A canonical finite-temperature mean-field approximation and a higher-order approach, which includes particular two-body correlations, are developed and compared with the exact (canonical) and the usual mean-field (grand-canonical) results within the context of an exactly solvable fermion model. Special projected statistics in a particular canonical subspace are also discussed.

Isospin effects in NN¯ scattering and annihilation are studied here using the optical model. Real part of the effective NN¯ potential was chosen to be the G-parity-transformed Bonn NN potential (OBEPQ). Parameters of the imaginary part of the optical potential were obtained by fitting the total pp¯→pp¯, pp¯→nn¯, and n¯p→n¯p cross sections to averaged experimental data represented here by analytical formulas. The model reproduces reasonably well the differential and total cross sections of NN¯ scattering and charge-exchange reactions as well as the characteristics of p¯ atoms. There is no evident relationship between the peculiar behavior of the real-to-imaginary ratio of the pp¯ forward elastic scattering amplitude and isospin effects.

Charge-independence breaking is investigated theoretically and numerically in the three-nucleon (3N) system. Illustrations for the 3N bound states and for cross sections and spin observables in elastic nucleon-deuteron scattering and breakup processes are given, using exact solutions of the Faddeev equations with meson-theoretical 2N interactions.

We compare density-dependent distorted-wave impulse-approximation (DD-DWIA) calculations with experimental (p,n) cross-section angular distributions at 135 MeV for ten nuclei from A=14 to 208. The DD-DWIA calculations use a G-matrix interaction based on the Bonn one-boson-exchange potential and empirical optical-model parameters. The agreement between the calculations and the experimental results is excellent with normalization factors required that are within 10% of unity; these factors are within the experimental scale uncertainties.

Experiments designed to provide more information on the spectroscopy of ${}_{}{}^{214}{}_{}{}^{}\mathrm{Bi}$, and on ${}_{}{}^{214}{}_{}{}^{}\mathrm{Pb}$(${\mathrm{\beta }}^{\mathrm{-}}$${)}^{214}$Bi in particular, were undertaken because of interest in first-forbidden β decay in the lead region. The experiments consisted of γ-γ coincidences and angular correlations, conversion electron measurements, level lifetime determinations, and precision γ-ray energy measurements. The 352-keV level of ${}_{}{}^{214}{}_{}{}^{}\mathrm{Bi}$ was found to be a strong candidate (and the only candidate) for the $0_1^{\mathrm{-}}$ state. Recent additions to the ${}_{}{}^{214}{}_{}{}^{}\mathrm{Pb}$ decay scheme are confirmed by γ-γ coincidence measurements. A careful evaluation of the ${}_{}{}^{214}{}_{}{}^{}\mathrm{Bi}$ level scheme is made with emphasis on separating experimentally based conclusions from speculations based on systematics and other ‘‘weak’’ arguments. Shell-model calculations of the spectroscopy of ${}_{}{}^{210,212}{}_{}{}^{}\mathrm{Bi}$ and ${}_{}{}^{210,212}{}_{}{}^{}\mathrm{Pb}$(${\mathrm{\beta }}^{\mathrm{-}}$${)}^{210,212}$Bi were performed using a modification of the Kuo-Herling realistic interaction. These calculations and a generalized seniority model provide a basis for an examination of the systematics of the A=210, 212, 214 spectroscopy and β decay. The generalized seniority model is found to be a quite good approximation which provides a quantitative understanding of the ${}_{}{}^{214}{}_{}{}^{}\mathrm{Pb}$ decay rates.

The probability per K capture for double K-shell ionization in the electron capture decay of ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ was obtained by fitting a model spectrum to the x-ray spectrum recorded to very high statistics in a high-resolution Si(Li) detector. The result, ${\mathit{P}}_{\mathit{K}\mathit{K}}$=(1.3±0.2)×${10}^{\mathrm{-}4}$, confirms the trend wherein experimental data decrease smoothly with Z, and are intermediate between the theoretical predictions of Intemann and of Suzuki and Law. Corrections to some recently published ${\mathit{P}}_{\mathit{K}\mathit{K}}$ values reconcile them with this trend.

