The theoretical reaction cross sections that were calculated using an intranuclear-cascade model were compared with recent experimental results for protons at 30, 40, 50, and 60 MeV on complex nuclei. 15 reactions were selected arbitrarily, and the agreement was found to be within 10% in all 15 cases.

The integrodifferential equation obtained by Meldner is reduced to two coupled differential equations which are solved by using Buck's algorithm in about one hundreth of the time previously necessary. This powerful method for finding self-consistent solutions allows extensive searches on the model parameters and should make it possible to perform realistic calculations for deformed heavy nuclei. Preliminary results show improved agreement with the experimental radii of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

The continuous spectrum of photons accompanying the electron-capture transition from ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ to the first excited state in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ has been measured in coincidence with the nuclear $\gamma$ rays from the deexcitation of this state. The end-point energy of the photon spectrum was determined to be 388 ± 8 keV, in good agreement with accepted mass differences. The probability of $1s+2s$ radiative capture giving a photon energy greater than 50 keV per nuclear $\gamma$ ray was determined to be (10.3 ± 0.6) × ${10}^{-5\mathrm{}}$. This result should be compared with the value 9.2 × ${10}^{-5\mathrm{}}$ predicted by the theory of Martin and Glauber. At energies higher than 120 keV the shape of the spectrum agrees with the predictions of theory. At energies lower than 120 keV the intensity falls off faster than expected from the theory. Exchange and overlap corrections to the radiative-capture theory have been calculated and shown to be too small to account for the observed discrepancy.

A variational principle for the bound-state Faddeev equations is given. This principle takes the form of a variational expression for the linear eigenvalues of the Faddeev kernel. The variational expression is investigated for the case in which the wave function is expanded in terms of known functions. In this case it can be reduced to the variational method of Rosenberg, and hence the energies obtained are variational upper bounds for the bound-state energy. The variational expression is also used to generate a new set of one-dimensional integral equations for the bound-state problem.

A simple model is employed in a preliminary investigation of the influence on measurable quantities of the many-body nature of the interaction experienced by a nucleon participating in a transfer reaction. The model describes a nucleon in dynamic interaction with a microscopically specified core and takes antisymmetry fully into account. Bound and resonant eigenfunctions are determined by the generalized $R$-matrix method. The nucleon-nucleon interaction is treated phenomenologically and contains central, spin-orbit, and Coulomb terms. Two strength parameters are adjusted to reproduce the observed bound-state energies and low-energy phase shifts of a nucleon in interaction with ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The resulting bound form factors have rms radii smaller than those of standard-geometry Woods-Saxon eigenfunctions, leading to important enhancements of spectroscopic factors determined by distorted-wave Born-approximation analyses of reaction data.

Angular distributions of the 6.92- and 7.12-MeV $\gamma$ radiation from the reaction ${\mathrm{C}}^{12}({\mathrm{Li}}^6,d){\mathrm{O}}^{16}$ were measured as functions of bombarding energy in order to obtain information about the reaction mechanism. Bombarding energies were at, and below, the Coulomb barrier for these low, negative-$Q$ reactions. The tendency to proceed by a direct-reaction mechanism should be enhanced under these conditions. Results are compared with plane-wave calculations and are in reasonable agreement for the 6.92-MeV radiation but in strong disagreement for the 7.12-MeV radiation.

An expansion for the nuclear wave-function density matrix in relative and c.m. coordinates is developed such that the leading term is the corresponding nuclear-matter density matrix at the local neutron and proton density. Truncation of all derivatives beyond second order yields an extremely simple form for the energy density which retains all the computational simplicity of the modified $\delta$ interaction and the Skyrme force, while maintaining contact with nuclear-matter theory based on a realistic interaction and reproducing the results of more-complicated density-dependent Hartree-Fock calculations.

Conditions are given and proven that are sufficient to insure the saturation property of nuclear binding energies. Interactions mediated by two-body local static potentials are considered. For some classes of potentials these sufficient conditions are also necessary for saturation.

