We analyze the ability of a restricted variation after projection method to achieve the full variation after projection solution in a pairing Hamiltonian. The study of the projected potential energy surfaces defined along the fluctuations of the particle number $(\Delta N){}^2$ and $(\Delta N){}^4$ allows the enlargement of the variational space to take into account more correlations within the projection after the variation framework. The results show the equivalence of the full variational projected solution to a restricted projected solution with an educated choice of the restricted variational space. Finally, we show that the Lipkin-Nogami approach can be derived, under certain conditions, in an variational context and that the projected Lipkin-Nogami approach represents an approximation to a restricted variation after projection method with the $(\Delta N){}^2$ as degree of freedom.

Based on the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts, simultaneous ${\chi }^2$ analyses are performed for elastic scattering, DR, and fusion cross section data for the ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ system at near-Coulomb-barrier energies. Similar ${\chi }^2$ analyses are also performed by taking into account only the elastic scattering and fusion data as was previously done by the present authors, and the results are compared with those of the full analysis including the DR cross section data as well. We find that the analyses using only elastic scattering and fusion data can produce very consistent and reliable predictions of cross sections, particularly when the DR cross section data are incomplete. Discussions are also given on the results obtained from similar analyses made earlier for the ${}^9\mathrm{Be}+{}^{209}\mathrm{Bi}$ system.

The fission processes of ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ and ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ are simulated with the combination of the Langevin equation and the statistical decay model. The masses of two fission fragments are given by assuming the process of symmetric fission or asymmetric fission by Monte Carlo sampling with the Gaussian probability distribution. From the analysis of the isotopic/isotonic ratios of the fission fragments from both reactions, the isoscaling behavior has been observed and investigated in detail. Isoscaling parameters α and β are extracted as a function of the charge number and neutron number, respectively, in different widths of the sampling Gaussian probability distribution. It seems that α is sensitive to the width of fission probability distribution of the mass asymmetrical parameter, but β is not. Both α and β drop with increasing beam energy and reduced friction parameter.

We describe in detail how the different components of a multiphase transport (AMPT) model that uses the heavy ion jet interaction generator (HIJING) for generating the initial conditions, Zhang's parton cascade (ZPC) for modeling partonic scatterings, the Lund string fragmentation model or a quark coalescence model for hadronization, and a relativistic transport (ART) model for treating hadronic scatterings are improved and combined to give a coherent description of the dynamics of relativistic heavy ion collisions. We also explain the way parameters in the model are determined and discuss the sensitivity of predicted results to physical input in the model. Comparisons of these results to experimental data, mainly from heavy ion collisions at the BNL Relativistic Heavy Ion Collider, are then made in order to extract information on the properties of the hot dense matter formed in these collisions.

We derive a general formula for the correlation function of two identical particles with the inclusion of multiple elastic scatterings in the medium in which the two particles are produced. This formula involves the propagator of the particle in the medium. As an illustration of the effect we apply the formula to the special case where the scatterers are static, localized two-body potentials. In this illustration both $R_{\mathrm{side}}^2$ and $R_{\mathrm{out}}^2$ are increased by an amount proportional to the square of the spatial density of scatterers and to the differential cross section. Specific numbers are used to show the expected magnitude of the rescattering effect on kaon interferometry.

If the deconfinement phase transformation of strongly interacting matter is of first order and the expanding chromodynamic matter created in a high-energy nuclear collision enters the corresponding region of phase coexistence, a spinodal phase separation might occur. The matter would then condense into a number of separate blobs, each having a particular net strangeness that would remain approximately conserved during the further evolution. We investigate the effect that such strangeness trapping may have on strangeness-related hadronic observables. The kaon multiplicity fluctuations are significantly enhanced and thus provide a possible tool for probing the nature of the phase transition experimentally.

To study isovector dipole responses of neutron-rich nuclei, we applied a time-dependent method of antisymmetrized molecular dynamics. The dipole resonances in Be, B, and C isotopes were investigated. In ${}^{10}\mathrm{Be}$, ${}^{15}\mathrm{B}$, and ${}^{16}\mathrm{C}$, collective modes of the vibration between a core and valence neutrons cause soft resonances at the excitation energy $E_x=10$–15 MeV below the giant dipole resonance (GDR). In ${}^{16}\mathrm{C}$, we found that a remarkable peak at $E_x=14$ MeV corresponds to the coherent motion of four valence neutrons against a ${}^{12}\mathrm{C}$ core, whereas the GDR arises in the $E_x>20$ MeV region because of vibration within the core. In ${}^{17}\mathrm{B}$ and ${}^{18}\mathrm{C}$, the dipole strengths in the low-energy region decline compared with those in ${}^{15}\mathrm{B}$ and ${}^{16}\mathrm{C}$. We also discuss the energy-weighted sum rule for the $E1$ transitions.

