Calculations of the decay widths of three-body resonances are considered using both $R$-matrix and dynamical three-body theoretical models. The $R$-matrix approach, which treats the three-body decay as two, ordered two-body decays, has both simultaneous and sequential particle emission pathways, each with an associated decay width. The question of how these two widths should be combined to determine the total resonance width is considered using comparisons with the width deduced from fully dynamical three-body model calculations. We use the decay of the well-understood ${}^6\mathrm{He}$($2^{+}$, $1.8$ MeV) resonance (into ${}^4\mathrm{He}+n+n$) as a benchmark case.

In an earlier paper we developed a QCD-inspired theoretical parton bubble model (PBM) for RHIC/LHC. The motivation for the PBM was to develop a model that would reasonably quantitatively agree with the strong charged particle pair correlations observed by the STAR Collaboration at RHIC in $\mathrm{Au}+\mathrm{Au}$ central collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in the transverse momentum range 0.8 to 2.0 GeV/$c$. The model was constructed to also agree with the Hanbury Brown and Twiss (HBT) observed small final-state source size $~2$ fm radii in the transverse momentum range above 0.8 GeV/$c$. The model assumed a substructure of a ring of localized adjoining $~2$ fm radius bubbles perpendicular to the collider beam direction, centered on the beam, at midrapidity. The bubble ring was assumed to be located on the expanding fireball surface of the $\mathrm{Au}+\mathrm{Au}$ collision. These bubbles consist almost entirely of gluons and form gluonic hot spots on the fireball surface. We achieved a reasonable quantitative agreement with the results of both the physically significant charge-independent (CI) and charge-dependent (CD) correlations that were observed. In this paper we extend the model to include the changing development of bubbles with centrality from the most central region where bubbles are very important to the most peripheral where the bubbles are gone. Energy density is found to be related to bubble formation and as centrality decreases the maximum energy density and bubbles shift from symmetry around the beam axis to the reaction plane region, causing a strong correlation of bubble formation with elliptic flow. We find reasonably quantitative agreement (within a few percent of the total correlations) with a new precision RHIC experiment that extended the centrality region investigated to the range 0%–80% (most central to most peripheral). The characteristics and behavior of the bubbles imply they represent a significant substructure formed on the surface of the fireball at kinetic freezeout.

We establish that QED3 can possess a critical number of flavors, $N_f^c$, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalization and photon vacuum polarization are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarization and fermion-photon vertex are used to illustrate these observations. The existence and value of $N_f^c$ are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.

Wigner symmetry in nuclear physics provides a unique example of a nonperturbative medium and long distance symmetry, a symmetry strongly broken at short distances. We analyze the consequences of such a concept within the framework of one-boson exchange potentials in $\mathit{NN}$ scattering and keeping the leading $N_c$ contributions. Phenomenologically successful relations between singlet ${}^1{S}_0$ and triplet ${}^3{S}_1$ scattering phase shifts are provided in the entire elastic region. We establish symmetry breaking relations among noncentral phase shifts which are successfully fulfilled by even-$L$ partial waves and strongly violated by odd-$L$ partial waves, in full agreement with large $N_c$ requirements.

We study the influence of $\Lambda$ hyperons on neutron drip properties in hypernuclear matter and hypernuclei, using a microscopic $\Lambda N$ force. We find an extension of the neutron drip line in bulk matter and stabilization of neutron-rich isotopes due to added hyperons.

The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analyzed by comparison with the dynamical eikonal approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into account both nuclear and Coulomb interactions on the same footing within the computationally efficient eikonal model. Excellent results are found for the dissociation of ${}^{11}\mathrm{Be}$ on lead at 69 MeV/nucleon. This Coulomb-corrected eikonal approximation provides a competitive alternative to more elaborate reaction models for investigating breakup of three-body projectiles at intermediate and high energies.

We apply the parton recombination approach to study the energy dependence of the elliptic flow, $v_2$, in heavy ion collisions from BNL Alternating Gradient Synchrotron (AGS) to CERN Large Hadron Collider (LHC) energies. The relevant input quantities ($T,{\mu }_B,{\eta }_T$) at the various center of mass energies are obtained from fits to the available data. The model yields a good description of the integrated $v_2$ data for charged particles at midrapidity from AGS to BNL Relativistic Heavy Ion Collider (RHIC) energies. In stark contrast to the current expectations, we observe a decrease of the integrated $v_2$ values above the highest RHIC energy. Thus, we predict a decrease of $v_2$ at LHC energies compared to the RHIC results. This drop is attributed to negative $v_2$ values for the underlying parton distributions at low to moderate transverse momenta that develop if the transverse flow velocity is high enough. At energies above the LHC regime, the present approach predicts even negative values for the integrated $v_2$.

