A dipole band of six transitions built upon a firmly established $I^{\pi }=31/2^{-}$ isomeric state has been identified in ${}^{189}\text{Pb}$ using recoil-isomer tagging. This is the lightest odd-mass Pb nucleus in which a dipole band is known. The dipole nature of the new transitions has been confirmed through angular-intensity arguments. The evolution of the excitation energy and the aligned-angular momentum of the states in the new dipole band are compared with those of dipole bands in heavier, odd-mass lead isotopes. This comparison suggests that the new band in ${}^{189}\text{Pb}$ is based upon a $\pi {\left[s_{1/2}^{-2}{h}_{9/2}{i}_{13/2}\right]}_{{11}^{-}}\otimes \nu {\left[i_{13/2^{+}}^{-1}\right]}_{13/2^{+}}$ configuration. However, the increased aligned-angular momentum in ${}^{189}\text{Pb}$ may suggest evidence for a reduced repulsive proton/neutron-hole interaction compared to dipole bands in the heavier mass isotopes.

Resonances play a critical role in the formation of many physical phenomena. The complex scaled Green function method provides a powerful tool for the exploration of resonances. In the paper, we extend this method to the relativistic framework. With ${}^{120}\mathrm{Sn}$ as an example, we present the details of the scheme and seek resonant states in real nuclei. The results are compared, and are in satisfactory agreement with those from frequently used methods. In particular, the present method gathers the advantages of the complex scaling method and Green function method, and can be used to determine more accurately resonance parameters such as energy and lifetime of decay.

The properties of recently predicted thermally fissile Th and U isotopes are studied within the framework of the relativistic mean-field approach using the axially deformed basis. We calculate the ground, first intrinsic excited state for highly neutron-rich thorium and uranium isotopes. The possible modes of decay such as $\alpha$ decay and $\beta$ decay are analyzed. We found that neutron-rich isotopes are stable against $\alpha$ decay, however, they are very unstable against $\beta$ decay. The lifetime of these nuclei is predicted to be tens of seconds against $\beta$ decay. If these nuclei are utilized before their decay time, a lot of energy can be produced with the help of multifragmentation fission. Also, these nuclei have great implications from the astrophysical point of view. In some cases, we found that the isomeric states with energy range from 2 to 3 MeV and three maxima in the potential energy surface of ${}^{228-230}\mathrm{Th}$ and ${}^{228-234}\mathrm{U}$ isotopes.

We investigate heavy-ion multinucleon transfer reactions using the coupled-channels formalism. We first use the semiclassical approximation and show that a direct coupling between the entrance and the pair transfer channels improves a fit to the experimental one- and two-neutron transfer cross sections for the ${}^{40}\text{Ca}+{}^{96}\text{Zr}$ and ${}^{60}\text{Ni}+{}^{116}\text{Sn}$ systems. We then discuss the validity of the perturbative approach and highlight the effect of high-order terms. The effect of absorption is also investigated for energies around the Coulomb barrier. Finally, we use a quantal coupled-channels approach to achieve a simultaneous description of the fusion cross sections and the transfer probabilities for the ${}^{40}\text{Ca}+{}^{96}\text{Zr}$ reaction. We find a significant effect of the couplings to the collective excited states on the transfer probabilities around the Coulomb barrier.

Background: Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasiparticle mean-field Hartree-Fock-Bogoliubov theory with temperature-dependent occupation numbers for the quasiparticle states.

Purpose: Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust.

Method: Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons.

Results: The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity.

Conclusions: We present the first modelization of stellar matter containing at the same time a statistical distribution of clusters at finite temperature, and pairing correlations in the unbound neutron component. The effect of the nuclear distribution on the superfluid properties can be easily added in future calculations of the neutron star cooling curves. A strong influence of resonance population on the heat capacity at high temperature is observed, which deserves to be further studied within more microscopic calculations.

