A complete angular momentum reduction of the Faddeev equations is carried out for the case of realistic, nonrelativistic three-nucleon systems with (local and/or nonlocal) interactions having general spin, isospin, and velocity dependence. Antisymmetrization of states with respect to particle exchange is properly accounted for by using properties of the permutation group and the isospin formalism. Expressions for the Faddeev equations, in the form of coupled two-variable integral equations, are obtained in two different coupling schemes; $J-j$ [coupling of the (relative orbital plus total spin) angular momentum of a nucleon pair with the total angular momentum of the third nucleon (in the c.m. system) to give the total angular momentum (in the c.m. system)]; and $\mathcal{L}-\mathcal{S}$ [coupling of the total orbital angular momentum (relative orbital angular momentum of a nucleon pair plus the orbital angular momentum of the third nucleon) in the c.m. system with the total spin angular momentum (total spin angular momentum of a nucleon pair plus the spin angular momentum of the third nucleon) to give the total angular momentum in the c.m. system].

Projected Hartree-Fock states are used as a representation in calculating nuclear wave functions. The rotational energy is determined consistently through $\frac{J(J+1\mathrm{})\mathrm{}}{〈J^2〉}$, and the moment of inertia thus obtained is compared with the expressions of other authors. The formulas of Peierls and Yoccoz and Thouless and Valatin yield approximately the same results as ours, but all of these formulas exhibit discrepancies with the Inglis independent-particle cranking-model formula. We find that the spurious state $J_x|\phi 〉$ plays a dominant role, in agreement with Banerjee, D'Oliveira, and Stephenson. Interesting observations are made for the case of the soluble $\mathrm{SU}\left(3\right)\mathrm{}$ model of Elliott.

Higher-order corrections to internal conversion and $\gamma$-ray emission involving atomic electrons have been calculated. Experimental anomalies in low-energy $E2\mathrm{}$ $L$-subshell ratios are shown to be substantially explained by these calculations.

A calculation of the correction, second order in $\frac{v}{c}$, to the binding energy of nuclear matter in the first-order Hartree-Fock approximation yields a result of +0.5 MeV per particle at $k_F=1.36\mathrm{}$. The correction becomes large very quickly as the Fermi momentum increases. These results are based on the nonlocal separable potential of Tabakin.

Electron scattering experiments from oriented nuclei have so far been carried out for one heavy nucleus only, that of holmium. Scattering from light nuclei has the advantages that the elastic scattering is unencumbered by unresolved low-level excitations and that the small distortion of the electron wave function renders orientation effects relatively quite pronounced despite small quadrupole moments, thus permitting the use of the Born approximation. Assuming 100% alignment, we calculate large orientation effects for elastic and also for inelastic scattering from oriented ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, as well as for 180° magnetic elastic scattering; for more realistic alignments we predict easily measurable effects.

The relationship between scattering resonances and $R$-function states is explored by investigation of the separate properties of the "hard-sphere" and "$R$-function" portions of the phase shift. The $R$-function states are found to be good models for bound states and for some resonances below potential barriers, but they have no direct relation to scattering resonances above barriers. An $R$-function proof and explication are given for Levinson's theorem, according to which the number of scattering resonances is in general finite and small even though the spectrum of $R$-function states is infinite. Implications of the lack of high-energy resonances for the many-body problem are mentioned.

The Wigner-Eisenbud $R$-matrix theory is applied to the calculation of neutron total and inelastic scattering cross sections for a system consisting of two neutrons interacting with an inert ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core through a spherically symmetric Woods-Saxon potential and interacting with each other through a $\delta$-function force. The calculational method employed has the advantages that it includes the effects of shell-model configurations in which both neutrons are unbound, that it presents no obstacles to inelastic or reaction calculations, that it permits antisymmetrization of the compound space wave functions, and that it requires only one shell-model diagonalization for the computation of cross sections up to 5-MeV neutron energy. Use of antisymmetrized wave functions is shown to reduce substantially the number of compound-nucleus resonances and to reduce the magnitude of the inelastic cross section. By the correct calculation of the distant resonance contribution to the $R$ matrix, it is shown that the calculated cross sections are independent of the choice of channel radii. The application of the method to more complex systems with larger numbers of neutrons as well as protons and holes and also with direct coupling between channels is discussed. A selection rule encountered in the calculations suggests a possible $J^{\pi }$ dependence of the absorptive part of the optical-model potential.