The phonon and quasiparticle structure of the low-lying states in ${}^{188,190,192}\mathrm{Os}$ is investigated within the microscopic quasiparticle-phonon model. An overall agreement with the data is obtained for energies and transitions. The properties of the $0^{+}$ states are found to be correlated with the evolution of the nuclear shape toward the $\gamma$-soft region. Special attention is devoted at the $4_3^{+}$ state. This state is found to be composed of a large double-$\gamma$ phonon component coexisting with an even larger one-phonon hexadecapole piece. Such a mixed phonon structure explains the observed, apparently contradictory, properties of the $4_3^{+}$ states in Os isotopes.

We investigate analytically and numerically a random-matrix model for $m$ fermions occupying ${\ell }_1$ single-particle states with positive parity and ${\ell }_2$ single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit defined by $m,{\ell }_{1,2}\to \infty$ and $m/{\ell }_{1,2}\to 0$, ground states with positive and negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.

Theoretical $\beta$-delayed-neutron spectra are calculated based on the Quasiparticle Random-Phase Approximation (QRPA) and the Hauser-Feshbach statistical model. Neutron emissions from an excited daughter nucleus after $\beta$ decay to the granddaughter residual are more accurately calculated than in previous evaluations, including all the microscopic nuclear structure information, such as a Gamow-Teller strength distribution and discrete states in the granddaughter. The calculated delayed-neutron spectra agree reasonably well with those evaluations in the ENDF decay library, which are based on experimental data. The model was adopted to generate the delayed-neutron spectra for all 271 precursors.

We review the formulation of Landau hydrodynamics and find that the rapidity distribution of produced particles in the center-of-mass system should be more appropriately modified as $\mathit{dN}/\mathit{dy}\propto \exp \{\sqrt{y_b^2-y^2}\}$, where $y_b=\ln \{\sqrt{s_{\mathit{NN}}}/m_p\}$ is the beam nucleon rapidity, instead of Landau's original distribution, $\mathit{dN}/\mathit{dy}(\mathrm{Landau})\propto \exp \{\sqrt{L^2-y^2}\}$, where $L=\ln \{\sqrt{s_{\mathit{NN}}}/2m_p\}$. The modified distribution agrees better with experimental $\mathit{dN}/\mathit{dy}$ data than the original Landau distribution and can be represented well by the Gaussian distribution, $\mathit{dN}/\mathit{dy}(\mathrm{Gaussian})\propto \exp \{-y^2/2L\}$. Past successes of the Gaussian distribution in explaining experimental rapidity data can be understood, not because it is an approximation of the original Landau distribution, but because it is in fact a close representation of the modified distribution. Predictions for pp and AA collisions at LHC energies in Landau hydrodynamics are presented.

Absolute transition probabilities for the first $2^{+}$ states in ${}^{110,114}\mathrm{Pd}$ were measured using the recoil distance Doppler shift technique following projectile Coulomb excitation at intermediate beam energy. This technique was applied for the first time to projectiles produced in a primary fragmentation reaction, which get Coulomb excited in a secondary reaction. The ${}^{110}\mathrm{Pd}$ data was used to check the novel experimental technique as well as the data analysis procedure, which is based on the examination of $\gamma$-ray line shapes. Whereas the measured $B(E2)$ value for ${}^{110}\mathrm{Pd}$ agrees very well with the literature, the value obtained for ${}^{114}\mathrm{Pd}$ differs considerably. The new experimental data are compared to calculations in the framework of the Interacting Boson Model. The data are also used to test the novel concept of valence proton symmetry, which allows for extrapolation of nuclear properties to very neutron-rich nuclei.

Three-pion correlations are conventionally analyzed using a chaotic component and a single coherent component of the emitted pions. The existence of source coherence in these experiments is suggested, but the detailed structure of the coherent component remains obscure. An improved understanding of the coherent processes is obtained by incorporating into the model general properties of pulsed radiation, inspired by the free-electron laser operation with multiple, mutually independent coherent source currents due to electron microbunching. This approach with multiple coherent components solves an inconsistency in the earlier three-pion data analysis and leads to a more appealing description of the experimental results.

