neutrons. Using the Faddeev formalism with the realistic neutron-neutron potential and the neutron-core potential, we calculate the ground-state properties of ${}^{23}\mathrm{N}$ including its two-neutron separation energy, and obtain good agreement with the experiments. We also find an excited ${}^{23}\mathrm{N}$ state with a shallow two-neutron separation energy at about 0.18 MeV. By evaluating the root-mean-square matter radii, the average distances between the two valence neutrons, and the average distances from the core to the center of mass of the valence-neutron pair, we show that the excited state of ${}^{23}\mathrm{N}$ has a distinct halo structure. The large radius and very extended spatial distribution of the weakly bound excited state indicate the evidence of Efimov physics in the drip-line nucleus ${}^{23}\mathrm{N}$.

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANCs of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the $S$-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the ${}^5\mathrm{He},{}^5\mathrm{Li}$, and ${}^{16}\mathrm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei ${}^5\mathrm{He}$ and ${}^5\mathrm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the ${}^{16}\mathrm{O}$ resonances which lie slightly above the threshold for the $\alpha {}^{12}\mathrm{C}$ channel.

In this paper we construct an approach to extract the Wigner energy $\left[B_{\mathrm{w}}(N,Z)=-W\left(A\right)|N-Z|-d\left(A\right){\delta }_{N,Z}{\pi }_{np}\right]$ by using local mass relations, in the first-order approximation. We obtain $W\left(A\right)=(42.7\pm 1.2)/A$ MeV, $d\left(A\right)=(28.7\pm 1.5)/A$ MeV. By using the Wigner energies such obtained as well as empirical pairing and symmetry energies, the resultant binding-energy difference between the lowest $T=0$ and $T=1$ states of odd-odd $N=Z$ nuclei is in good agreement with experimental data.

In this paper we study odd-even staggering of the empirical neutron-proton interaction between the last neutron and the last proton, denoted as $\delta V_{1n-1p}$, and its consequence in the Garvey-Kelson mass relations (GKs) and nuclear mass models. The root-mean-squared deviations of predicted masses respectively for even-$A$ and odd-$A$ nuclei by using two combinatorial GKs suggest a large odd-even staggering of $\delta V_{1n-1p}$ between even-odd and odd-even nuclei, while the odd-even difference of $\delta V_{1n-1p}$ between even-even and odd-odd nuclei is much smaller. The contribution of the odd-even staggering of $\delta V_{1n-1p}$ between even-$A$ and odd-$A$ nuclei in deviations of theoretical $\delta V_{1n-1p}$ values of the Duflo-Zuker model and the improved $\mathrm{Weizs}\ddot{\mathrm{a}}\mathrm{cker}\text{−}\mathrm{Skyrme}$ model are well represented by an isospin-dependent term. The consideration of this odd-even staggering improves our description of binding energies and one-neutron separation energies in both the Duflo-Zuker model and the improved $\mathrm{Weizs}\ddot{\mathrm{a}}\mathrm{cker}\text{−}\mathrm{Skyrme}$ model.

To clarify the effects of $\alpha$-cluster breaking on $3\alpha$-cluster structures in ${}^{12}\mathrm{C}$, we investigate ${}^{12}\mathrm{C}$ using a hybrid model that combines the Brink-Bloch cluster model with the $p_{3/2}$ subshell closure wave function. We have found that $\alpha$-cluster breaking caused by spin-orbit force significantly changes cluster structures of excited $0^{+}$ states through orthogonality to lower states. Spatially developed cluster components of the $0_2{}^{+}$ state are reduced. The $0_3{}^{+}$ state changes from a vibration mode in the bending motion of three $\alpha$ clusters to a chainlike $3\alpha$ structure having an open triangle configuration. As a result of these structure changes of $0^{+}$ states, the band assignment for the $2_2{}^{+}$ state is changed by the $\alpha$-cluster breaking effect. Namely, in model calculations without the $\alpha$-cluster breaking effect, the $0_2{}^{+}$ state is assigned to be the band-head of the $2_2{}^{+}$ state. However, when we incorporate $\alpha$-cluster breaking caused by the spin-orbit force, the $0_3{}^{+}$ state is regarded as the bandhead of the $2_2{}^{+}$ state.

Background: The reaction mechanism in the low mass region particularly at low projectile energies in heavy-ion fusion processes has not been fully understood. More and more experimental data on fusion processes are required for the accurate description of reaction processes involved at low projectile energies. In the literature, cross section data for the fusion process using a ${}^{12}\mathrm{C}$ beam in the lower mass region and at low projectile energies are scarce.

Purpose: To understand the dynamics of fusion processes and to test various existing theoretical models, the measurements of reaction cross sections in the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ system have been carried out.

Method: The experiments were performed for the measurement of the cross sections for the residues produced in the interaction of the ${}^{12}\mathrm{C}$ ion with a ${}^{27}\mathrm{Al}$ target nucleus at 20 different energies covering the energy range from $\approx 39$ to $85\mathrm{MeV}$. The off-line $\gamma -\text{ray}$ spectrometry based activation technique has been used to measure the cross sections.

