We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g., neutrons) and addresses the problem of how many seniority-conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.

The nucleus ${}^{34}\mathrm{S}$ has been studied up to relatively high spin ($I=10\hslash$) and up to an excitation energy of 16.64 MeV. Data are compared with different shell model calculations where effective interactions involving two main shells, the sd and the fp, are used. For the first time in an $N\ne Z$ nucleus, it is observed that the promotion of an isoscalar ($T=0$) proton-neutron pair to the fp shell becomes energetically favored at high spin.

The scaling functions $f({\psi }^{\text{'}})$ and $F(y)$ from the ${\psi }^{\text{'}}$- and $y$-scaling analyses of inclusive electron scattering from nuclei are explored within the coherent density fluctuation model (CDFM). In addition to the CDFM formulation in which the local density distribution is used, we introduce a new equivalent formulation of the CDFM based on the one-body nucleon momentum distribution (NMD). Special attention is paid to the different ways in which the excitation energy of the residual system is taken into account in $y$ and ${\psi }^{\text{'}}$ scaling. Both functions, $f({\psi }^{\text{'}})$ and $F(y)$, are calculated using different NMDs and compared with the experimental data for a wide range of nuclei. The good description of the data for $y<0$ and ${\psi }^{\text{'}}<0$ (including ${\psi }^{\text{'}}<-1$) makes it possible to show the sensitivity of the calculated scaling functions to the peculiarities of the NMDs in different regions of momenta. It is concluded that the existing data on ${\psi }^{\text{'}}$ and $y$ scaling are informative for NMDs at momenta not larger than $2.0–2.5{\text{fm}}^{-1}$. The CDFM allows us to study simultaneously and on the same footing the role of both basic quantities—the momentum and density distributions—for the description of scaling and superscaling phenomena in nuclei.

Excitation functions for ${}^{208–211}\mathrm{Fr}$ isotopes produced in the ${}^{18}\mathrm{O}+{}^{197}\mathrm{Au}$ fusion-evaporation reaction have been measured at $E_{\mathrm{lab}}=75\text{–}130$ MeV via characteristic $\alpha$ decays by means of an electrostatic deflector and a semiconductor detector. Data have been compared with calculations giving barrier-passing (capture) cross sections and probabilities of the compound nucleus decay into different channels according to the standard statistical model.

Before a quantum-mechanical calculation involving electromagnetic interactions is performed, the gauge to be used in expressing the potentials must be chosen. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations, approximations are made, which can destroy the gauge invariance of the predictions. We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is $\ge 2\mathrm{GeV}$, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.

Elliptic flow systematics for different hadron species have been explained by quark coalescence models. It has been argued that the elliptic anisotropy $v_2$ should scale with the number of quarks that comprise the hadron. We show how these arguments are sensitive to the relative role of anisotropies in the phase space density vs. anisotropies in the effective volume of emission. We also discuss the degree to which coalescence arguments differ from thermal models. Illustrative calculations based on solving the Boltzmann equation are presented along with the results of blast wave models. Although the issue is complicated, ambiguities might be clarified by measurements of source-size parameters for nucleons at higher transverse momenta.

The properties of possible ${\Theta }^{+}$ bound states in nuclei are described in relativistic mean-field formalism (RMF), in which the ${\Theta }^{+}$-meson coupling constants are deduced from the underlying quark structure of ${\Theta }^{+}$ baryon. Our RMF results show that there is an attractive ${\Theta }^{+}$-nucleus interaction and the ${\Theta }^{+}$ particle can be bound in nuclei to form ${\Theta }^{+}$ hypernuclei, which are predicted to be bound much more strongly than λ hypernuclei. The potential depth of ${\Theta }^{+}$ in nuclear matter is estimated. The general range found for the depth is from 50 to 90 MeV at normal nuclear matter density, depending on the values we used for the coupling constants. Our RMF results are compatible with an evaluation of ${\Theta }^{+}$ self-energy in the nucleus.