The spherical to $\gamma$-unstable nuclei shape-phase transition in odd-$A$ nuclei is investigated by using the dual algebraic structures and the affine $\widehat{\mathrm{SU}(1,1)}$ Lie algebra within the framework of the interacting boson-fermion model. The new algebraic solution for odd-$A$ nuclei is introduced. In this model, single $j=1/2$ and 3/2 fermions are coupled with an even-even boson core. Energy spectra, quadrupole electromagnetic transitions, and an expectation value of the $d$-boson number operator are presented. Experimental evidence for the ${\mathrm{U}}^{BF}\left(5\right){\mathrm{-O}}^{BF}\left(6\right)$ transition in odd-$A$ Ba and Rh isotopes is presented. The low-states energy spectra and $B\left(E2\right)$ values for these nuclei are also calculated and compared with the experimental data.

Double-polarization observables in the reaction $\vec{e}p\to e^{\prime }\vec{p}{}^{\prime }\gamma$ have been measured at $Q^2=0.33{(\mathrm{GeV}/c)}^2$. The experiment was performed at the spectrometer setup of the A1 Collaboration using the 855 MeV polarized electron beam provided by the Mainz Microtron (MAMI) and a recoil proton polarimeter. From the double-polarization observables the structure function $P_{LT}^{\perp }$ is extracted for the first time, with the value $(-15.4\pm 3.3_{(\mathrm{stat}.)}{}_{-2.4}^{+1.5}{}_{(\mathrm{syst}.)}){\mathrm{GeV}}^{-2}$, using the low-energy theorem for virtual Compton scattering. This structure function provides a hitherto unmeasured linear combination of the generalized polarizabilities of the proton.

The energies of the ${}^{12}\mathrm{C},{}^{16}\mathrm{O},{}^{20}\mathrm{Ne},{}^{24}\mathrm{Mg},$ and ${}^{32}\mathrm{S} 4n$ nuclei have been determined within a generalized liquid drop model and assuming different planar and three-dimensional shapes of the $\alpha$ molecules: linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octagon, and cube. The potential barriers governing the entrance and decay channels via $\alpha$ absorption or emission as well as more symmetric binary and ternary reactions have been compared. The rms radii of the linear chains differ from the experimental rms radii of the ground states. The binding energies of the three-dimensional shapes at the contact point are higher than the ones of the planar configurations. The $\alpha$ particle plus A-4 daughter configuration leads always to the lowest potential barrier. The binding energy can be reproduced within the sum of the binding energy of $n \alpha$ particles plus the number of bonds multiplied by 2.4 MeV or by the sum of the binding energies of one $\alpha$ particle and the daughter nucleus plus the Coulomb energy and the proximity energy.

Excited states have been studied in ${}^{28}\mathrm{Na}$ using the $\beta$-decay of implanted ${}^{28}\mathrm{Ne}$ ions at the Grand Accélérateur National d'Ions Lourds/LISE as well as the in-beam $\gamma$-ray spectroscopy at the National Superconducting Cyclotron Laboratory/S800 facility. New states of positive $\left(J^{\pi }=3^{+},4^{+}\right)$ and negative $\left(J^{\pi }=1^{-}–5^{-}\right)$ parity are proposed. The former arise from the coupling between $0d_{5/2}$ protons and $0d_{3/2}$ neutrons, while the latter are attributable to couplings of $0d_{5/2}$ protons with $1p_{3/2}$ or $0f_{7/2}$ neutrons. While the relative energies between the $J^{\pi }=1^{+}–4^{+}$ states are well reproduced with the USDA interaction in the $N=17$ isotones, a progressive shift in the ground-state binding energy (by about 500 keV) is observed between ${}^{26}\mathrm{F}$ and ${}^{30}\mathrm{Al}$. This points to a possible change in the proton-neutron $0d_{5/2}\text{−}0d_{3/2}$ effective interaction when moving from stability to the drip line. The presence of $J^{\pi }=1^{-}–4^{-}$ negative-parity states around 1.5 MeV as well as of a candidate for a $J^{\pi }=5^{-}$ state around 2.5 MeV give further support to the collapse of the $N=20$ gap and to the inversion between the neutron $0f_{7/2}$ and $1p_{3/2}$ levels below $Z=12$. These features are discussed in the framework of shell-model and energy-density-functional calculations, leading to predicted negative-parity states in the low-energy spectra of the ${}^{26}\mathrm{F}$ and ${}^{25}\mathrm{O}$ nuclei.

