The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for reactions as well as bound-state problems. The utility of the $R$-matrix approach is demonstrated in relativistic impulse approximation calculations where exchange terms can be calculated exactly and scattering waves made orthogonal to bound-state wave functions.

The two-body photodisintegration of ${}^3\mathrm{He}$ has been investigated using tagged photons with energies from $14\text{−}31$ MeV at MAX-lab in Lund, Sweden. The two-body breakup channel was unambiguously identified by the (nonsimultaneous) detection of both protons and deuterons. This approach was made feasible by the overdetermined kinematic situation afforded by the tagged-photon technique. Proton- and deuteron-energy spectra were measured using four silicon surface-barrier detector telescopes located at a laboratory angle of ${90}^{°}$ with respect to the incident photon-beam direction. Average statistical and systematic uncertainties of $5.7\%$ and $6.6\%$ in the differential cross section were obtained for $11$ photon-energy bins with an average width of $1.2$ MeV. The results are compared to previous experimental data measured at comparable photon energies as well as to the results of two recent Faddeev calculations which employ realistic potential models and take into account three-nucleon forces and final-state interactions. Both the accuracy and precision of the present data are improved over those obtained in the previous measurements. The data are in good agreement with most of the previous results, and favor the inclusion of three-nucleon forces in the calculations.

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a $k$-particle Hilbert subspace can be mapped onto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Feng Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis shows that the standard pairing model with the first step approximation displays similar pair structures of the first few exact low-lying states of the model, which, therefore, provides a link between the two models.

An anisotropic harmonic oscillator Hamiltonian can be brought into invariant form under $\mathrm{SU}(3)$ transformations by applying nonlinear transformations to the oscillator bosons. The classification of the single-particle levels based on this covering group predicts magic numbers for the triaxial oscillator. It is shown that when the deformation $\left|\delta \right|$ is not too large, the physical operators are approximated by the group operators. Estimation is carried out for the alignment of orbital angular momentum in a triaxial field.

$\gamma$-rays following the $\beta$ and $\beta \text{−}n$ decays of the very neutron rich ${}_{31}^{84}{\mathrm{Ga}}_{53}$ produced by the photofission of ${}^{238}\mathrm{U}$ have been studied at the newly built ISOL facility of IPN Orsay: ALTO. Two activities were observed and assigned to two $\beta$-decaying states: ${}^{84}\mathrm{Ga}$${}^g$, $I^{\pi }=(0^{-})$ and ${}^{84}\mathrm{Ga}$${}^m$, $I^{\pi }=(3^{-},4^{-})$. Excitation energies of the $2_1^{+}$ and $4_1^{+}$ states of ${}_{32}^{84}{\mathrm{Ge}}_{52}$ were measured at $E(2_1^{+})=624.3$ keV and $E(4_1^{+})=1670.1$ keV. Comparison with HFB $+$ GCM calculations allows to establish the collective character of this nucleus. The excitation energy of the $1/2_1^{+}$ state in ${}_{32}^{83}{\mathrm{Ga}}_{51}$ known to carry a large part of the neutron $3s_{1/2}$ strength was measured at $247.8$ keV. Altogether these data allow to confirm the new single particle state ordering which appears immediately after the double $Z=28$ and $N=50$ shell closure and to designate ${}^{78}\mathrm{Ni}$ as a fragile and easily polarized doubly-magic core.

The ${}^{211,212}\mathrm{At}$ yields resulting from the interaction of the radioactive projectile ${}^8\mathrm{Li}$ with a ${}^{208}\mathrm{Pb}$ target have been measured at energies between $3$ and $8.5$ MeV above the Coulomb barrier. They are signatures for fusion of the whole charge but not necessarily the whole mass of the projectile, so they are included in a corresponding operational definition of complete fusion. Within this definition, a fusion suppression factor of $0.70\pm 0.02$ (stat.) $\pm 0.04$ (syst.) is deduced from a comparison to a one-dimensional barrier-penetration-model calculation using parameters extrapolated from values for ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ and ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ taken from the literature. Possible incomplete fusion processes are discussed and the results are fitted with a phenomenological model assuming breakup prior to fusion followed by capture of a ${}^7\mathrm{Li}$ fragment.

