The description of electromagnetic reactions at intermediate energies, such as pion electroproduction or (virtual) Compton scattering, traditionally starts from covariant tree-level Feynman diagrams (Born or pole terms). Internal hadron structure is included by means of (on-shell) form factors in the vertices while free propagators are used. To overcome problems with gauge invariance, simple prescriptions, such as, choosing $F_1^V{(q}^2{)=F}_{\pi }{(q}^2)$ in pion electroproduction or the “minimal substitution,” are used. We discuss the inherent assumptions of such approaches and study the general structure of electromagnetic vertices and propagators for pions and nucleons. We show which part of the vertex is entirely determined through the Ward-Takahashi identity and point out that detailed features of the $q^2$ dependence of the form factors cannot be derived from this condition. Recipes to enforce gauge invariance, including the minimal substitution, are critically examined in the light of the exact treatment. The interplay between irreducible contact terms and “off-shell effects” in vertices and propagators is demonstrated for real Compton scattering on a pion. The need for a consistent microscopic treatment of reaction amplitudes is stressed and illustrated by an example in the framework of chiral perturbation theory. Shortcomings of the minimal substitution method when applied to effective Lagrangians are pointed out.

An approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main feature of this approach is the method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz covariance of the current is ensured. In the electromagnetic case the current conservation law is also ensured. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for the lepton decay constant of pions.

One-proton and two-proton separation energies are calculated for proton-rich nuclei in the region $A=41\mathrm{}–75.$ The method is based on Skyrme Hartree-Fock calculations of Coulomb displacement energies of mirror nuclei in combination with the experimental masses of the neutron-rich nuclei. The implications for the proton drip line and the astrophysical $\mathrm{rp}$ process are discussed. This is done within the framework of a detailed analysis of the sensitivity of $\mathrm{rp}$ process calculations in type I x-ray burst models on nuclear masses. We find that the remaining mass uncertainties, in particular for some nuclei with $N=Z,$ still lead to large uncertainties in calculations of x-ray burst light curves. Further experimental or theoretical improvements of nuclear mass data are necessary before observed x-ray burst light curves can be used to obtain quantitative constraints on ignition conditions and neutron star properties. We identify a list of nuclei for which improved mass data would be most important.

Using the generalized Skyrme force SkSP1, we calculate the equation of state (EOS) of nuclear matter appropriate to stellar collapse; we consider the full density range corresponding to the passage from the droplet phase (isolated nuclei) through the bubble phase up to homogeneous nuclear matter. This force, having a term with simultaneous momentum and density dependence, is able to give a good fit to nuclear masses in Hartree-Fock-BCS calculations while having the nuclear-matter value of the effective nucleon mass. We find that in the two inhomogeneous phases the new EOS resembles closely that given by a conventional Skyrme force fitted to nuclear masses, while in the homogeneous phase it rapidly crosses over with increasing density to approach the EOS given by a conventional Skyrme force with the correct nuclear-matter value of the effective mass. Thus it is possible with a Skyrme-type force to obtain an EOS with the correct effective-mass properties at both extremities of the density range.

We present results of microscopic calculations of the strength function $S\left(E\right)\mathrm{}$ and $\alpha$-particle excitation cross sections $\sigma \mathrm{}\left(E\right)\mathrm{}$ for the isoscalar giant dipole resonance (ISGDR). An accurate and general method to eliminate the contributions of spurious state mixing is presented and used in the calculations. Our results provide a resolution to the long standing problem that the nuclear matter incompressibility coefficient K deduced from $\sigma \mathrm{}\left(E\right)\mathrm{}$ data for the ISGDR is significantly smaller than that deduced from data for the isoscalar giant monopole resonance.