New cross-section and analyzing-power data are presented for elastic and inelastic scattering of 200-MeV protons from ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, which has a ${\frac{3}{2}}^{-}$, $T=\frac{1}{2}$ ground state. A microscopic foldingmodel optical potential, obtained by convoluting a Pauli-corrected effective nucleon-nucleon ($\mathrm{NN}$) interaction with ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ground-state densities constrained by weak and electromagnetic data, produces a satisfactory description of the elastic data. The effects of the nonspherical terms in the optical potential, estimated via the distorted-wave approximation (DWA), are appreciable. The inelastic transitions leading to the ${\mathrm{½}}^{-}$, $T=\frac{1}{2} \mathrm{and} {\frac{7}{2}}^{-}$, $T=\frac{1}{2}$ states at 0.48 and 4.63 MeV, respectively, are also examined within the framework of the microscopic folding model and the DWA. Transition potentials are generated by convoluting the effective $\mathrm{NN}$ interaction considered with target transition densities constrained by weak, electromagnetic, and low-energy proton and neutron scattering data. These potentials are employed in DWA calculations along with the folded optical potential that is consistent with the transition potentials. These self-consistent calculations also provide a good description of the inelastic data. The results provide a clear indication that there are important shape differences between the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ radial densities and that the two inelastic transitions in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, which are primarily quadrupole in character, have $\frac{{\rho }_{2n}^m}{{\rho }_{2p}^m}\approx 0.9 \mathrm{and} 0.9-1.2$, respectively.

The giant multipole resonances in ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ have been studied using the (e,e’n) reaction. Data were taken at effective momentum transfers of 0.37, 0.45, and 0.55 ${\mathrm{fm}}^{\mathrm{-}1}$ and a multipole analysis of the data was performed. The inferred multipole strength functions identify the E2 and E0 resonances as distinct peaks at 12.2 and 17.9 MeV, respectively. The energy-weighted sum-rule strengths for the E2 and E0 resonances, obtained using a Lorentzian fit to the data, are 34±13% and 93±37%. When compared with results from alpha scattering and pion scattering the sum-rule strengths exhibit approximate agreement, but the E0 strength identified in this measurement lies at higher excitation energy, consistent with the trend observed in heavier nuclei. The (e,e’n) data are compared with a continuum random phase approximation (RPA) calculation of the E2 and E0 strengths, and with an open-shell RPA calculation of the E2 strength. Both calculations disagree with the data in the region of the E2 resonance.

The stripping reaction (α${,}^3$He) at 183 MeV bombarding energy has been used to study the neutron-particle response function on ${}_{}{}^{124,122,120,118,116,112}{}_{}{}^{}\mathrm{Sn}$ target nuclei up to 25 MeV excitation energy. Strong transitions to high-lying neutron states are observed beyond 4 MeV excitation energy. These transitions, arising from neutron stripping to high-spin outer subshells, appear as a sharp and strong peak located around 5 MeV excitation energy for the heavier tin isotopes (125, 123, and 121) and a broader structure extending up to 10 MeV. A clear broadening of the whole structure and the disappearance of the sharp component is observed with decreasing mass number, leading to a structureless spectrum in the case of ${}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$. Our investigation reveals a strong excitation of the 1${\mathit{i}}_{13/2}$ neutron strength, with possible mixture with the neighboring 1${\mathit{h}}_{9/2}$ and 2f subshells between 5 and 10 MeV excitation energy. The empirical data are compared with the theoretical predictions from the quasiparticle-phonon nuclear model. The present investigation, on a wide range of the tin isotopic chain, allows us to establish a comparison between the damping of high-lying particle and deep-hole states in heavy nuclei.

The ${\mathrm{\beta }}^{\mathrm{-}}$ decay of ${}_{}{}^{136}{}_{}{}^{}\mathrm{I}$ isomers to levels in ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ was studied using sources isolated at the on-line mass separator TRISTAN. Conversion-electron and gamma-ray singles data have been collected. Evidence for excited ${\mathrm{O}}^{+}$ states at 2582.4 and 4320 keV has been obtained. A shell-model study elucidating the salient features related to the first excited ${\mathrm{O}}^{+}$ state in the N=82 nuclei has been carried out. Comparing two-particle, four-particle exact shell-model and two-quasiparticle shell-model calculations using both a Gaussian and surface-delta interaction in the latter case, an explanation could be given for the Z dependence in the ${\mathit{E}}_{\mathit{x}}$(${\mathrm{O}}_2^{+}$) excitation energy. We also calculate the E0 reduced matrix elements for ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$.

