The ($d,t$) and ($d,p$) reactions induced by 20.65-MeV deuterons have been used to study the levels of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$ and ${}_{}{}^{85}{}_{}{}^{}\mathrm{Sr}$ up to an excitation of 3 MeV. The mass defect of ${}_{}{}^{83}{}_{}{}^{}\mathrm{Sr}$ has been determined by the ($d,t$) reaction, and its level structure below 3 MeV has been investigated. The cross sections have been analyzed with the distorted-wave Born approximation (DWBA) to determine the $l$ values of the neutron transfers and the spectroscopic factors. Tentative spin assignments have been made on the basis of sum rules and the $j$ dependence of the cross sections.

The half-life of ${}_{}{}^{169}{}_{}{}^{}\mathrm{Hf}$ was found to be 3.26 ± 0.05 min. Several $\gamma$ rays of ${}_{}{}^{169}{}_{}{}^{}\mathrm{Hf}$ were determined, and a partial decay scheme of ${}_{}{}^{169}{}_{}{}^{}\mathrm{Hf}$ proposed. The previously reported 1.5 h ${}_{}{}^{169}{}_{}{}^{}\mathrm{Hf}$ was found to be in error. The half-lives of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{170}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{171}{}_{}{}^{}\mathrm{Hf}$ were redetermined to be 25.95 ± 0.20 min, 15.92 ± 0.15 h, and 12.09 ± 0.35 h, respectively. Several new $\gamma$ rays of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Hf}$ were observed. $\gamma$ spectra of ${}_{}{}^{170}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{171}{}_{}{}^{}\mathrm{Hf}$ were redetermined, and comparisons were made with previous investigations.

In spite of ingenious investigations of the isomeric decay of 253-day ${\mathrm{Ag}}^{110m}$ by several groups of authors, the missing low-energy first excited (2-) state in ${\mathrm{Ag}}^{110}$ has so far escaped detection. High-precision studies of the $\gamma$ rays from the ${\mathrm{Ag}}^{109}(n,\gamma ){\mathrm{Ag}}^{110}$ reaction, as well as coincidence studies, now provide conclusive evidence for this level at an energy of 1.28 ± 0.10 keV.

Recently a high-resolution proton recoil spectrometer was used to measure the neutron spectrum from 20-MeV proton bombardment of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$. Evidence for levels in ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ at 1.4- and 3.2-MeV excitation was presented. Using time-of-flight techniques, we have remeasured the neutron spectrum and find no evidence for these levels.

The second-order ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ mechanism proposed by Noble can account for the recent observation of fine structure if the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}$ and ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ nuclei are coupled to states of definite $J^{\pi }$.

An exact shell-model framework, used in an earlier paper to interpret the odd-parity ($T=\frac{1}{2}$) states of ${\mathrm{O}}^{17}$ below 8-MeV excitation, is extended to the even-parity ($T=\frac{1}{2}$) states in this range. Good agreement between experimental and theoretical energies is achieved. A negative result is that the lowest ${\frac{3}{2}}^{+}$ state is calculated to have essentially zero single-particle strength.

The pair-distribution coefficients of the ground state of even nickel and tin isotopes are determined using both the standard BCS state and its number-projected component. The comparison of the results shows that a consistent number-conserving determination of the coefficients is, in general, necessary in the framework of the so-called projected quasiparticle Tamm-Dancoff approximations.

A comprehensive investigation of the ${\mathrm{Li}}^6$ + ${\mathrm{C}}^{12}$ reaction has been carried out for particle groups corresponding to the following states of the residual nuclei involved: 0.0, 0.871, 3.058, 3.846, and 4.551 MeV for $0^{17}$; 0.0, 6.05+6.13 (unresolved), 6.92+7.12, and 8.88 MeV for $0^{16}$; 0.0 MeV for $0^{15}$; and 0.0, 3.945, and 4.91 + 5.10 MeV for ${\mathrm{N}}^{14}$. Yield curves were measured for protons, deuterons, and $\alpha$ particles at laboratory angles of 0° and 40°, at ${\mathrm{Li}}^6$ bombarding energies from 5.6 to 14.0 MeV. Angular distributions were measured at 9.0, 10.0, 11.2, 12.0, 13.0, and 14.0 MeV for all of the above groups and from 5.6 to 6.6 MeV at 0.200-MeV intervals for most of the groups.

