Recent measurements of the ratio of the elastic electromagnetic form factors of the proton, $G_{\mathrm{Ep}}{/G}_{\mathrm{Mp}},$ using the polarization transfer technique at Jefferson Lab, show that this ratio decreases dramatically with increasing $Q^2,$ in contradiction to previous measurements using the Rosenbluth separation technique. Using these new high quality data as a constraint, we have reanalyzed most of the world $\mathrm{ep}$ elastic cross section data. In this paper, we present a new empirical fit to the reanalyzed data for the proton elastic magnetic form factor in the region $0<\mathrm{}{Q}^2<30\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^2.$ As well, we present an empirical fit to the proton electromagnetic form factor ratio, $G_{\mathrm{Ep}}{/G}_{\mathrm{Mp}},$ which is valid in the region $0.1<\mathrm{}{Q}^2<6\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^2.$

The yrast band of the $N=Z$ nucleus ${}^{84}\mathrm{Mo}$ has been extended up to the ${10}^{+}$ state. Its moment of inertia varies smoothly up to this state (rotational frequency 0.6 MeV). The new data confirm the systematic delay of the particle alignment frequency in $N=Z$ nuclei with respect to the neighboring $N>Z$ nuclei, which has been suggested as a signature of the neutron-proton pairing interaction. Projected shell model calculations performed for the heaviest $N=Z$ nuclei studied so far, ${}^{84}\mathrm{Mo}$ and ${}^{88}\mathrm{Ru},$ predict that the confirmation of a possible enhancement of the neutron-proton residual interaction requires the observation of still higher spins in these nuclei.

We implement a high order discrete derivative analysis of the low-lying collective energies of even-even nuclei with respect to the total number of valence nucleon pairs N in the framework of F-spin multiplets appearing in an algebraic $\mathrm{sp}\mathrm{}(4,R)\mathrm{}$ classification scheme. We find that for the nuclei of any given F multiplet the respective experimental energies exhibit a $\Delta N=2\mathrm{}$ staggering behavior and for the nuclei of two united neighboring F multiplets well pronounced $\Delta N=1\mathrm{}$ staggering patterns are observed. Those effects have been reproduced successfully through a generalized $\mathrm{sp}\mathrm{}(4,R)\mathrm{}$ model energy expression and explained in terms of the steplike changes in collective modes within the F multiplets and the alternation of the F-spin projection in the united neighboring multiplets. On this basis we suggest that the observed $\Delta N=2\mathrm{}$ and $\Delta N=1\mathrm{}$ staggering effects carry detailed information about the respective systematic manifestation of both high order $\alpha$-particle-like quartetting of nucleons and proton (neutron) pairing interaction in nuclei.

The three-dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for given values of the three components of the rotational vector which determines the orientation of the angular momentum in the intrinsic frame. Tilted rotations are established by numerical means for triaxial nuclei. The onset of tilted rotations is related to an instability of the mean field as verified by the random phase approximation. Analytic expressions are derived for the critical rotational frequencies associated with the mean-field instability.

We present a study of the complex absorbing potential (CAP) method to solve resonance states in a nuclear physics problem. Compared to atomic physics cases, nuclear potentials have a short-range property, and the resonances generally have large decay widths. We find that an appropriate functional form of the CAP method is necessary for an accurate calculation. The functional form dependence of the CAP method and the convergence of the resonance eigenvalues are investigated in a two-body system. We also apply the CAP method to examine a three-body system. Our results are in good agreement with others in the literature.

The dependence of fusion on the nuclear shell structure was investigated for the two reaction systems ${}^{82}\mathrm{Se}{+}^{138}\mathrm{Ba}$ and ${}^{82}\mathrm{Se}{+}^{134}\mathrm{Ba},$ where the nucleus ${}^{138}\mathrm{Ba}$ has a closed neutron shell $N=82\mathrm{}$ while the nucleus ${}^{134}\mathrm{Ba}$ has a neutron number $N=78,$ four neutrons less than the closed shell. Evaporation residues for these reaction systems were measured in the vicinity of the Coulomb barrier. The measured evaporation residue cross sections of $\mathrm{xn}$ and $\mathrm{pxn}$ channels for the reaction system ${}^{82}\mathrm{Se}{+}^{138}\mathrm{Ba}$ were considerably larger than those for the reaction system ${}^{82}\mathrm{Se}{+}^{134}\mathrm{Ba},$ almost 100 times larger at the excitation energy ${(E}_{\mathrm{ex}})$ region of 20–30 MeV. The fusion probabilities for these reaction systems were obtained from the evaporation residue cross sections with the aid of calculated survival probability and compared with those of the other reaction systems that make the same compound nucleus as the present systems. It was found that the fusion reaction ${}^{82}\mathrm{Se}{+}^{138}\mathrm{Ba}$ occurs without hindrance, while that of ${}^{82}\mathrm{Se}{+}^{134}\mathrm{Ba}$ is considerably hindered as commonly seen in the massive reaction system with the charge product $Z_{\mathrm{p}}{Z}_{\mathrm{t}}>~1800$ of projectile and target. The present result suggests that the neutron shell closure $N=82\mathrm{}$ promotes fusion.