Sideward flow values have been determined with the INDRA multidetector for Ar+Ni, Ni+Ni, and Xe+Sn systems studied at GANIL in the $30A$ to $100A$ MeV incident energy range. The balance energies found for Ar+Ni and Ni+Ni systems are in agreement with previous experimental results and theoretical calculations. Negative sideward flow values have been measured. The possible origins of such negative values are discussed. They could result from a more important contribution of evaporated particles with respect to the contribution of promptly emitted particles at midrapidity. But effects induced by the methods used to reconstruct the reaction plane cannot be totally excluded. Complete tests of these methods are presented and the origins of the “autocorrelation” effect have been traced back. For heavy fragments, the observed negative flow values seem to be mainly due to the reaction plane reconstruction methods. For light charged particles, these negative values could result from the dynamics of the collisions and from the reaction plane reconstruction methods as well. These effects have to be taken into account when comparisons with theoretical calculations are done.

We present results obtained in the calculation of nuclear ground-state properties in relativistic Hartree approximation using a Lagrangian whose QCD-scaled coupling constants are all natural (dimensionless and of order one). Our model consists of four-, six-, and eight-fermion point couplings (contact interactions) together with derivative terms representing, respectively, two-, three-, and four-body forces and the finite ranges of the corresponding mesonic interactions. The coupling constants have been determined in a self-consistent procedure that solves the model equations for representative nuclei simultaneously in a generalized nonlinear least-squares adjustment algorithm. The extracted coupling constants allow us to predict ground-state properties of a much larger set of even-even nuclei to good accuracy. The fact that the extracted coupling constants are all natural leads to the conclusion that QCD scaling and chiral symmetry apply to finite nuclei.

We point out that the proton-neutron energy contribution, for low multipoles (in particular, for the quadrupole component), effectively renormalizes the strength of the pairing interaction acting amongst identical nucleons filling up a single-$j$ or a set of degenerate many-$j$ shells. We carry out the calculation in lowest-order perturbation theory. We perform a study of this correction in various mass regions. These results may have implications for the use of pairing theory in medium-heavy nuclei and for the study of pairing energy corrections to the liquid drop model when studying nuclear masses.

We present theoretical results on the non-flux-averaged ${}^{208}\mathrm{Pb}({\nu }_e{,e}^{-}{)}^{208}\mathrm{Bi}$ and ${}^{208}\mathrm{Pb}({\nu }_{\mu },{\mu }^{-}{)}^{208}\mathrm{Bi}$ reaction cross sections, obtained within the charge-exchange random-phase-approximation. A detailed knowledge of these cross sections is important in different contexts. In particular, it is necessary to assess the possibility of using lead as a detector in future experiments on supernova neutrinos, such as OMNIS and LAND, and eventually detect neutrino oscillation signals by exploiting the spectroscopic properties of ${}^{208}\mathrm{Bi}.$ We discuss the present status on the theoretical predictions of the reaction cross sections.

Using the particle-rotor model in which one high-$j$ quasiparticle is coupled to the core of triaxial shape, wobbling excitations are studied. The family of wobbling phonon excitations can be characterized by: (a) very similar intrinsic structure while collective rotation shows the wobbling feature; (b) strong $B(E2;\overrightarrow{I}I-1)$ values for $\Delta n_w=1\mathrm{}$ transitions where $n_w$ expresses the number of wobbling phonons. For the Fermi level lying below the high-$j$ shell with the most favorable triaxiality γ≈+20°, the wobbling phonon excitations may be more easily identified close to the yrast line, compared with the Fermi level lying around the middle of the shell with γ≈-30°. The spectroscopic study of the yrast states for the triaxial shape with -60°<γ<0 are illustrated by taking a representative example with γ=-30°, in which a quantum number related with the special symmetry is introduced to help the physics understanding.