A comparison has been made of the accumulated $\alpha$-particle data and two-mode plane-wave and single-mode distorted-wave direct-reaction models. The proton, deuteron, and $\alpha$-particle data were also compared with the statistical compound-nucleus model.

Phillips found a linear relation between the triton energy $E_t$ and the doublet $n-d$ scattering length ${}_{}{}^2{}_{}{}^{}a$ for a variety of separable tensor potentials. We have treated many more separable potentials, and also the Tabakin and Mongan rank-two separable potentials. The linear relation holds well for two-body potentials that fit the energies of the two-body triplet bound and singlet antibound states.

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,\gamma ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ capture cross section was measured for $\alpha$-particle energies between 1.86 MeV ($\sigma =1.1\mathrm{}\pm 0.4$ nb) and 3.11 MeV ($\sigma =29\mathrm{}\pm 4$ nb) using a pulsed ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ beam from the ORNL 6-MV Van de Graaff accelerator and a 23- by 30-cm NaI(Tl) crystal viewed by six matched, bialkali photomultiplier tubes. An upper limit was obtained for the capture cross section at $E_{\alpha }=1.6\mathrm{}$ MeV. The over-all time resolution (full width at half maximum) of the system for 8-10-MeV pulses due to $\gamma$ rays is 2.7 nsec. Enriched (99.94%) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ targets ranging in thickness from 98 to 178 μg/${\mathrm{cm}}^2$ were used. Pulses resulting from fast neutrons [from the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\alpha ,n){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction] interacting with the NaI(Tl) crystal were further separated from true $\gamma$ pulses through the use of a new technique based on rise-time distribution differences of the respective neutron- and $\gamma$-ray-produced pulses. The face of the crystal (shielded with a 10.2 cm thickness of ${}_{}{}^6{}_{}{}^{}\mathrm{LiH}$) was 12.2 cm from the target. The astrophysical significance of this reaction in the helium-burning sequence of stellar nucleosynthesis is also discussed.

The experimental cross section for radiative $\mathrm{np}$ capture is 334.2±0.5 mb. Theoretical calculations to date yield a result about 10% lower. In this work we calculate a number of mesonic exchange currents, using a simple phenomenological method and nonrelativistic wave functions. We obtain an increase of about 2-3%, almost entirely due to $\pi$ exchange. Since this is numerically too small to resolve the discrepancy, we discuss other possible contributions to the cross sections. A review section is included in which we discuss previous work on the impulse approximation and the meson exchange effect; no discrepancies remain between the numerically accurate theoretical treatments, and the errors in the remaining treatments are discussed.

The Green's-function theories of nuclear matter have been extended to include three-particle correlations, with the result that one particular two-particle Green's-function theory, namely the ${\lambda }_{10}$ theory of Puff, Reiner, and Wilets and of Foster, is found to have the very desirable property that it contains all two-particle correlations. A case is built for expending some effort to calculate the nonperturbative ${\lambda }_{10}$ theory using realistic forces, in the hope of obtaining a value for the binding energy of nuclear matter close to the semiempirical value. Three-particle corrections to the "semirealistic" ${\lambda }_{10}$ calculation of Foster are found to be a few tenths of an MeV, in good agreement with Bethe's results.

Realistic, generalized, and regularized, velocity-dependent one-boson-exchange potential models of the nucleon-nucleon interaction are applied to calculate the low-lying energy levels of the nucleus ${\mathrm{O}}^{18}$ in the harmonic-oscillator shell model. In these calculations, we neglect (a) the short-range correlations which, if they were included, would suppress the repulsive core, and (b) core-polarization effects, which take account of the excitations of the ${\mathrm{O}}^{16}$ core. It is found that the shell-model matrix elements are too repulsive, and the energy levels lie too high. Good agreement with experiment is obtained after weakening the $\omega$-meson interaction to compensate for the neglect of the effects (a) and (b). This also provides a simple way of incorporating the effect of the nuclear medium upon the nuclear interaction.