The properties of the nuclear isoscaling at finite temperature are investigated and the extent to which its parameter $\alpha$ holds information on the symmetry energy is examined. We show that, although finite temperature effects invalidate the analytical formulas that relate the isoscaling parameter $\alpha$ to those of the mass formula, the symmetry energy remains the main ingredient that dictates the behavior of $\alpha$ at finite temperatures, even for very different sources. This conclusion is not obvious as it is not true in the vanishing temperature limit, where analytical formulas are available. Our results also reveal that different statistical ensembles lead to essentially the same conclusions based on the isoscaling analysis, for the temperatures usually assumed in theoretical calculations in the nuclear multifragmentation process.

Currently, the only known way to obtain experimental information about the space-time structure of a heavy-ion collision is through two-particle momentum correlations. Azimuthally sensitive Hanbury-Brown–Twiss (HBT) intensity interferometry can complement elliptic flow measurements by constraining the spatial deformation of the source and its time evolution. Performing these measurements on photons allows us to access the fireball evolution at earlier times than with hadrons. Using ideal hydrodynamics to model the space-time evolution of the collision fireball, we explore theoretically various aspects of two-photon intensity interferometry with transverse momenta up to $2$ GeV, in particular the azimuthal angle dependence of the HBT radii in noncentral collisions. We highlight the dual nature of thermal photon emission, in both central and noncentral collisions, resulting from the superposition of QGP and hadron resonance gas photon production. This signature is present in both the thermal photon source function and the HBT radii extracted from Gaussian fits of the two-photon correlation function.

The suppression of large transverse momentum ($P_T$) hadrons in heavy-ion ($A$-$A$) collisions as compared to their scaled expectation from proton-proton ($p$-$p$) collisions due to the interaction of hard partons with the hot and dense QCD medium in $A$-$A$ collisions is experimentally a well-established phenomenon. Focusing on leading hadrons produced in hard processes, the medium effect appears as energy loss. Beyond that, the question is how the lost energy is redistributed in the medium. With increased experimental statistics and most importantly the kinematic range of the CERN Large Hadron Collider (LHC), studying the properties of full jets rather than leading hadrons is becoming feasible. On the theory side, analytic models and Monte-Carlo (MC) codes for in-medium shower evolution are being developed to describe jets in the medium. In this paper, expectations for medium-modified jet observables, the jet shapes, the thrust distribution, and the $n$-jet fraction, are computed with the MC code YaJEM for various scenarios of the parton-medium interaction which are all consistent with high-$P_T$ hadron suppression data. The computation is done at 20 and 100 GeV jet energy, corresponding to probing the kinematics typical of the BNL Relativistic Heavy Ion Collider (RHIC) and LHC, and the possibility of making an unbiased measurement of the observables is discussed.

We study theoretically the in-flight $(K^{-},N)$ reactions for the formation of light kaonic nuclear systems to get deeper physical insights on the spectra and to investigate the formation spectra of the reaction that will be observed at new facilities like the Japan Proton Accelerator Research Complex (J-PARC). We show the expected spectra for the formation of the $K^{-}\mathit{pp}$, $K^{-}\mathit{pn}$, $K^{-}\mathit{nn}$, and $K^{-}$-${}^{11}\mathrm{B}$ systems that are accessible by the $(K^{-},N)$ experiments. By considering the conversion part of the Green’s function, we show the missing mass spectra of the $(K^{-},N)$ reactions in coincident with the particle emissions due to $\overline{K}$ absorption. To calculate the cross sections, we use the so-called $T\rho$ approximation to evaluate the optical potential. As for the amplitude $T$, we adopt the chiral unitary amplitude of $\overline{K}N$ channel in vacuum for simplicity. The effects of the $p$-wave optical potential of $\Sigma (1385)$ channel and the contributions from ${\overline{K}}^0$ mixing in ${}^3\mathrm{He}$$(K^{-},n)$ reaction are also evaluated numerically. We also study the behavior of the poles of kaon Green’s function in nuclear matter. We conclude that ${}^3\mathrm{He}$$(K^{-},n)$ and ${}^3\mathrm{He}$$(K^{-},p)$ reaction spectra in coincident with the $\pi \Sigma$ emission may show the structure in the kaon bound region indicating the existence of the unstable kaonic nuclear states. As for the ${}^{12}\mathrm{C}$$(K^{-},p)$ spectra with the $\pi \Sigma$ emission, we may also observe the structure in the bound region, however, we need to evaluate the medium effects carefully for larger nuclei.