Results: The measured excitation functions were compared to those evaluated with the code pace4 based on the statistical approach and Monte Carlo procedure. The enhancement of experimental cross sections as compared to the theoretical predictions of code pace4 has been observed. The SUMRULE model predictions indicate that incomplete fusion processes are associated with smaller values of the angular momenta than that of its critical value required for complete fusion processes.

Conclusions: In the lower mass region, phenomena such as incomplete fusion and direct reaction processes are of importance even at energies as low as $\approx 3–7\mathrm{MeV}/\text{nucleon}$, where fusion evaporation channels are expected to be dominant.

The yields of the $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ resonances are measured in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV through their hadronic decays using the ALICE detector. The measurements are performed in multiple centrality intervals at mid-rapidity $\left(\right|y|<0.5)$ in the transverse-momentum ranges $0.3<p_{\mathrm{T}}<5 \mathrm{GeV}/c$ for the $K^{*}{\left(892\right)}^0$ and $0.5<p_{\mathrm{T}}<5 \mathrm{GeV}/c$ for the $\varphi \left(1020\right)$. The yields of $K^{*}{\left(892\right)}^0$ are suppressed in central Pb-Pb collisions with respect to $pp$ and peripheral Pb-Pb collisions (perhaps due to rescattering of its decay products in the hadronic medium), while the longer-lived $\varphi \left(1020\right)$ meson is not suppressed. These particles are also used as probes to study the mechanisms of particle production. The shape of the $p_{\mathrm{T}}$ distribution of the $\varphi \left(1020\right)$ meson, but not its yield, is reproduced fairly well by hydrodynamic models for central Pb-Pb collisions. In central Pb-Pb collisions at low and intermediate $p_{\mathrm{T}}$, the $p/\varphi \left(1020\right)$ ratio is flat in $p_{\mathrm{T}}$, while the $p/\pi$ and $\varphi \left(1020\right)/\pi$ ratios show a pronounced increase and have similar shapes to each other. These results indicate that the shapes of the $p_{\mathrm{T}}$ distributions of these particles in central Pb-Pb collisions are determined predominantly by the particle masses and radial flow. Finally, $\varphi \left(1020\right)$ production in Pb-Pb collisions is enhanced, with respect to the yield in $pp$ collisions and the yield of charged pions, by an amount similar to the $\Lambda$ and $\Xi$.

The sequential breakup of $E/A=65.5\text{-MeV}{}^7\mathrm{Be}$ and $E/A=36.6\text{-MeV}{}^6\mathrm{Li}$ projectiles excited through inelastic interactions with ${}^9\mathrm{Be}$ target nuclei has been studied. For events where the target nucleus remained in its ground state, significant alignment of the excited projectile's spin axis parallel or antiparallel to the beam direction was observed. This unusual spin alignment was found to be largely independent of the projectile's scattering angle and it was deduced that the target nucleus has a significant probability of changing its spin orientation during the interaction. It is proposed that the unusual spin alignment is a consequence of the molecular structure of the ${}^9\mathrm{Be}$ nucleus.

The Monte Carlo results in lattice QCD for the pressure and energy density at small temperature $T<155$ MeV and zero baryonic chemical potential are analyzed within the hadron resonance gas model. Two extensions of the ideal hadron resonance gas are considered: the excluded volume model, which describes a repulsion of hadrons at short distances, and the Hagedorn model with an exponential mass spectrum. Considering both of these models we do not find conclusive evidence in favor of either of them. The controversial results appear because of rather different sensitivities of the pressure and energy density to both excluded volume and Hagedorn mass spectrum effects. On the other hand, we have found clear evidence for a simultaneous presence of both of them. They lead to rather essential contributions: suppression effects for thermodynamical functions of the hadron resonance gas due to the excluded volume effects and enhancement due to the Hagedorn mass spectrum.

Following a recent letter [J.-Y. Guo, S.-W. Chen, Z.-M. Niu, D.-P. Li, and Q. Liu, Phys. Rev. Lett. 112, 062502 (2014)], we present more details for the relativistic symmetry research by using the similarity renormalization group. With the theoretical formalism expressed in detail, we explore the origin and breaking mechanism of relativistic symmetries for an axially deformed nucleus. By comparing the energy splitting between the (pseudo-) spin doublets, it is shown that the spin energy splitting arises almost completely from the spin-orbit coupling, while the pseudospin energy splitting arises from a combination of the nonrelativistic, dynamical, and spin-orbit terms. Furthermore, these splittings are correlated with nuclear deformation as well as with the quantum numbers of the doublets. The origin of relativistic symmetries is disclosed and the breaking mechanism of spin and pseudospin symmetries is clarified.