In this paper we seek a measure of the neutron density of ${}^{208}\mathrm{Pb}$ from analyses of intermediate-energy nucleon elastic scattering. The pertinent model for such analyses is based on coordinate space nonlocal optical potentials obtained from model nuclear ground-state densities. Those potentials give predictions of integral observables and of angular distributions, which show sensitivity to the neutron density. When compared with experiment, and correlated with analyses of electron scattering data, the results suggest that ${}^{208}\mathrm{Pb}$ has a neutron skin thickness of $\sim 0.17\hspace{0.5em}\mathrm{fm}.$

The series of high-$K$ multiquasiparticle bands in ${}^{172,173,174,175}\mathrm{Hf}$ are investigated using the particle-number-conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. The experimental results, including the moments of inertia and angular momentum alignments relative to the ground state band ${}^{172}\mathrm{Hf}(\mathrm{g}.\mathrm{s}.\mathrm{b}.\mathrm{})$ are reproduced quite well by the PNC calculation, in which no free parameter is involved. The difference in the $\omega$ variation of the moments of inertia between the high-$K$ multiquasiparticle bands and ${}^{172}\mathrm{Hf}(\mathrm{g}.\mathrm{s}.\mathrm{b}.\mathrm{})$ is mainly due to the blocking effects of high j intruder orbitals near the Fermi surface. The $\omega$ variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each major shell and from each cranked orbital are investigated.

We have observed seven γ rays following subthermal-neutron capture by ${}^{208}\mathrm{Pb}$ and incorporated them into a level scheme of ${}^{209}\mathrm{Pb}$ consisting of five excited levels. The measured neutron separation energy of ${}^{209}\mathrm{Pb}$ is 3938.0±0.5 keV. The thermal-neutron capture cross section of ${}^{208}\mathrm{Pb}$ was determined to be 230±12 μb. The theoretical estimates are 860 μb or 550 μb, depending on the model used for the compound-nuclear component; however, these values are not inconsistent with the data if the statistical distribution of the theoretical estimates is taken into account. The thermal-neutron capture cross sections for ${}^{206}\mathrm{Pb}$ and ${}^{207}\mathrm{Pb}$ were also determined and found to be 26.6±1.2 mb and 610±30 mb, respectively.

Excited states in ${}^{181}\mathrm{Hf},$ populated in the ${}^{180}\mathrm{Hf}\mathrm{}(d,p)\mathrm{}$ deuteron breakup reactions, were investigated by in-beam $\gamma$-ray spectroscopy. The ${1/2}^{-}\left[510\right]$ ground band and the ${3/2}^{-}\left[512\right]$ and ${7/2}^{-}\left[503\right]$ excited bands are extended to higher spins than previously known. The Coriolis coupling of the ${1/2}^{-}\left[510\right]$ and ${3/2}^{-}\left[512\right]$ bands is found to be consistent with that derived for the same bands in the classic case of ${}^{183}\mathrm{W}.$

Recent experiments have confirmed the existence of rotational bands in the $A\sim 110$ mass region with very extended shapes lying between super- and hyperdeformation. Using the projected shell model, we make a first attempt to describe quantitatively such a band structure in ${}^{108}\mathrm{Cd}.$ Excellent agreement is achieved in the dynamic moment of inertia ${\mathfrak{I}}^{\mathrm{}\left(2\right)\mathrm{}}$ calculation. This allows us to suggest the spin values for the energy levels, which are experimentally unknown. It is found that, at this large deformation, the sharply down-sloping orbitals in the proton $i_{13/2}$ subshell are responsible for the irregularity in the experimental ${\mathfrak{I}}^{\mathrm{}\left(2\right)\mathrm{}},$ and the wave functions of the observed states have a dominant component of two-quasiparticles from these orbitals. Measurement of transition quadrupole moments and g factors will test these findings, and thus can provide a deeper understanding of the band structure at very extended shapes.