The isotopic dependence of the capture cross section is analyzed in the reactions ${}^{37,39,41,43,45,46,47}\text{K}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ with stable and radioactive beams. A comparison between the reactions ${}^{46}\text{K}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ and ${}^{48}\text{Ca}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ is performed. The sub-barrier capture cross sections are larger in the reactions with a stable beam at fixed $E_{\mathrm{c}.\mathrm{m}.}\text{−}{V}_b$.

We investigate the survival rate of an initial momentum anisotropy $\left(v_2^{\mathrm{ini}}\right)$, not spatial anisotropy, to the final state in a multiphase transport (AMPT) model in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. It is found that both the final-state parton and charged hadron $v_2$ show a linear dependence versus $v_2^{\mathrm{ini}}\left\{\mathrm{PP}\right\}$ with respect to the participant plane (PP). It is found that the slope of this linear dependence (referred to as the survival rate) increases with transverse momentum $p_T$, reaching $\sim 100\%$ at $p_T\sim 2.5$ GeV/$c$ for both parton and charged hadron. The survival rate decreases with collision centrality and energy, indicating decreasing survival rate with increasing interactions. It is further found that a $v_2^{\mathrm{ini}}\left\{\mathrm{Rnd}\right\}$ with respect to a random direction does not survive in $v_2\left\{\mathrm{PP}\right\}$ but in the two-particle cumulant $v_2\left\{2\right\}$. The dependence of $v_2\left\{2\right\}$ on $v_2^{\mathrm{ini}}\left\{\mathrm{Rnd}\right\}$ is quadratic rather than linear.

The inelastic heavy quark and quarkonium photoproduction through the ultra-incoherent photon channel in ultra-peripheral collisions is studied. Considering the ultra-relativistic hadrons as a beam of freely moving elementary constituents, the inclusive photoproduction cross sections for charm quark, bottom quark, $J/\psi$, and $\mathrm{{\rm Y}}\left(1S\right)$ are calculated by using the incoherent photon spectrum from the individual quarks in the nucleus. Comparing with the predictions of the coherent photon channel in the literatures, it is shown that the ultra-incoherent photon channel provides non-negligible contributions to the heavy quarks and heavy quarkonia photoproduction in ultra-peripheral collisions.

The standard variational derivation of stellar-matter structure in the Wigner-Seitz approximation is generalized to the finite-temperature situation where a wide distribution of different nuclear species can coexist in the same density and proton fraction condition, possibly out of $\beta$ equilibrium. The same theoretical formalism is shown to describe on one side the single-nucleus approximation (SNA), currently used in most core-collapse supernova simulations and on the other side the nuclear statistical equilibrium (NSE) approach, routinely employed in $r$- and $p$-process explosive nucleosynthesis problems. In particular, we show that in-medium effects have to be accounted for in NSE to have a theoretical consistency between the zero-temperature and the finite-temperature modeling. The bulk part of these in-medium effects is analytically calculated in the local density approximation and shown to be different from a Van der Waals excluded-volume term. This unified formalism allows controlling quantitatively the deviations from the SNA in the different thermodynamic conditions, as well as having a NSE model which is reliable at any arbitrarily low value of the temperature, with potential applications for neutron-star cooling and accretion problems. We present different illustrative results with several mass models and effective interactions, showing the importance of accounting for the nuclear species distribution even at temperatures lower than 1 MeV.