Following the lead of a recent work, I perform a variational principle model calculation for the nuclear caloric curve. A Skyrme-type interaction with and without momentum dependence is used. The calculation is done for a large nucleus, i.e., in the nuclear matter limit. Thus I address the issue of volume fragmentation only. Nonetheless, the results are similar to the previous, largely phenomenological calculation for a finite nucleus. I find that the onset of fragmentation can be sudden as a function of temperature or excitation energy.

It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels derived from chiral effective Lagrangians.

This Rapid Communication describes the measurement of elliptic flow for charged particles in Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The measured azimuthal anisotropy is presented over a wide range of pseudorapidity for three broad collision centrality classes for the first time at this energy. Two distinct methods of extracting the flow signal were used to reduce systematic uncertainties. The elliptic flow falls sharply with increasing $\left|\eta \right|$ at 200 GeV for all the centralities studied, as observed for minimum-bias collisions at $\sqrt{s_{\mathit{NN}}}=130$ GeV.

Pseudospin symmetry for the resonant states in ${}^{208}\mathrm{Pb}$ is investigated by solving the Dirac equation with Woods-Saxon vector and scalar potentials in combination with an analytic continuation in the coupling-constant method, where the influences of the coupling-constant interval and the Padé approximant order are analyzed, and the stable and convergent energies and widths are obtained. Pseudospin breaking is shown in correlation with the nuclear mean field shaped by the central depth ${\Sigma }_0$, a radius (range) R, and a diffusivity a, which play an important role in the splittings of energy and width. The energy-level crossings appear in several pseudospin partners of resonant states, where the decay time is found to be different for the pseudospin doublets even when their energies are fully degenerate.

The degree of collectivity in the neutron-rich nuclei ${}^{32}\mathrm{Mg}$ and ${}^{34}\mathrm{Mg}$ has been determined via intermediate-energy Coulomb excitation in inverse kinematics. Measured energies of the first excited $2^{+}$ states and reduced electric quadrupole transition probabilities $B(E2;0_{\text{g.s.}}^{+}\to 2_1^{+})$ are presented for ${}^{32}\mathrm{Mg}$ and ${}^{34}\mathrm{Mg}$. The results agree with previous measurements and confirm the placement of both nuclei within the “island of inversion.”

The β-decay of odd-A, neutron-rich ${}^{57}\mathrm{Ti}$ and ${}^{59}\mathrm{V}$ are studied. More precise β-decay half-lives of $98\pm 5$ and $97\pm 2$ ms are deduced for ${}^{57}\mathrm{Ti}$ and ${}^{59}\mathrm{V}$, respectively. In addition, β-delayed γ-ray spectroscopy is used to deduce β-decay branching ratios and establish the low-energy-level structures of the daughter nuclides. The new data for levels in ${}^{57}\mathrm{V}$ and ${}^{59}\mathrm{Cr}$ are compared with the results of shell-model calculations completed in the full pf model space. Both ${}^{57}\mathrm{V}$ and ${}^{59}\mathrm{Cr}$ show evidence of modest oblate deformation near the ground state.

A generalization of the complex shell model formalism is presented that includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation in which all states are treated on the same footing. Two-particle states are evaluated within this formalism, and observable two-particle resonances are defined. The formalism is illustrated in the well-known case of ${}^{11}\mathrm{Li}$ in its bound ground state and in ${}^{70}\mathrm{Ca}$(g.s.), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized complex shell model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.

Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a β-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong $\beta \text{−}\gamma$ coupling effects. The validity of the approximate separation of variables introduced with the $X(5)$ model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed.