The particle-$\gamma$-ray angular-correlation method of Litherland and Ferguson was used to gain information on the multipole mixing ratios for the 1.97→0.0-MeV, 2.31→0.84-MeV, and 2.31→0.0-MeV transitions in ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$. Ions of ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{++}{}_{}{}^{}$ with $E=7.52\mathrm{}$ MeV populated the excited states through the reaction ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(\alpha ,n){}_{}{}^{33}{}_{}{}^{}S_{}^{*}{}_{}{}^{}$. Neutrons were detected in the direction of the beam axis. Pulse-shape discrimination for determining neutron-$\gamma$-ray coincidence was studied. $\gamma$ rays were detected by 3-in.×3-in. NaI(Tl) crystals at angles of 45, 55, 65, and 90° with respect to the beam axis. Results are examined with regard to predictions of the strong-coupling rotational model.

Radioactive ${}_{}{}^{40}{}_{}{}^{}\mathrm{Cl}$ was produced by the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}\mathrm{}(n,p)\mathrm{}{}_{}{}^{40}{}_{}{}^{}\mathrm{Cl}$ through bombardment of a liquidargon target with 14.9-MeV neutrons. $\gamma$ rays were observed with 6-, 15-, and 35-cc Ge(Li) crystal detectors, and with two NaI(Tl) crystal detectors in coincidence. Twenty-three $\gamma$ rays with energies from 262 to 6334 keV were assigned to transitions in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$. The $\beta$-ray relative intensities were deduced from the relative intensities of the $\gamma$ rays, and $log\mathrm{ft}$ values were calculated. It was concluded that all levels in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ up to and including the 3518-keV level have even parity. Seven levels from 3681 to 6335 keV in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ have odd parity and spin of 1, 2, or 3. The ground energy level of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Cl}$ has spin-parity $2^{-}$, if in fact the 3681-keV level of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ has spin-parity $3^{-}$.

Cross sections for the production of ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ have been determined with 550-MeV protons on 19 target elements ranging from titanium to uranium. The main features of the results are an exponential decrease of the cross sections with increasing target mass up to zinc, a broad maximum between zirconium and tin, and an increase in cross section with increasing target mass between tantalum and uranium. All of the features have been correlated with similar results for ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$. In addition, an analytic function has been used to represent the experimental results in the region where ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ are produced primarily as spallation products.

The ${\mathrm{Mg}}^{24}(t,\alpha \gamma ){\mathrm{Na}}^{23}$ reaction has been used to investigate the spins and decay modes of many of the levels in ${\mathrm{Na}}^{23}$ below an excitation energy of 6 MeV, as well as the multipole mixing ratios of the radiative transitions between these levels. $\gamma$ radiation was detected in NaI(Tl) detectors located at angles between 0 and 90°, while outgoing $\alpha$ particles were detected in an annular detector placed at 180° with respect to the beam direction. Two-parameter techniques were used to measure the $\alpha -\gamma$ coincidence spectra. Analysis of the resultant $\gamma$- ray angular correlations, when combined with already existing data, enabled the following unambiguous spin assignments to be made: 2.98-MeV level $J=\frac{3}{2}$, 3.68-MeV level $J=\frac{3}{2}$, 3.91-MeV level $J=\frac{5}{2}$. Limitations on the possible spins of the 4.78-, 5.38-, and 5.74-MeV levels were obtained. The results are discussed in terms of the Nilsson model for ${\mathrm{Na}}^{23}$.

The ($\alpha ,{\alpha }^{\prime }$) reaction on ${\mathrm{Zn}}^{64}$ and ${\mathrm{Zn}}^{66}$ has been studied using the 31-MeV $\alpha$-particle beam from the Massachusetts Institute of Technology cyclotron, with an over-all energy resolution of 80-120 keV. Angular distributions are presented, both for levels with known spin, and for levels whose spin and parity have not been previously determined. New $3^{-}$, $4^{+}$, and $5^{-}$ assignments are made both by comparison with levels of known spin and with the distorted-wave Born approximation. Good angular distributions are presented for the weak states at 1.81 MeV ($2^{+}$) and 2.32 MeV ($4^{+}$) in ${\mathrm{Zn}}^{64}$. They are both out of phase with the $2^{+}$ and $4^{+}$ single-excitation states. The slope of the angular distribution for the 2.32-MeV ($4^{+}$) level is shallower than for the single-excitation $4^{+}$ state, while the slopes are the same for the $2^{+}$ states. Transition strengths in ${\mathrm{Zn}}^{64}$ and ${\mathrm{Zn}}^{66}$ are compared. Fractionation of $3^{-}$ strength in ${\mathrm{Zn}}^{64}$ has been observed, but it is smaller than that found in the calcium isotopes.

The proton transfer reactions on ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ were studied using the reactions ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ at 17.85-MeV bombarding energy. Transitions to $T_{>}$ and $T_{<}$ levels were obtained. The spectroscopic factors from distorted-wave Born-approximation analysis were compared with information obtained at lower bombarding energies. The number of $T_{<}$ states is discussed qualitatively in terms of fragmentation caused by core-polarization states. The value for the isovector potential responsible for the splitting of the $T_{>}$ and $T_{<}$ states was determined for several orbits. Charge radii calculated for Coulomb energy differences indicated that ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ requires a larger radius parameter than ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$.