Many-body techniques are used to develop a practical formalism for including an energy-transfer dependence in the nucleon-nucleon interaction used in nuclear linear response models. An energy-transfer dependence is naturally expected from the exchange of finite mass, finite velocity mesons. The formalism is applied in a Tamm-Dancoff approximation model structure calculation for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The importance of meson retardation effects on the structure calculation is studied as a function of the magnitude of unperturbed particle-hole energies. The relative importance of ring and ladder contributions is also investigated. It is found that retardation effects can become qualitatively important when particle-hole energies are comparable to the mass of the exchanged meson as would be the case for ${\mathit{N}}^{\mathrm{*}}$ particle-nucleon hole configurations. While ladder kernels exhibit a significant energy-transfer dependence, the actual results obtained including retardation when solving for the ladder polarization propagator follow closely the results obtained using an instantaneous ladder kernel. This result suggests a simple procedure for including retardation effects.

The ground-state bands in even-even nuclei are studied by treating the variation of moment of inertia with angular momentum in terms of the relative increase of moment of inertia with angular momentum, called the softness parameter. Such a reformulation of the variable moment of inertia (VMI) model in terms of the various orders of softness of the nuclear softness (NS) model extends the range of validity of the new model, called VMINS, to 2.0≤${\mathit{R}}_{42}$≤3.33. This gradual softening of the rigid rotator throughout the Periodic Table requires softness parameter to, at least, second order, with the vibrational energy also becoming important for very soft nuclei.

A broken pair approach is developed to describe the high-spin band structures in rotating nuclei. The alignment processes are tacitly considered by including the higher angular momentum broken pairs.

The structure of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ is investigated using electron scattering measurements at 90° and 160° for momentum transfers between about 1.0 and 2.5 ${\mathrm{fm}}^{\mathrm{-}1}$. In addition to the 3/$2^{\mathrm{-}}$ ground state and the narrow 5/$2^{\mathrm{-}}$ state at 2.43 MeV, detailed line-shape analysis was used to extract cross sections for broad states at 1.68, 3.05, 4.70, 6.38, 6.76, 11.28, and 13.79 MeV. The previously unknown state at 6.38 MeV was isolated from the known 6.76 MeV state in both (e,e’) and (p,p’) data using the dependence of peak position upon momentum transfer. On the basis of the form factor, the 6.38 MeV state replaces the 6.76 MeV state as the 7/$2^{\mathrm{-}}$ member of the ground-state rotational band and the 6.76 MeV state is identified with the lowest 9/$2^{+}$ state predicted by the shell model. The data for all states are compared with a shell-model calculation that uses the full 0ħω and 1ħω model spaces. Calculations are also presented for the narrow states between 14 and 18 MeV excitation.

Cross section and analyzing power measurements for the scattering of 180 MeV protons are used to investigate the structure of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$. Data were collected for 24 states below 21 MeV of excitation. Detailed line-shape analysis was used to isolate several broad states. Most notably, the dependence of apparent peak position upon momentum transfer was used to separate the strong resonance listed as 6.76 MeV in standard compilations into two contributions identified as the 7/$2^{\mathrm{-}}$ member of the ground-state rotational band, located at 6.38 MeV, and the 9/$2^{+}$ weak-coupling state, located at 6.76 MeV. Calculations of proton scattering were made using a density-dependent effective interaction in the local density approximation. The quadrupole contribution to elastic scattering was included in distorted wave Born approximation and found to have an important effect upon the analyzing power. For states dominated by a single multipolarity, neutron transition densities were fitted to (p,p’) data and compared with the corresponding proton transition densities fitted to (e,e’) data. We find that excitation of the rotational states and the 9/$2^{+}$ state are essentially isoscalar. Shell model calculations were performed in the full 0ħω and 1ħω model spaces. Suggested assignments for most states are made by comparisons of shell model calculations with data for both (p,p’) and (e,e’). Similar calculations for analog states observed with the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(p,n${)}^9$B reaction at 135 MeV support the proposed assignments. Finally, several relatively narrow states are observed between 18 and 21 MeV that are candidates for positive-parity states with T=3/2.