The binding energy of a $\Lambda$ particle in nuclear matter, $B_{\Lambda }\left(\infty \right)$, is calculated self-consistently with the help of the Brueckner theory. In the $K$-matrix equations for the $\Lambda -N$ interaction, pure kinetic energies in the intermediate states are used. The $K$-matrix equations are solved numerically. The rearrangement energy is taken into account. The values of $B_{\Lambda }\left(\infty \right)$ calculated with several central $\Lambda -N$ potentials $v_{\Lambda N}$- though smaller than the values obtained by other authors - are, in general, larger than the empirical value of $B_{\Lambda }\left(\infty \right)$. An agreement with this value is obtained only if $v_{\Lambda N}$, adjusted to the binding energy of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^5{}_{}{}^{}$, has a sufficiently large hard core and is sufficiently suppressed in odd states. Possible ways of reducing the calculated value of $B_{\Lambda }\left(\infty \right)$ are discussed. A critical discussion of the independent-pair approximation applied by other authors in calculating $B_{\Lambda }\left(\infty \right)$ is presented.

A velocity-dependent nucleon-nuclear potential approximated to the well-known Morse function has been employed to generate the single-particle wave functions and eigenvalues for all nuclei. A general method of treating the perturbation is prescribed which gives a very good agreement with the data on separation energies and with other theoretical work.

We introduce a simple phenomenological model of the vertex functions (virtual decay amplitudes) describing the reactions ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\mathrm{g}.\mathrm{s}.\mathrm{})\to \alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\left(6.056\mathrm{} \mathrm{MeV}\right)\to \alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. These vertex functions (under certain assumptions) can be used to predict the elastic and inelastic electron scattering monopole form factors, as well as describing hadronic reactions such as $\alpha$-cluster transfer and excitation. The monopole form factors are compared with recent data: The ratio of the inelastic form factor to experiment is about 4 (as compared with deformed and spherical shell-model predictions which give <½ for this ratio), owing to the excessive collectiveness of this description of the transition.

By means of a Faddeev-like method, a formulation of nuclear reactions leading to three-fragment final channels is presented. It is a shell-model theory of nuclear reactions in which one can, in principle, deal with two particles in the continuum in the intermediate states. The amplitude also includes as one term the distorted-wave $t$-matrix approximation (DWTA). An approximate treatment of the resonance-type term leads to a two-step process for ($p, 2p$) reactions. The importance of such a mechanism, which proceeds via the 1p-1h or 2p-2h states of the target nucleus, is presented for reactions which heretofore have been analyzed by means of the DWTA.

An off-shell effective-rangelike theory is developed for the low-energy two-nucleon $T$ matrix. It is shown that the parameters in the theory can be determined from on-shell scattering data. The parameters are determined from the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ two-nucleon phase shifts, and the validity of the off-shell formula is tested by means of examples. For the cases considered, the formula is found to work very well. A new proof for the separability of the two-body $T$ matrix near bound-state and resonance energies is given. This proof is based on the properties of the $T$ matrix in configuration space. A theorem on the factorization of the Jost function is developed and used to solve the inversion problem for rank-two separable potentials. Results are given for phase shifts that become hard-core phase shifts at high energies and for tensor forces. These results allow one to construct a separable potential that has the same on-shell $T$ matrix and bound-state wave function as a realistic local potential.

The question of how nonlocal effects might be observed in elastic scattering is investigated under the assumption that the interaction is describable by a Hamiltonian. The energy dependence of the real part of the forward-scattering amplitude is related to a dynamic quantity with dimensions of length, which we refer to as the nonlocal distance. Possible off-energy-shell effects can be discussed in terms of this nonlocal distance.

Electron wave functions for nuclear $\beta$ decay are derived which include exactly the effects due to the nuclear charge change at the instant of decay. Although these wave functions are of general interest for $\beta$-decay theory, the main motivation for this work is that the first-order (in the fine-structure constant $\alpha$) static Coulomb charge-change correction to $\beta$ decay comprises a large part (two thirds) of the total first-order radiative correction. The present work does not require a perturbation expansion in powers of $\alpha$ for this part of the radiative correction. It is thus particularly suited for an investigation of some problems with the radiative corrections which are directly, or which may be indirectly, related to such an expansion: (1) the validity of previous assumptions concerning the $Z$ dependence of the radiative corrections to $\beta$ decay, and (2) the comparison of the exact point-nucleus limit of this part of the radiative correction with the logarithmically divergent character of the first-order result. The first problem is treated in the present paper and the second will be given later. We find that the two previous $Z$-dependence assumptions are incorrect for the static Coulomb charge-change part of the radiative correction.