We systematically analyze the coherence length in even-even nuclei. The pairing coherence length in the spin-singlet channel for the effective density-dependent delta (DDD) and Gaussian interaction is estimated. We consider in our calculations bound states as well as narrow resonances. It turns out that the pairing gaps given by the DDD interaction are similar to those of the Gaussian potential if one renormalizes the radial width to the nuclear radius. The correlations induced by the pairing interaction have, in all considered cases, a long-range character inside the nucleus and a decrease towards the surface. The mean coherence length is larger than the geometrical radius for light nuclei and approaches this value for heavy nuclei. The effect of the temperature and states in the continuum is investigated. Strong shell effects are put in evidence, especially for protons. We generalize this concept to quartets by considering similar relations, but between proton and neutron pairs. The quartet coherence length has a similar shape, but with larger values on the nuclear surface. We provide evidence of the important role of proton-neutron correlations by estimating the so-called alpha coherence length, which takes into account the overlap with the proton-neutron part of the $\alpha$-particle wave function. It turns out that it does not depend on the nuclear size and has a value comparable to the free $\alpha$-particle radius. We have shown that pairing correlations are mainly concentrated inside the nucleus, while quarteting correlations are connected to the nuclear surface.

The Cabibbo-Kobayashi-Maskawa matrix in the standard model is currently the only experimentally confirmed source of CP violation. The intrinsic electric dipole moment of the nucleon induced by this CP phase via hadronic loop and pole diagrams was studied more than two decades ago, but is subject to various theoretical issues such as the breakdown of chiral power counting and uncertainties in the determination of low energy constants. I carry out an up-to-date re-analysis on both one-loop and pole diagram contributions to the nucleon electric dipole moment based on heavy baryon chiral perturbation theory in a way that preserves power counting, and I redo the determination of the low-energy constants following the results of more recent articles. Combined with an estimation of higher-order contributions, I expect the long-distance contribution to the standard model nucleon electric dipole moment to be approximately $(1\times {10}^{-32}–6\times {10}^{-32})e\mathrm{cm}$.

We present calculated fission-barrier heights for 5239 nuclides for all nuclei between the proton and neutron drip lines with $171\le A\le 330$. The barriers are calculated in the macroscopic-microscopic finite-range liquid-drop model with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than 5 000 000 different shapes, defined by five deformation parameters in the three-quadratic-surface shape parametrization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid $\left(\epsilon \right)$ and the spherical-harmonic $\left(\beta \right)$ parametrizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the $(\epsilon ,\gamma )$ parametrization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about 1 MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative and, when possible, quantitative agreement and/or consistency with data on $\beta$-delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. These studies all indicate that the model is realistic at considerable distances in $Z$ and $N$ from the region of nuclei where its parameters were determined.

We calculate open heavy-flavor (HF) production in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ GeV utilizing a nonperturbative transport approach as previously applied in nuclear collisions at top Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. The effects of hot QCD matter are treated in a strong-coupling framework, by implementing heavy-quark diffusion, hadronization, and heavy-flavor meson diffusion within a hydrodynamic background evolution. Since in our approach the heavy-flavor coupling to the medium is strongest in the pseudocritical region (including the effects of resonance recombination), it is of interest to test its consequences at lower collision energies where the sensitivity to this region should be enhanced relative to the initially hotter fireball temperatures reached at top RHIC and LHC energies. We find that the suppression and flow pattern of the nonphotonic electrons from heavy-flavor decays at 62.4 GeV emerges from an intricate interplay of thermalization and initial-state effects, in particular a Cronin enhancement which is known to become more pronounced toward lower collision energies.

The half-lives of the $I^{\pi }=5^{-}$ and $I^{\pi }=7^{-}$ yrast states with $E_x=1978$ keV and $E_x=2307$ keV in the $N=78$ isotone ${}^{136}\mathrm{Ce}$, have been measured to be 496(23) ps and 270(24) ps, respectively, using the coincident fast-timing spectroscopy technique following population by a ${}^{124}\mathrm{Sn}({}^{16}\mathrm{O},4\mathrm{n})$ fusion-evaporation reaction at an incident beam energy of 68 MeV. The extracted $B(E1;5^{-}\to 4^{+})=1.8\left(3\right)\times {10}^{-6}$ W.u. value is compared with the systematics of the region and is found to be in line with typical $E1$ strengths for single-particle-type decays, rather than showing any evidence for the additional $E1$ decay hindrance associated with $K$-quantum number violation in axially deformed systems observed in lighter Ce isotopes.

An experiment has been carried out using the ${}^9\mathrm{Be}({}^3\mathrm{He},t){}^9\mathrm{B}^{*}$ reaction at a beam energy of 33 MeV. A large acceptance silicon-strip array was used to detect the ${}^9\mathrm{B}^{*}$ break-up in coincidence with the triton ejectiles in the high-resolution Munich-Q3D spectrograph. The excitation energy regime $<3$ MeV has been explored and the spectrum resulting from proton decaying states, isolated and characterized. Additional resonance strength is observed at 1.86 MeV $\pm 70$ keV(stat) $\pm 35$ keV(syst), in agreement with two other recent measurements at higher energies and different angles. The consequences for the “missing” ${½}^{+}$ first excited state are discussed. Additionally, the branching ratios for the 2.36 MeV ${5/2}^{-}$ state have been measured as ${\Gamma }_{\alpha 0}/\Gamma =0.98\pm 0.12$ and ${\Gamma }_{p0}/\Gamma =0.016\pm 0.008$, in close agreement with earlier work.