The zero-degree cross section for the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(p,n${)}^{13}$N reaction has been measured at 200 MeV incident energy, with an energy resolution of 800 keV. Of particular interest is the transition to the ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$(15.06 MeV, 3/$2^{\mathrm{-}}$ T=3/2) level, since a previous measurement of this cross section is inconsistent with that for the isobaric analog level excited in the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(n,p${)}^{13}$${\mathrm{B}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ reaction. The present measurement yields a cross section significantly less than that previously reported, and in agreement with that for the (n,p) reaction.

Using a track-recording phosphate glass detector with a standard deviation ${\mathrm{\sigma }}_{\mathit{Z}}$=0.24 charge unit, we have collected ∼${10}^3$ tracks of energetic Ne clusters emitted from ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ and have obtained a branching ratio B(Ne/α)=(7.2±0.5±0.7)×${10}^{\mathrm{-}13}$. This is consistent with the previous value of (7.5±2.5)×${10}^{\mathrm{-}13}$ which was based on 16 events. The larger of our two errors is that estimated to be due to uncertainty in absorption in our source. No candidate for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Mg}$ emission survived our energy and angle cuts, from which we infer a branching ratio B(Mg/Ne)<0.0018 (90% C.L.). The smallness of the Mg branch is inconsistent with predictions of the quantitatively most successful models of cluster emission heretofore used. The inconsistency is removed if the cluster emission models are modified by taking into account the Nilsson states of the parent and daughter nuclei for the two decay modes.

Gamma-ray angular correlations have been measured for the damped reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{28}$Si${,}^{12}$C${)}^{28}$Si between ${\mathrm{\theta }}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=120° and 160° for ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=43.5 and 48 MeV. The spin alignments and density matrices have been deduced from the observed angular distribution of the gamma rays for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ states in -10<Q<0 and -16<Q<0 MeV for ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=43.5 and 48 MeV, respectively, and for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($2_1^{+}$) state in strongly damped region Q<-10 MeV. We find that the spin angular momenta of the nuclei are poorly aligned with respect to the normal to the reaction plane and the density matrices for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($2_1^{+}$) and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ states are almost diagonal with respect to the direction of motion of the outgoing particle. We also find qualitatively similar behavior of the spin alignments for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ states in strongly damped region. The measured density matrices and spin alignments are consistent with the picture of formation of a long-lived dinuclear complex undergoing orbiting, bending, and wriggling motions, but not with those obtained from statistical compound nucleus or sticking-model calculations.

Differential cross sections for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(γ,${\mathrm{\pi }}^{+}$${)}^6$${\mathrm{He}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ have been measured for an incident photon energy of 200 MeV at laboratory angles of 23.5°, 64°, 90°, and 135°. Good agreement is obtained with several calculations based on the distorted-wave impulse approximation.

Two-proton correlation functions have been measured at ${\mathrm{\theta }}_{\mathrm{lab}}$≊25° for the ‘‘forward kinematics’’ reactions ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$${+}^{27}$Al, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$${+}^{197}$Au at E/A=75 MeV, for the ‘‘inverse kinematics’’ reaction ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$${+}^{27}$Al at E/A=31 MeV, and for the nearly symmetric reaction ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$${+}^{122}$Sn at E/A=31 MeV. For the reactions at 75 MeV per nucleon, the correlation functions exhibit pronounced maxima at relative proton momenta, q≊20 MeV/c, and minima at q≊0 MeV/c. These correlations indicate emission from fast, nonequilibrium processes. They are analyzed in terms of standard Gaussian source parametrizations and compared to microscopic simulations performed with the Boltzmann-Uehling-Uhlenbeck equation. For the reactions at 31 MeV per nucleon, the two-proton correlation functions do not exhibit maxima at q≊20 MeV/c, but only minima at q≊0 MeV/c. These correlations indicate emission on a slower time scale. They can be reproduced by calculations based on the Weisskopf formula for evaporative emission from fully equilibrated compound nuclei. For all reactions, the measured longitudinal and transverse correlation functions are very similar, in agreement with theoretical predictions.