A calculation of the angular distribution of recoil products resulting from compound nuclear ($\alpha , n$) reactions has been programmed on the basis of the spin-dependent statistical theory of nuclear reactions. The program, which is based on the Monte Carlo technique, considers the emission of neutrons, protons, $\alpha$ particles, and $\gamma$ rays, and uses either the Fermi-gas or the superconductor model of the nucleus. The computed angular distributions have been compared with the experimental results for various ($\alpha , n$) reactions and, in agreement with experiment, exhibit a smooth dropoff from a peak close to 0°. This contrasts with the marked disagreement between the experimental results and previous spin-independent calculations, which predicted a peak at large angles to the beam. The difference is ascribed to the effect of competitive $\gamma$-ray emission, which is not adequately considered in spin-independent calculations. The present calculation predicts a faster decrease with angle in the magnitude of the differential cross section than is observed experimentally. This result is independent of the specific parameterization of the calculation and may reflect a small contribution from direct interactions.

The giant resonance region of ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$ is investigated using a continuum model, which is based on configuration mixing of negative-parity particle-hole states, with the particle in the continuum. Using this model $T=1\mathrm{}$, $J^{\pi }=1^{-}, \mathrm{and} 2^{-}$ electron-scattering spectra are calculated as well as the $0^{-}$, $1^{-}$, and $2^{-}$ nuclear-excitation spectra (or equivalently the neutrino spectra) in $\mu$ capture. The $\mathrm{SU}\left(4\right)\mathrm{}$ relationship ${M_P}^2={M_V}^2={M_A}^2$ is tested and found to be satisfied in both nuclei to better than 10%. In addition, the relationship $\left({M_V}^2\right)={\left({M_V}^2\right)}_{\mathrm{UD}}{\left|F_{\mathrm{el}}\right({{\nu }_{\mathrm{res}}}^2\left)\right|}^2$ is tested and found to hold to within 3%. Both of these results justify the previous work of Foldy and Walecka on calculations of total-muon-capture rates. The detailed behavior of the electron scattering spectra is examined as a function of momentum transfer with emphasis on the magnetic contribution to the $1^{-}$ transverse electric spectra and the giant magnetic quadrupole resonances. The momentum dependence of integrated form factors for certain regions of the excitation spectra is also investigated.

The scattering matrix is derived for the scattering of nucleons by nuclei lacking one nucleon from being doubly magic. It is assumed that an average field has been determined through a Hartree-Fock procedure (HF). The residual interaction is treated in the random-phase approximation (RPA). In contrast to previous treatments, it is not assumed that this interaction is separable. The RPA ground state of the compound system is given by a correlated wave function $|{\Psi }_0〉$. It is assumed that states of the target and residual nucleus can be described as one-hole states in this correlated ground state $|{\Psi }_0〉$. It is found that the RPA equations allow for a proper definition of asymptotic states only if the full Hamiltonian (including the c.m. energy) is used in the HF procedure. A general, yet explicit, expression for the $S$ matrix is obtained by applying to the channel-channel part of the residual interaction a method first proposed by Weinberg. The correlations contained in $|{\Psi }_0〉$ give rise to poles of the scattering matrix for real negative energies below the energy of the lowest bound state, i.e., the ground state $|{\Psi }_0〉$. In the energy region of physical interest, these poles have two effects on the scattering matrix. First, a constant background term is introduced. Second, the partial widths ${\Gamma }_{\lambda c}$ for decay of a compound state ($\lambda$) into an open channel ($c$) are complex. The sum of the partial widths, ${\Sigma }_{\lambda c}{\Gamma }_{\lambda c}$, is compared with the sum of the total widths, ${\Sigma }_{\lambda }{\Gamma }_{\lambda }$. It is found that the two sums differ by terms of second order in the admixture of correlations in the ground state. The influence of symmetry properties of the Hamiltonian on the RPA solutions is discussed. It is shown that the scattering matrix derived is that in the c.m. frame, and it is completely independent of the total momentum of the nucleus.

Hartree-Fock calculations have been performed for the even-even $N=Z$ nuclei from $A=4\mathrm{}$ to $A=40\mathrm{}$. The calculations use a velocity-dependent interaction which contains two-body spin-orbit and tensor terms, and which was especially derived for use in HF calculations. Effects of truncation are made minimal by using a basis of Cartesian harmonic-oscillator wave functions. Nuclear sizes and single-particle energies are in reasonable agreement with experiment; however, total binding energies are much too small. Comparison is made with other recent calculations.

A formalism, proposed previously, which represents a generalization of the separable-potential model is applied to the four-nucleon system. It consists essentially in approximating the off-shell nucleon-deuteron scattering amplitude—as obtained in the separable-potential model—again by separable expressions. We arrive thereby at effective two-particle equations which are solvable by standard methods. The determination of the required separable terms is studied in detail. A first attempt to solve approximately our final integral equations is made. The results demonstrate the applicability of the method.

The Thomas-Fermi integral theory of the nuclear surface is shown to have singular solutions for the nuclear density. This failure is traced to its inadequate representation of the behavior of wave functions in a potential. A new theory based on approximate wave functions is developed and shown to be asymptotic to the Thomas-Fermi theory in the interior of the nucleus. An improved treatment of exchange forces is shown to be essential to obtaining realistic solutions.