The spectral emission of neutrinos from a plasma in nuclear statistical equilibrium (NSE) is investigated. Particular attention is paid to the possible emission of high-energy ($>10$ MeV) neutrinos or antineutrinos. A newly developed numerical approach for describing the abundances of nuclei in NSE is presented. Neutrino emission spectra, resulting from general Fuller-Fowler-Newman conditions, are analyzed. Regions of T-$\rho$-$Y_e$ space favoring detectability are selected. The importance of critical $Y_e$ values with zero net rate of neutronization (${\dot{Y}}_e$) is discussed. Results are provided for the processing of matter under conditions typical for thermonuclear and core-collapse supernovae, presupernova stars, and neutron star mergers.

We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the $\sigma$ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

By making use of the isospin conservation by strong interaction, the Fermi $0\nu \beta \beta$ nuclear matrix element $M_F^{0\nu }$ is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total $M_F^{0\nu }$ provided a small isospin-breaking Fermi matrix element between the isobaric analog state in the intermediate nucleus and the ground state of the daughter nucleus could be measured, e.g., by charge-exchange reactions. Such a measurement could set a scale for the $0\nu \beta \beta$ nuclear matrix elements and help to discriminate between the different nuclear structure models in which calculated $M_F^{0\nu }$ may differ by as much as a factor of 5 (that translates to about 20% difference in the total $M^{0\nu }$).

High-spin states in ${}^{83}\mathrm{Rb}$ were populated in the reaction ${}^{11}\mathrm{B}+{}^{76}\mathrm{Ge}$ at beam energies of 45 and 50 MeV. $\gamma$ rays were detected with the spectrometer GASP. The level scheme of ${}^{83}\mathrm{Rb}$ was extended up to 13.9 MeV. Mean lifetimes of 23 levels were determined using the Doppler-shift-attenuation method. Among the bands newly established is a sequence comprising intense $M1$ transitions and crossover $E2$ transitions. This sequence turns out to be irregular and thus shows that magnetic rotation as observed in the neighboring odd-odd isotopes is not realized in this odd-even nuclide. Excited states in ${}^{83}\mathrm{Rb}$ were interpreted in terms of the shell model using the model space $\pi (0f_{5/2},1p_{3/2},1p_{1/2},0g_{9/2})\hspace{0.5em}\nu (1p_{1/2},0g_{9/2})$. The configurations predicted for the negative-parity $M1$ sequence reproduce the $M1$ transition strengths fairly well.

The ${}^{233}\mathrm{U}(n,f)$ cross section has been measured at the white neutron source n_TOF in a wide energy range with a dedicated fission ionization chamber. We report here the results from $~30$ meV to $1$ MeV neutron energy. The ${}^{233}\mathrm{U}(n,f)$ cross section has been determined relative to a reference sample of ${}^{235}\mathrm{U}(n,f)$ measured simultaneously with the same detector. The very high instantaneous neutron flux and the intrinsically low background of the n_TOF installation result in an accuracy around $3\%$ in the whole energy range, while the energy resolution of the neutron beam allows for an accurate description of the fission cross section by means of $R$-matrix analysis over a wide energy range. The results are, in general, in good agreement with the most recent high-accuracy measurement of this fission cross section, over the more limited range of the previous measurements, and indicated that even the latest evaluations underestimate the cross section in the epithermal region. The present high-quality data provide the basis for a more precise evaluation of the ${}^{233}\mathrm{U}$ fission cross section and for improving the reliability of databases needed for the design of new energy systems based on the Th/U cycle.