We evaluate two-meson couplings of ${\Theta }^{+}$, using experimental information of nucleon resonances decaying into $\pi \pi N$ channels, in which the two pions are in scalar- and vector-type correlations. We examine two assignments of spin and parity of $J^P=1/2^{+}$ and $3/2^{-}$, for which the experimental spectra of known resonances with exotic baryons are properly reproduced by an octet-antidecuplet representation mixing scheme. With the obtained coupling constants, total cross sections of the reactions ${\pi }^{-}p\to K^{-}{\Theta }^{+}$ and $K^{+}p\to {\pi }^{+}{\Theta }^{+}$ are calculated. Substantial interference of two terms may occur in the reaction processes for the $J^P=1/2^{+}$ case, whereas the interference effect is rather small for the $3/2^{-}$ case.

Baryon chiral perturbation theory with explicit $\Delta (1232)$ degrees of freedom is considered. The most general interactions of pions, nucleons, and Δ consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon σ term, and the pole of the Δ propagator.

The ground-state Gamow-Teller transition in the decay of ${}^{14}\mathrm{O}$ is strongly hindered and the electron spectrum shape deviates markedly from the allowed shape. A reanalysis of the only available data on this spectrum changes the branching ratio assigned to this transition by seven standard deviations: Our new result is $(0.54\pm 0.02)\%$. The Kurie plot data from two earlier publications are also examined, and a revision to their published branching ratios is recommended. The required nuclear matrix elements are calculated with the shell model, and, for the first time, consistency is obtained between the M1 matrix element deduced from the analog γ transition in ${}^{14}\mathrm{N}$ and that deduced from the slope in the shape-correction function in the β transition, a requirement of the conserved-vector current hypothesis. This consistency is obtained, however, only if renormalized rather than free-nucleon operators are used in the shell-model calculations. In the mirror decay of ${}^{14}\mathrm{C}$, a similar situation occurs. Consistency among the ${}^{14}\mathrm{C}$ lifetime, the slope of the shape-correction function, and the M1 matrix element from γ decay can be achieved only with renormalized operators in the shell-model calculation.

Results are reported from the complete salt phase of the Sudbury Neutrino Observatory experiment in which NaCl was dissolved in the ${}^2\mathrm{H}$${}_2\text{O}$ (“${\text{D}}_2\text{O}$”) target. The addition of salt enhanced the signal from neutron capture as compared to the pure ${\text{D}}_2\text{O}$ detector. By making a statistical separation of charged-current events from other types based on event-isotropy criteria, the effective electron recoil energy spectrum has been extracted. In units of ${10}^6{\text{cm}}^{-2}{\text{s}}^{-1}$, the total flux of active-flavor neutrinos from ${}^8\mathrm{B}$ decay in the Sun is found to be ${4.94}_{-0.21}^{+0.21}{\text{(stat)}}_{-0.34}^{+0.38}\text{(syst)}$ and the integral flux of electron neutrinos for an undistorted ${}^8\mathrm{B}$ spectrum is ${1.68}_{-0.06}^{+0.06}{\text{(stat)}}_{-0.09}^{+0.08}\text{(syst)}$; the signal from (${\nu }_x,e$) elastic scattering is equivalent to an electron-neutrino flux of ${2.35}_{-0.22}^{+0.22}{\text{(stat)}}_{-0.15}^{+0.15}\text{(syst)}$. These results are consistent with those expected for neutrino oscillations with the so-called large mixing angle parameters and also with an undistorted spectrum. A search for matter-enhancement effects in the Earth through a possible day-night asymmetry in the charged-current integral rate is consistent with no asymmetry. Including results from other experiments, the best-fit values for two-neutrino mixing parameters are $\Delta m^2=({8.0}_{-0.4}^{+0.6})\times {10}^{-5}$ eV${}^2$ and $\theta =33.9_{-2.2}^{+2.4}$ degrees.

It has been argued by Buckley et al. [1] that nuclear matter is a type-I rather than a type-II superconductor. The suggested mechanism is a strong interaction between neutron and proton Cooper pairs, which arises from an assumed U(2) symmetry of the effective potential, which is supposed to originate in isospin symmetry of the underlying nuclear interactions. To test this claim, we perform an explicit mean-field calculation of the effective potential of the Cooper pairs in a model with a simple four-point pairing interaction. In the neutron star context, matter is very neutron rich with less than 10% protons, so there is no neutron-proton pairing. We find that under these conditions our model shows no interaction between proton Cooper pairs and neutron Cooper pairs at the mean-field level. We estimate the leading contribution beyond mean field and find that it is small and attractive at weak coupling.