The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters, which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using Lüscher's method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.

Using the variational principle, we compute mass spectra and decay constants of ground state pseudoscalar and vector mesons in the light-front quark model (LFQM) with the QCD-motivated effective Hamiltonian including the hyperfine interaction. By smearing out the Dirac $\delta$ function in the hyperfine interaction, we avoid the issue of negative infinity in applying the variational principle to the computation of meson mass spectra and provide analytic expressions for the meson mass spectra. Our analysis with the smeared hyperfine interaction indicates that the interaction for the heavy meson sector including the bottom and charm quarks gets more point-like. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of $(\omega ,\varphi )$ and $(\eta ,{\eta }^{\prime })$. Our variational analysis with the trial wave function including the two lowest order harmonic oscillator basis functions appears to improve the agreement with the data of meson decay constants and the heavy meson mass spectra over the previous computation handling the hyperfine interaction as perturbation.

We study the ${\mathrm{\Lambda }}_c$ decay process to ${\pi }^{+}$ and the meson-baryon final state for the analysis of $\mathrm{\Lambda }$ resonances. Considering the Cabibbo-Kobayashi-Maskawa matrix, color suppression, diquark correlation, and the kinematical condition, we show that the final meson-baryon state should be in a pure $I=0$ combination, when the meson-baryon invariant mass is small. Because the $I=1$ contamination usually makes it difficult to analyze $\mathrm{\Lambda }$ resonances directly from experiments, the ${\mathrm{\Lambda }}_c$ decay is an ideal process to study $\mathrm{\Lambda }$ resonances. Calculating the final-state interaction by chiral unitary approaches, we find that the $\pi \mathrm{\Sigma }$ invariant mass distributions have the same peak structure in the all charge combination of the $\pi \mathrm{\Sigma }$ states related to the higher pole of the two poles of the $\mathrm{\Lambda }\left(1405\right)$. Furthermore, we obtain a clear $\mathrm{\Lambda }\left(1670\right)$ peak structure in the $\overline{K}N$ and $\eta \mathrm{\Lambda }$ spectra.

The existence of possible $\eta$-nuclear bound states is closely related to the corresponding scattering lengths. While the sign of its real part may indicate a bound state, a large (always positive) imaginary part can prevent such a state. Most theoretical calculations for, e.g., ${}^3\text{He}$ predict quite sizable imaginary parts with no bound state. It is shown that a generalization of the conventional phenomenological optical model potential to coupled channels, based otherwise on the same assumptions but treating the pionic channel explicitly, can yield much smaller inelasticity still starting with elementary $\eta N$ interactions giving the same $\eta N$ scattering lengths. As representative examples this decrease is argued by model calculations in the cases of $\eta {}^3\text{He}$ and $\eta {}^{12}\text{C}$.

Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the $t$ channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process $\gamma +p\to K^{+}+{\mathrm{\Sigma }}^{*0}$ are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this paper we tackle this problem by employing a simple hybrid polynomial approach. The method is found to be robust and is valid for both deformed and nearly spherical nuclei. It also provides important and convenient initial guesses for spherical systems with large degeneracy. As an example, we apply the method to study the shape coexistence in neutron-rich Ni isotopes.

We investigate low-energy ${}^9\text{Be}$ elastic scattering on two different targets (heavy, light) within a four-body framework using the continuum-discretized coupled-channels (CDCC) method. The ${}^9\text{Be}$ projectile is described in an $\alpha +\alpha +n$ three-body model using the analytical transformed harmonic oscillator (THO) basis in hyperspherical coordinates. We show that continuum couplings are important in describing the elastic cross section, especially at low energies and on heavy targets. The dipolar contribution to the elastic cross section at energies around the Coulomb barrier is important but small compared to that of halo nuclei. The effect of the projectile low-energy resonances is also relevant. The agreement with the available experimental data supports the reliability of the method in describing reactions induced by three-body projectiles which include more than one charged particle.