Angular distributions of neutrons elastically scattered from natural carbon have been measured at 32 neutron energies between 3 and 7 MeV with energy spreads ranging from 37 to 165 keV. The angular distributions of neutrons inelastically scattered from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have also been measured at the nine highest neutron energies. A phase-shift analysis of the elastic scattering cross sections yields the following spin and parity assignments for the excited states of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C} (E_x,J): 8.3 \mathrm{MeV},{\frac{3}{2}}^{+}; 8.88 \mathrm{MeV},{\frac{1}{2}}^{-}; 9.50 \mathrm{MeV},{(\frac{1}{2},\frac{3}{2})}^{-}; 9.90 \mathrm{MeV},{\frac{3}{2}}^{-}; 10.75 \mathrm{MeV},{\frac{7}{2}}^{-}; 11.00 \mathrm{MeV},\left({\frac{1}{2}}^{+}\right)$. Neutron polarizations calculated from the extracted phase shifts agree fairly well with most of the available polarization measurements. A polarization contour map is given showing that carbon may be useful as a polarization analyzer between 4.5 and 7 MeV.

Various tests of $T$ invariance involving allowed nuclear $\beta$ decays are discussed. $T$-violating correlations are calculated to first order in recoil terms $\frac{E}{M}$ and electromagnetic final-state scattering corrections are given.

An explicit formula for Talmi-Moshinsky transformation brackets of unequal-mass particles is given which is the sum of simple expressions over five variables; it is especially suited for numerical calculations.

The magnitude of nuclear transition matrix elements calculated in the particle-hole model often must be renormalized to give agreement with experiment. We introduce 2p-2h state admixtures in the ground state (of "closed-shell nuclei") and consider transitions to the usual configuration-mixed p-h states. The resulting renormalized transition matrix elements are, for reasonable choices of the ground-state correlations, in better agreement with experiment. Because proper treatment of the excited states is also required for detailed comparison with experiment in the case of partial transitions, we study the total muon-capture rate using the closure approximation. It is found that introduction of 2p-2h states in the ground state does not remove the theoretical-experimental discrepancy for the total capture rate in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ if the usual range of values for the "average" neutrino momentum is adopted.

In the Jastrow theory applied to low cluster order it is necessary to restrict the variation of the two-body correlation factor $f\left(r\right)\mathrm{}$ to the domain of functions corresponding to acceptable convergence of the cluster expansion for the energy. We examine in detail two constraints which have received some attention: the "normalization condition" and the "orthogonality (or average Pauli) conditions." The former constraint is motivated by the requirement that the liquid structure factor $S\left(k\right)\mathrm{}$ vanish at zero wave number; the latter, by the Pauli principle in the Fermi medium. It is shown that two-body Jastrow theory cannot obey both constraints exactly for a state-independent correlation factor $f\not\equiv 1$, but that the requirement $S\left(0\right)=0\mathrm{}$ is automatically satisfied in (two-body) Brueckner reaction-matrix theory as a trivial consequence of the fulfillment, by definition of this theory, of the Pauli principle in the medium.

The 2.335-MeV isobaric analog resonance in ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(p,n)\mathrm{}{}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ and ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(p,p)\mathrm{}{}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ was studied experimentally. Detailed analysis was not possible because of the complexity of the excitation function in this energy region. ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(p,n)\mathrm{}{}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ angular distributions at 4.013- and 5.016-MeV bombarding energies were analyzed via statistical-model formalism. 12 states in ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ were observed up to an excitation energy of 2.39 MeV. The $\gamma$ rays from the transitions (777→749 keV) and (749 keV → ground state) have been observed and their angular distributions determined to be isotropic. Angular distributions of the 1165-, 1480-, and 2001-keV $\gamma$ rays leading to the ground state of ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ have been measured at proton bombarding energies of 4.0 and 4.4 MeV. Spins of ${\frac{9}{2}}^{-}$ and ${\frac{11}{2}}^{-}$ are assigned to the 1165- and the 1480-keV levels, respectively, in agreement with other investigators. The angular distribution for the 2001-keV level is isotropic indicating a spin of $\frac{7}{2}$ or less. Higher excited states in ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ were observed through the ($p,n$) reaction at 2256, 2313, and 2380 keV. The ($p,n$) yield coupled with the failure to observe the ground-state transition from the 2256-keV level in the $\gamma$-ray spectra indicates that the spin of this level is greater than $\frac{13}{2}$.

It is possible to extract the nuclear part of the forward-scattering amplitude from small-angle proton-nucleus elastic scattering. The process is complicated in practice by the effects of experimental errors and theoretical approximations. Optical-model calculations are done, using 14.5-MeV protons on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, to examine the effects of these uncertainties on the determination of the nuclear forward amplitude.