The quasielastic-two-body-scattering (QTBS) hypothesis is studied in the inclusive inelastic scattering of protons by nuclei. A sum rule and other quantitative tests are introduced to examine to what extent observed scaling is a confirmation of the QTBS assumptions. The scaling properties of electron-nucleus and proton-nucleus inelastic scattering reactions are compared. While the electron data generally scale well and satisfy the QTBS tests, there are several cases where the proton data do not scale well. Also the proton data are seen to fail some of the QTBS tests we have performed. This indicates that QTBS is not an effective mechanism for proton-nucleus inelastic scattering.

The hidden local symmetry Lagrangian is used to study the interactions of $\phi$ mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small $\phi$ mean free path (less than 2.4 fm at $T>\mathrm{}170\mathrm{}\hspace{0.5em}\mathrm{MeV})$ due to large collision rates with $\rho$ mesons, kaons, and predominantly $K^{*}$ in spite of their heavy mass. This implies that $\phi$ mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the $\phi$ density in the expanding hadronic fireball is investigated.

For the first time a comprehensive level and decay scheme has been obtained for a $T=\frac{5}{2}$ nucleus in the $s-d$ shell ${(}^{27}\mathrm{Na})$ by using a radioactive beam and target. Particle-$\gamma$ and $p-\gamma -\gamma$ coincidences were measured following the ${}^{14}\mathrm{C}{(}^{14}\mathrm{C},p\gamma {)}^{27}\mathrm{Na}$ reaction at $E_{\mathrm{lab}}=22\mathrm{}\hspace{0.5em}\mathrm{MeV}.$ The results do not support an inversion of the ${2s}_{1/2}$ and ${1d}_{5/2}$ orbitals, as previously proposed for $T_z>~3,$ but they do suggest an increased $N=16\mathrm{}$ gap between the ${2s}_{1/2}$ and ${1d}_{3/2}$ orbitals due to the neutron excess. A consistent interpretation of the level scheme in terms of the $s-d$ shell model using the USD Hamiltonian is possible below 4 MeV, but differences increase at higher excitation energies. Another interpretation is that the influences of both the $p_{1/2}$ and $f_{7/2}$ intruder orbitals increase simultaneously with increasing T, an effect not included in the USD Hamiltonian.

Many approaches to nucleon-nucleus elastic and inelastic scattering are based on the use of the free-space nucleon-nucleon transition amplitude. In calculations where the full spin dependence of this amplitude is needed, its use is more tractable when it is expressed in terms of irreducible tensor operators of the spins of the interacting nucleons. We present general formulas for this representation, which is particularly useful for inelastic scattering studies involving spin-flip transitions of a target nucleon.

The ${}^6\mathrm{He}$ $\beta$ decay and ${}^7\mathrm{Be}$ electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne $v_{18}$ two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one- and two-body operators with the strength of the leading two-body term—associated with $\Delta$-isobar excitation of the nucleon—adjusted to reproduce the Gamow-Teller matrix element in tritium $\beta$ decay. The measured half-life of ${}^6\mathrm{He}$ is underpredicted by theory by $\simeq 8\%,$ while that of ${}^7\mathrm{Be}$ for decay into the ground and first excited states of ${}^7\mathrm{Li}$ is overpredicted by $\simeq 9\%.$ However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a $\simeq 1.7\%$ (4.4%) increase in the value of the Gamow-Teller matrix element of ${}^6\mathrm{He}$ ${(}^7\mathrm{Be}),$ obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible.

The concept of y scaling has been demonstrated in the scattering of high-energy electrons to the nuclear continuum, demonstrating the incoherent elastic scattering of the projectile from individual bound nucleons. Scattering of intermediate energy ${\pi }^{-}$ and $K^{+}$ from complex nuclei also shows scaling for cases of low density or small cross sections, but not for all nuclei. These results are used to evaluate the use of such mesonic y scaling as a means to measure meson-nucleon elastic differential cross sections within the nuclear medium.

The radiative corrections of order α for the charged- and neutral-current neutrino-deuterium disintegration for energies relevant to the SNO experiment are evaluated. Particular attention is paid to the issue of the bremsstrahlung detection threshold. It is shown that the radiative corrections to the total cross section for the charged current reaction are independent of that threshold, as they must be for consistency, and amount to a slowly decreasing function of the neutrino energy $E_{\nu },$ varying from about 4% at low energies to 3% at the end of the ${}^8\mathrm{B}$ spectrum. The differential cross section corrections, on the other hand, do depend on the bremsstrahlung detection threshold. Various choices of the threshold are discussed. It is shown that for a realistic choice of the threshold and for the actual electron energy threshold of the SNO detector, the deduced ${}^8\mathrm{B}\hspace{0.5em}{\nu }_e$ flux should be decreased by about 2%. The radiative corrections to the neutral-current reaction are also evaluated.