Interactions of neutrons with silicon have been studied by measuring $\gamma$-ray production cross sections. For incident mean neutron energies $E_n=5.35,5.85,6.4,6.9,7.45,7.95,8.5, \mathrm{and} 9.0$ MeV, spectra were obtained for a natural silicon sample. The $\gamma$ rays were detected using a coaxial Ge(Li) detector of 30-${\mathrm{cm}}^3$ active volume. Data were obtained for $\gamma$-ray scattering angles of 55 and 90° for all $E_n$, of 35° for $E_n=7.45\mathrm{} \mathrm{and} 8.5$ MeV, and of 75° for $E_n=6.4\mathrm{} \mathrm{and} 7.45$ MeV. Time of flight was used with the detector to discriminate against pulses due to neutrons and background radiation. Data were also obtained at $E_n=5.9\mathrm{}$ MeV, ${\theta }_{\gamma }={55}^{\circ }$ for a sample of ${}_{}{}^{29}{}_{}{}^{}\mathrm{SiO}_2^{}{}_{}{}^{}$ enriched to 95% in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, and for a similarly enriched sample of ${}_{}{}^{30}{}_{}{}^{}\mathrm{SiO}_2^{}{}_{}{}^{}$. These data have been studied to obtain absolute cross sections for production of $\gamma$ rays for the incident neutron energies quoted above. The cross sections have been compared, where possible, with previously measured values; agreement was fair.

The spectra were studied for $\gamma$ rays which could be associated with deexcitation of nuclear levels having unknown decay modes. For ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, $\gamma$ rays were found having energies appropriate for decay of levels at excitation energies $E_x=4.736,4.836,4.893, \mathrm{and} 5.249$ MeV. For ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, $\gamma$ rays were found for decay of levels at excitation energies $E_x>~4.826$ MeV. The spin of the 4.826-MeV state in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ is reasonably limited to 2, 3, or 4. No previously unknown transitions were found for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ or ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$; for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$, the evidence suggests that the 1.624-MeV level is a doublet of 3-keV separation.

Relativistic nucleon-meson field theory is cast in a form appropriate to the nuclear many-body problem. Martin-Schwinger thermodynamic Green's functions are employed. The $n$-nucleon Green's functions satisfy a set of coupled equations which is formally identical to those of the usual potential many-body problem. Here, however, the two-body potential is replaced by a time-dependent interaction in which the mesons are formally eliminated in favor of higher-order nucleon correlations. A general program of increasing complexity for obtaining approximate solutions to the equations is discussed. It is necessary to solve the "vacuum" (one-, two-, etc., nucleon propagator) first. This has been done in the "Hartree-Fock" approximation which sums all diagrams containing a single continuous nucleon line with all possible uncrossed $\pi$ and $\omega$ meson lines. Peaks in the spectral function are identified with masses of known $N^{*}$ resonances. The appearance of ghost states, which arise in the process of mass and wave-function renormalization, is discussed. The resultant Green's function is used to calculate the magnetic moment of the nucleon, yielding a significantly better isovector component of the magnetic moment than the usual perturbation theory, although the isoscalar component is poor in both cases.

The generalized Hartree-Fock approximation of Kerman and Klein is extended to include continuum states of a collective nature. The equations for scattering in the random-phase approximation are rederived.

The binding energy of ${\mathrm{He}}^4$ and ${\mathrm{O}}^{16}$ was calculated using reaction matrix elements of Tabakin's potential. A separable form of the potential has been used to reduce the basic equation to a simple linear algebraic system. The Pauli operator $Q$ defined in terms of harmonic-oscillator intermediate states permits an easy and accurate calculation. Our numerical results for the binding energies include the first- and second-order contributions. A very resonable agreement between the experimental and theoretical values has been obtained, since the occupied-state energies are made nearly self-consistent and a cancellation of other important higher-order contributions has been achieved by a shift of the entire harmonic-oscillator spectra.

A systematic study of the effective two-body $\Lambda -N$ interaction is made in an exact manner from the binding-energy data of the $p$-shell hypernuclei within the framework of the intermediate-coupling shell model. The binding energy is expressed in terms of the five independent potential integrals of the two-body $\Lambda -N$ interaction, and the latter are determined by a least-squares fit to the experimental data. The energy levels and the $\gamma$ transitions are calculated, and the structures of the $p$-shell hypernuclei are discussed. The potential integrals are then analyzed in terms of phenomenological potentials. A large contribution to the binding energy by noncentral forces, especially the tensor forces, is found. The effect of the existence of a three-body $\Lambda \mathrm{NN}$ force is also discussed.