$\gamma -\gamma$ angular correlations were measured for $\gamma$ rays resulting from transitions in ${}_{}{}^{42}{}_{}{}^{}\mathrm{K}$ which was formed by 6-MeV deuteron bombardment of separated ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$. Litherland and Ferguson's Method I was used to study the cascade $\gamma$ rays from the 252- and 104-keV states. Acceptable spin sequences of 432 and 322, respectively, were found. Mixing ratios and population parameters are given.

The modified Tamm-Dancoff approximation (MTDA) for pairing vibrations is studied. It is shown that the previously reported success of the method is connected with the fact that seniority is a fairly good quantum number for nuclear ground states. It is pointed out that the MTDA may be useful for the treatment of pairing correlations in deformed nuclei. Numerical calculations are presented for ${\mathrm{Mg}}^{24}$. The random-phase-approximation extension of the method is carried out and used to calculate pairing correlations in ground and excited states of the Pb isotopes.

The decay of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Br}$ has been studied with high-resolution Ge(Li) detectors by applying online mass-separation techniques to ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ fission products. 19 transitions were positively assigned to this decay through half-life comparisons, and for 10 of them direct measurements of the half-life were performed, yielding an average value of 59 ± 4 sec. Levels for ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ are proposed at ($\left(J^{\pi } \mathrm{within}\mathrm{parentheses}\right):1564.62\mathrm{}\pm 0.09 \mathrm{keV} \left(2^{+}\right), 2349.60\pm 0.14 \mathrm{keV} \mathrm{}(1,2), 2850.2\pm 0.4 \mathrm{keV}, 2926.24\pm 0.13 \mathrm{keV} \mathrm{}(1,2), 3099.20\pm 0.16 \mathrm{keV} \left(3^{-}\right), 4315.75\pm 0.17 \mathrm{keV} (2^{-},3^{-}), 5406.6\pm 0.5 \mathrm{keV} \mathrm{}(1,2), 5519.0\pm 0.9 \mathrm{keV} (1^{-},2^{-}), \mathrm{and} 6209.9\pm 0.5 \mathrm{keV} (1^{-},2^{-})$).

The reaction ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 40-MeV incident energy has been used to excite the following levels: g.s. ($0^{+}$), 3.352 ($0^{+}$), 3.734 ($3^{-}$), 3.903 ($2^{+}$), 4.487 ($5^{-}$), 5.25 ($0^{+}$, $2^{+}$, $4^{+}$), 6.51 ± 0.01, 6.62 ± 0.02, 6.945 ± 0.015, 7.575 ± 0.015, 7.69 ± 0.03 ($3^{-},T=1\mathrm{}$), 8.41 ± 0.03, 8.57 ± 0.02, 9.11 ± 0.02, and 9.30 ± 0.03. Results on the first two $0^{+}$ states are compared with theoretical predictions. There is no evidence for a 2p-2h, $0^{+}$, $T=0\mathrm{}$ state at an excitation ≲ 8 MeV, suggesting a fragmentation of this strength and/or that this state is higher in energy. The unreported ${(2\mathrm{}\mathrm{p}-2\mathrm{}\mathrm{h})}^{J=0^{+},T=1\mathrm{}}$ state has been observed at 9.30 ± 0.03 MeV. These results suggest that the monopole force discussed by Zamick is less isospin-dependent in the Ca region than is usually admitted.

About 65 levels in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ were populated by the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$ reaction. The angular distributions of deuterons leading to many of these states were obtained with a split-pole magnetic spectrograph. In many cases, comparison of these angular distributions with distorted-wave Born-approximation calculations permitted both the determination of the angular momentum of the transferred proton and the transition strength. These results are compared with previous work. Coincidences between deuterons and $\gamma$ rays from the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}({}_{}{}^3{}_{}{}^{}\mathrm{He},d\gamma )$ reaction were also studied to obtain the $\gamma$ decay of some levels in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$. The possibility of pairs of closely spaced levels, which has been suggested as an explanation for the discrepancies in some spin and parity assignments, is also investigated. Theoretical calculations are briefly compared with some of the existing experimental results on excited states in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$. Finally, the question of which states in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ are analogs of low-lying states in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ is discussed.