Superscaling analyses of few-GeV inclusive electron scattering from nuclei are extended to include not only quasielastic processes, but also the region where $\Delta$ excitation dominates. With reasonable assumptions about the basic nuclear scaling function extracted from data and information from other studies of the relative roles played by correlation and meson-exchange-current effects, it is shown that the residual strength in the resonance region can be accounted for through an extended scaling analysis. One observes scaling upon assuming that the elementary cross section by which one divides the residual to obtain a new scaling function is dominated by the $N\to \Delta$ transition and employing a new scaling variable suited to the resonance region. This yields a good representation of the electromagnetic response in both the quasielastic and $\Delta$ regions. The scaling approach is then inverted and predictions are made for charge-changing neutrino reactions at energies of a few GeV, with focus placed on nuclei that are relevant to neutrino oscillation measurements. For this, a relativistic treatment of the required weak interaction vector and axial-vector currents for both quasielastic and $\Delta$-excitation processes is presented.

We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and branch points of a quantum Hamiltonian in the complex-extended parameter space. This approach is applied in the interacting boson model, where it is shown to properly distinguish the first- and second-order phase transitions.

A study of the reaction ${}^{12}\mathrm{C}$($e,e^{\text{'}}p$)${}^{11}\mathrm{B}$ in parallel kinematics has been made for the missing-momentum region $250<p_m<310$ MeV/c at incident energies of 379 and 585 MeV. A Rosenbluth separation of the cross sections was carried out to extract the longitudinal and transverse structure functions $W_L$ and $W_T$. Calculations that include meson-exchange currents and isobar currents are seen to describe the data better than those using a one-body current only. For the first time, a comparison between the ${}^{12}\mathrm{C}$$(\gamma ,p)$ cross section and the transverse part of the ${}^{12}\mathrm{C}$$(e,e^{\text{'}}p$) cross section has been made versus an effective momentum that is defined in such a way as to minimize effects due to differences in final-state interactions. This comparison suggests that it may be possible to describe both reactions in one consistent framework if two-body currents are included.

Using an isospin- and momentum-dependent transport model we study near-threshold pion production in heavy-ion collisions induced by radioactive beams at the planned rare isotope accelerator (RIA). We revisit the question of probing the high-density behavior of nuclear symmetry energy $E_{\mathrm{sym}}(\rho )$ using the ${\pi }^{-}/{\pi }^{+}$ ratio. It is found that both the total and differential ${\pi }^{-}/{\pi }^{+}$ ratios remain sensitive to the $E_{\mathrm{sym}}(\rho )$ when the momentum-dependence of both the isoscalar and isovector potentials are consistently taken into account. Moreover, the multiplicity and spectrum of ${\pi }^{-}$ mesons are found more sensitive to the $E_{\mathrm{sym}}(\rho )$ than those of ${\pi }^{+}$ mesons. Finally, effects of the Coulomb potential on the pion spectra and ${\pi }^{-}/{\pi }^{+}$ ratio are also discussed.

A new method for obtaining the chemical potential dependence of the dressed quark propagator in the rainbow approximation of the Dyson-Schwinger equation is developed. In the above approximation we prove that the dressed quark propagator at finite chemical potential μ can be written as ${\mathcal{G}}_0^{-1}[\mu ]=i\gamma ·\tilde{p}A({\tilde{p}}^2)+B({\tilde{p}}^2)$ with ${\tilde{p}}_{\mu }=(\overrightarrow{p},p_4+i\mu )$. From this the chemical potential dependence of the “effective” two-quark condensate is evaluated. A comparison with previous results is given.

We apply a cluster model to an extensive set of heavy even-even nuclei in the rare-earth region and determine the optimal core-cluster decomposition of each nucleus from a least-squares fit to the energy spectrum of its ground-state band. Good fits are obtained using a mass-symmetric form of the core-cluster interaction. We find that the core-cluster charge products deduced from the fits and the corresponding $B(E2)$ values are strongly correlated, in support of an underlying cluster picture of these nuclei.

One of the non-Abelian features of parton energy loss is the ratio $\Delta E_g/\Delta E_q=9/4$ between gluon and quark jets. Since jet production rate is dominated by quark jets at high $x_T=2p_T/\sqrt{s}$ and by gluon jets at low $x_T$, high $p_T$ hadron suppression in high-energy heavy-ion collisions should reflect such a non-Abelian feature. Within a leading-order perturbative QCD parton model that incorporates transverse expansion and Woods-Saxon nuclear distribution, the energy dependence of large $p_T~5\text{−}20\mathrm{GeV}/$c hadron suppression is found to be sensitive to the non-Abelian feature of parton energy loss and could be tested by data from low-energy runs at Brookhaven National Laboratory's relativistic heavy-ion collider or data from the large hadron collider.