The properties of even-even O, Ca, Ni, Zr, Sn, and Pb isotopes from the $\beta$-stability line to the neutron drip line are studied with the relativistic continuum Hartree-Bogoliubov theory, where both the spin-orbit interaction and continuum are properly taken into account. The available experimental binding energies $E_b$ and two-neutron separation energies $S_{2n}$ are reproduced very well. The predicted neutron drip-line nuclei are, respectively, ${}^{74}\mathrm{Ca},$ ${}^{100}\mathrm{Ni},$ ${}^{140}\mathrm{Zr},$ ${}^{176}\mathrm{Sn},$ and ${}^{268}\mathrm{Pb}.$ Based on the analysis of two-neutron separation energies, single-particle energy levels, the orbital occupation, the contribution of continuum and nucleon density distribution, giant halo phenomena due to pairing, correlation and the contribution from the continuum are suggested to appear in Ca isotopes with $A>\mathrm{}60\mathrm{}$ apart from Zr isotopes predicted earlier.

The triaxial deformation in ${}^{10}\mathrm{Be}$ is investigated using a microscopic $\alpha +\alpha +n+n$ model. The states of two valence neutrons are classified based on the molecular-orbit (MO) model, and the π orbit is introduced about the axis connecting the two α clusters for the description of the rotational bands. There appear two rotational bands comprised mainly of $K^{\pi }{=0\mathrm{}}^{+}$ and $K^{\pi }{=2\mathrm{}}^{+},$ respectively, at low excitation energy, where the two valence neutrons occupy $K^{\pi }{=3/2\mathrm{}}^{-}$ or $K^{\pi }{=1/2\mathrm{}}^{-}$ orbits. The triaxiality and the K mixing are discussed in connection to the molecular structure, particularly to the spin-orbit splitting. The extent of the triaxial deformation is evaluated in terms of the electromagnetic transition matrix elements (Davydov-Filippov model, Q-invariant model) and density distribution in the intrinsic frame. The obtained values turned out to be γ=15°–20°.

The level structure of several Zr isotopes near $A=94\mathrm{}{(}^{92,93,94,95}\mathrm{Zr})$ has been studied in the fission of the compound nucleus ${}^{197}\mathrm{Pb},$ formed in the ${}^{24}\mathrm{Mg}{+}^{173}\mathrm{Yb}$ reaction at ${E(}^{24}\mathrm{Mg})=134.5\mathrm{}\hspace{0.5em}\mathrm{MeV}.$ Sequences of $\gamma$-ray transitions, observed in coincidence with known transitions in the complementary Mo fragments, have been newly assigned to ${}^{93,95}\mathrm{Zr}.$ The previously known level scheme of ${}^{94}\mathrm{Zr}$ has been considerably extended to higher excitations, and exhibits structural similarities to the level scheme of ${}^{92}\mathrm{Zr}$ up to spin $10ħ.$ The level schemes of ${}^{93}\mathrm{Zr}$ and ${}^{95}\mathrm{Zr}$ can be generally interpreted as the coupling of a $d_{5/2}$ neutron to the levels of ${}^{92,94}\mathrm{Zr}$ and ${}^{96}\mathrm{Zr},$ respectively. The observed experimental states are compared with theoretical shell-model calculations.

By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility $K_A$ has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of $K_A$ for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made.

An analysis of the available experimental data on the fusion and fission of the nuclei of ${}^{286}112,$ ${}^{292}114,$ and ${}^{296}116,$ produced in the reactions ${}^{48}\mathrm{Ca}{+}^{238}\mathrm{U},$ ${}^{48}\mathrm{Ca}{+}^{244}\mathrm{Pu},$ and ${}^{48}\mathrm{Ca}{+}^{248}\mathrm{Cm},$ as well as experimental data on the survival probability of those nuclei in evaporation channels with three- and four-neutron emission, enables the quite reliable conclusion that the fission barriers of those nuclei are really quite high, which results in their relatively high stability. The lower limits that we obtained for the fission barrier heights of ${}^{283-286}112,$ ${}^{288-292}114,$ and ${}^{292-296}116$ nuclei are 5.5, 6.7, and 6.4 MeV, respectively.