The interference response function $f_{\mathit{LT}}(R_{\mathit{LT}})$ of the ${}^2\mathrm{H}(e,e^{\text{'}}p)n$ reaction has been determined at squared four-momentum transfer $Q^2=0.33\hspace{0.5em}(\mathrm{GeV}/c){}^2$ and for missing momenta up to $p_m=0.29\hspace{0.5em}\mathrm{GeV}/c$. The results have been compared to calculations that reproduce $f_{\mathit{LT}}$ quite well but overestimate the cross sections by 10–20% for missing momenta between $0.1\hspace{0.5em}\mathrm{GeV}/c$ and $0.2\hspace{0.5em}\mathrm{GeV}/c$.

The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its maximum exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields provided that other effects can be reliably isolated. Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion [H. Zdunczuk, W. Satula, and R. A. Wyss, Phys. Rev. C 71, 024305 (2005)] that the relative energies of the terminating states in the $N\ne Z,A~44$ mass region given by $\Delta E$ provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction in density functional theories has been reanalyzed. The current investigation shows that the $\Delta E$ value is affected also by the relative placement of the states with different orbital angular momentum $l$, namely, the placement of the $d$ ($l=2$) and $f$ ($l=3$) states. This indicates the dependence of the $\Delta E$ value on the properties of the central potential.

A complete survey is presented of all half-life and branching-ratio measurements related to the isospin $T=1/2$ mirror β transitions ranging from ${}^3\mathrm{He}$ to ${}^{83}\mathrm{Mo}$. No measurements are ignored, although some are rejected for cause. Using the decay energies obtained in the 2003 Mass Evaluation experimental $\mathit{ft}$ values are then determined for the transitions up to ${}^{45}\mathrm{V}$. For the first time also all associated theoretical corrections needed to convert these results into “corrected” $\mathcal{F}t$ values, similar to the superallowed $0^{+}\to 0^{+}$ pure Fermi β transitions, were calculated. Precisions of the resulting values are in most cases between 0.1 and 0.4%. These $\mathcal{F}{t}^{\mathrm{mirror}}$ values can now be used to extract precise weak interaction information from past and ongoing correlation measurements in the beta decay of the $T=1/2$ mirror β transitions.

The spin-cutoff parameter σ has been determined for experimental spin distributions at low excitation energies of 310 nuclei between ${}^{18}\mathrm{F}$ and ${}^{251}\mathrm{Cf}$ (more than 8000 levels with their spin). The results indicate a weak dependence on the mass number $A$ of the spin-cutoff parameter ${\sigma }^2~A^{0.28}$, and an even-odd spin staggering in the spin distribution of the even-even nuclei, with a strong enhancement of the number of states with spin zero. A modification of the spin-cutoff distribution formula is proposed in order to describe the even-even nuclei data. These findings are in good agreement with recent predictions of shell-model Monte Carlo calculations.

The magnitude of the ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction rate in asymptotic giant branch stars depends directly on the neutron spectroscopic factors of low-lying ${}^{16}\mathrm{N}$ levels. A new study of the ${}^{15}\mathrm{N}(d,p){}^{16}\mathrm{N}$ reaction is reported populating the ground and first three excited states in ${}^{16}\mathrm{N}$. The measured spectroscopic factors are near unity as expected from shell model calculations, resolving a long-standing discrepancy with earlier measurements that had never been confirmed or understood. Updated ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction rates are presented.

The $({\beta }^{-}{\beta }^{-}){}_{0\nu }$ decay of ${}^{94,96}\mathrm{Zr}$, ${}^{98,100}\mathrm{Mo}$, ${}^{104}\mathrm{Ru}$, ${}^{110}\mathrm{Pd}$, ${}^{128,130}\mathrm{Te}$, and ${}^{150}\mathrm{Nd}$ isotopes for the $0^{+}\to 0^{+}$ transition is studied in the projected Hartree-Fock-Bogoliubov framework. In our earlier work, the reliability of HFB intrinsic wave functions participating in the ${\beta }^{-}{\beta }^{-}$ decay of the above-mentioned nuclei has been established by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2:0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$, gyromagnetic factors $g(2^{+})$ as well as half-lives $T_{1/2}^{2\nu }$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $({\beta }^{-}{\beta }^{-}){}_{0\nu }$ decay for the $0^{+}\to 0^{+}$ transition in a mechanism involving neutrino mass and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives $T_{1/2}^{0\nu }(0^{+}\to 0^{+})$ using nuclear transition matrix elements calculated with the same set of wave functions. Further, the effect of deformation on the nuclear transition matrix elements required to study the $({\beta }^{-}{\beta }^{-}){}_{0\nu }$ decay in such a mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately the same magnitude in $({\beta }^{-}{\beta }^{-}){}_{2\nu }$ and $({\beta }^{-}{\beta }^{-}){}_{0\nu }$ decay.