In the fusion-evaporation reaction ${}^{40}\mathrm{Ca}+{}^{24}\mathrm{Mg}$ at $104\text{MeV}$ beam energy, excited states have been observed for the first time in the isotope ${{}^{31}{}_{61}\mathrm{Ga}}_{30}$. The experimental setup comprised the Ge array CLARION, a recoil mass spectrometer and, in its focal plane, an ionization chamber. Five transitions in ${}^{61}\mathrm{Ga}$ are identified, out of which a cascade of three transitions has been established by means of recoil-$\gamma \gamma$ coincidences. The strong transitions at $271\text{keV}$ in ${}^{61}\mathrm{Ga}$ and $124\text{keV}$ in ${}^{61}\mathrm{Zn}$ are viewed as the “mirror” $5/2^{-}\to 3/2^{-}$ ground-state transitions. The rather large energy difference of $150\text{keV}$ is suggested to arise from Coulomb monopole contributions. Shell-model calculations support this interpretation.

Systematic analysis of the deformations of proton and neutron densities in even-even C isotopes was performed based on a method of antisymmetrized molecular dynamics. $E2$ transition strengths were discussed in relation to the deformations. We analyzed the $B(E2;2_1^{+}\to 0_1^{+})$ in ${}^{16}\mathrm{C}$, which has been found to be abnormally small in the recent measurement. The results suggest a difference between proton and neutron shapes in the neutron-rich C isotopes. It was found that the stable proton structure in C isotopes plays an important role in the enhancement of the neutron skin structure as well as in the systematics of $B(E2)$ in the neutron-rich C.

We have studied spin-isospin excitations in ${}^{58}\mathrm{Co}$ via the ($n$,$p$) type ${}^{58}\mathrm{Ni}$($d$,${}^2\mathrm{He}$)${}^{58}\mathrm{Co}$ reaction at small angles and an incident deuteron energy of 170 MeV. An energy resolution of 130 keV, full width at half maximum, was obtained allowing the extraction of Gamow-Teller strength to 13 individual levels in ${}^{58}\mathrm{Co}$ below an excitation energy of 4.1 MeV. These $\Delta L=0$ transitions were identified by comparing the measured angular distributions with distorted-wave Born approximation (DWBA) calculations. A multipole decomposition analysis based on those DWBA calculations allowed the determination of the fractions of the $\Delta L=0$, 1, 2 components in the excitation spectrum. The experimental results are in reasonable agreement with large-scale shell-model calculations.

An unexpected strong interaction between normal deformed and triaxial strongly deformed levels at high spin, $\sim 32\hslash$, is observed in ${}^{167}\mathrm{Lu}$. This constitutes the first observation of accidental degeneracy, at such high spins, causing cross talk between levels in the normal deformed and in the second potential well in any known mass region. Furthermore, evidence of quasi-particle excitations highly competing with the wobbling excitation mode in a triaxial superdeformed well has been established in ${}^{167}\mathrm{Lu}$.

Systematic calculations on spontaneous fission half-lives of heavy nuclei are carried out by Swiatecki's formula with new parameters and by its generalized form. A new formula with only four parameters is also proposed for spontaneous fission half-lives. Experimental half-lives are well reproduced by the three formulas. We have found from systematic analysis of available data that there is a long lifetime line of spontaneous fission $N=Z+52$ for heavy elements with $Z\ge 90$. The new formula can be used to predict the spontaneous fission half-lives of heavy nuclei not far away from this long lifetime line. The small deviation between experimental half-lives and theoretical ones from the new formula is analyzed and discussed.

Radiative pion photoproduction in the $\Delta (1232)$-resonance region is studied with the aim of accessing the ${\Delta }^{+}(1232)$ magnetic dipole moment. We present a unitary model of the $\gamma p\to \gamma \pi N$ ($\pi N={\pi }^{0}p,{\pi }^{+}n$) reactions, where the $\pi N$ rescattering is included in an onshell approximation. In this model, the low-energy theorem which couples the $\gamma p\to \gamma \pi N$ process in the limit of a soft final photon to the $\gamma p\to \pi N$ process is exactly satisfied. We study the sensitivity of the $\gamma p\to \gamma {\pi }^{0}p$ process at higher values of the final photon energy to the ${\Delta }^{+}(1232)$ magnetic dipole moment. We compare our results with existing data and give predictions for forthcoming measurements of angular and energy distributions. It is found that the photon asymmetry and a helicity cross section are particularly sensitive to the ${\Delta }^{+}$ magnetic dipole moment.