We point out that, in the standard resonance theory of parity violation in the compound nucleus, the longitudinal parity violating asymmetry in partial neutron capture cross sections is essentially independent of the partial gamma widths involved. Thus, the same asymmetry is expected for each partial cross section involving the same p-wave resonance. The asymmetries are expected to be enhanced $(\sim 10\%),$ and asymmetry measurements for several partial capture cross sections from a given p-wave resonance would provide a very strong test of the theory. In particular, such a measurement could shed light on the origin of the sign problem observed in ${}^{232}\mathrm{Th}$ and could provide more accurate determinations of the parity violating matrix elements between compound resonances. We propose a class of experiments and examine their feasibility.

A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exchange potentials by integrating out the model dependent high momentum modes of $V_{\mathrm{NN}}.$ The smooth and approximately unique $V_{low-k}$ is used as input for shell model calculations instead of the usual Brueckner G matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the G matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of ${}^{18}\mathrm{O},$ ${}^{134}\mathrm{Te},$ and ${}^{135}\mathrm{I}$ using the same input $V_{low-k}$ have been performed. For cut-off momentum Λ in the vicinity of 2 ${\mathrm{fm}}^{\mathrm{-}1}$, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on Λ.

Considering the finite volume of nucleons, a Lagrangian density is given. The first-order self-energy of the nucleon and the equation of state of nuclear matter are calculated in the framework of the relativistic mean-field approximation. Our results indicate that the effects of the volume of nucleons are not negligible.

A simultaneous analysis is made of the measured rates of ordinary muon capture (OMC) and radiative muon capture (RMC) in liquid hydrogen, using theoretical estimates for the relevant atomic capture rates that have been obtained in chiral perturbation theory with the use of the most recent values of the coupling constants. We reexamine the basic formulas for relating the atomic OMC and RMC rates to the liquid-hydrogen OMC and RMC rates, respectively. Although the analysis is significantly influenced by ambiguity in the molecular state population, we can demonstrate that, while the OMC data can be reproduced, the RMC data cannot be explained with the use of realistic values of the inputs; the degree of difficulty becomes even more severe when we try to explain the OMC and RMC data simultaneously.

Total photofission cross sections for ${}^{237}\mathrm{Np},$ ${}^{233}\mathrm{U},$ ${}^{235}\mathrm{U},$ ${}^{238}\mathrm{U},$ ${}^{232}\mathrm{Th},$ and ${}^{\mathrm{nat}}\mathrm{Pb}$ have been measured simultaneously, using tagged photons in the energy range $E_{\gamma }=0.17\mathrm{}–3.84\hspace{0.5em}\mathrm{GeV}$ in Hall B at Jefferson Lab. The fission fragments were detected using parallel-plate avalanche detectors. Our results show that, of these nuclei, ${}^{237}\mathrm{Np}$ has the largest photofission cross section per nucleon, and that the photofission cross section for ${}^{238}\mathrm{U}$ relative to that for ${}^{237}\mathrm{Np}$ is about 80% over the entire energy range. The relative photofission cross sections per nucleon increase with the fissility parameter $Z^2/A,$ approaching an apparent asymptote at the $Z^2/A$ value for ${}^{237}\mathrm{Np},$ and they do not depend strongly on the incident photon energy over this entire energy range. These results, together with a comparison of the ${}^{237}\mathrm{Np}$ photofission cross section per nucleon with total photoabsorption data, indicate that the photofission probability for ${}^{237}\mathrm{Np}$ is almost unity. If we make this assumption, we observe a significant shadowing of the interior nucleons starting below 1.5 GeV, so that the photoabsorption cross section decreases by 20% near 4 GeV.

We investigate the inner crust structure of neutron stars using the Skyrme-Hartree-Fock approach with the Coulomb interaction treated beyond the Wigner-Seitz approximation. Our results suggest that the shell effects associated with unbound neutrons play an important role and, in particular, lead to a complicated phase transition pattern between various nuclear phases (as a function of the density). Namely, we show that the relative energies of different phases are rapidly oscillating functions of the neutron density. In the semiclassical approach this behavior is explained as an interference effect due to periodic orbits of similar lengths. We discuss also the dependence of the shell effects on pairing correlations.

We study the transition from npe-type nuclear matter (consisting of neutrons, protons, and electrons) to matter containing strangeness, using a Walecka-type model predicting a first-order kaon-condensate phase transition. We examine the free energy of droplets of K matter as the density, temperature, and neutrino fraction are varied. Langer nucleation rate theory is then used to approximate the rate at which critical droplets of the new phase are produced by thermal fluctuations, thus giving an estimate of the time required for the new (mixed) phase to appear at various densities and various times in the cooling history of the protoneutron star. We also discuss the famous difficulty of “simultaneous weak interactions” which we connect to the literature on nontopological solitons. Finally, we discuss the implications of our results to several phenomenological issues involving neutron star phase transitions.