The renormalization, finiteness, and off-shellness of short distance inverse-power singular interactions are discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding on-shell amplitude without proliferation of new counterterms. We illustrate the result by complementary calculations both in coordinate as well as in momentum space in the simplest ${}^1{S}_0$ channel for chiral $\mathit{np}$ interactions including two pion exchange.

We verify that quasi-elastic (elastic$+$inelastic) backscattering barrier distributions for weakly-bound systems do not strictly correspond to fusion barrier distributions, but rather to a reaction threshold distribution, as proposed by Zagrebaev [Phys. Rev. C 78, 047602 (2008)] in a recent paper concerning very heavy systems.

Absolute branching ratios to unbound states in ${}^{12}\mathrm{C}$ populated in the $\beta$ decays of ${}^{12}\mathrm{N}$ and ${}^{12}\mathrm{B}$ are reported. Clean sources of ${}^{12}\mathrm{N}$ and ${}^{12}\mathrm{B}$ were obtained using the isotope separation on-line (ISOL) method. The relative branching ratios to the different populated states were extracted using single-alpha as well as complete kinematics triple-alpha spectra. These two largely independent methods give consistent results. Absolute normalization is achieved via the precisely known absolute branching ratio to the bound 4.44 MeV state in ${}^{12}\mathrm{C}$. The extracted branching ratios to the unbound states are a factor of three more precise than previous measurements. Branching ratios in the decay of ${}^{20}\mathrm{Na}$ are also extracted and used to check the results.

The two-body photodisintegration of ${}^4\mathrm{He}$ into a proton and a triton has been studied using the CEBAF Large-Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. Real photons produced with the Hall-B bremsstrahlung-tagging system in the energy range from $0.35$ to $1.55$ GeV were incident on a liquid ${}^4\mathrm{He}$ target. This is the first measurement of the photodisintegration of ${}^4\mathrm{He}$ above $0.4$ GeV. The differential cross sections for the $\gamma$${}^4\mathrm{He}$$\to \mathit{pt}$ reaction were measured as a function of photon-beam energy and proton-scattering angle and are compared with the latest model calculations by J.-M. Laget. At $0.6\text{−}1.2$ GeV, our data are in good agreement only with the calculations that include three-body mechanisms, thus confirming their importance. These results reinforce the conclusion of our previous study of the three-body breakup of ${}^3\mathrm{He}$ that demonstrated the great importance of three-body mechanisms in the energy region $0.5\text{−}0.8$ GeV.

Highly charged relativistic heavy ions have high cross sections for two-photon interactions. The photon flux is high enough that two-photon interactions may be accompanied by additional photonuclear interactions. Except for the shared impact parameter, these interactions are independent. Additional interactions like mutual Coulomb excitation are of experimental interest, because the neutrons from the nuclear dissociation provide a simple, relatively unbiased trigger. We calculate the cross sections, rapidity, mass, and transverse momentum $(p_T)$ distributions for exclusive $\gamma \gamma$ production of mesons and lepton pairs and for $\gamma \gamma$ reactions accompanied by mutual Coulomb dissociation. The cross sections for $\gamma \gamma$ interactions accompanied by multiple neutron emission $(\mathit{XnXn})$ and single-neutron emission ($1n1n$) are about $1/10$ and $1/100$ of that for the unaccompanied $\gamma \gamma$ interactions. We discuss the accuracy with which these cross sections may be calculated. The typical $p_T$ of $\gamma \gamma$ final states is several times smaller than for comparable coherent photonuclear interactions, so $p_T$ may be an effective tool for separating the two classes of interactions.