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.

Beryllium enriched to 5% in ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ has been extracted from neutron-irradiated carbon, and has been used for targets in nuclear spectroscopy. The cross section for the production of ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$ via deuteron bombardment of ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ has been measured from 0.67 to 3.0 MeV, and the production cross section of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ has been measured from 2.3 to 12 MeV. The yield for both reactions varies smoothly with bombarding energy, and no resonance in ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ is seen. From magnetic spectroscopy of the ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}(d, p)$ reaction, the mass excess of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ is found to be 20.174±0.007 MeV (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$=0) and the excitation energy of the first excited level to be 318 ± 7 keV. The angular distribution of protons populating the 318-keV level is an $l_n=1\mathrm{}$ pattern, implying $J^{\pi }={\frac{1}{2}}^{-} or {\frac{3}{2}}^{-}$.

We have formulated a theory of nuclear scattering for overlapping potentials between the incident particle and each of the target nucleons, without using the impact-parameter approximation of Feshbach. As the nuclear internal Hamiltonian is important for the overlap in the potentials, we include in the energy denominators a term which is dependent on the nuclear internal Hamiltonian, as well as the term which is linear in the momentum transfers. A correction to the Glauber model, due to the overlap in the potentials, is obtained from the principal part of the denominators. The correction reduces both the total cross section and the forward differential cross section by about 15%. We define the "effective solid angle for scattering" to be the total cross section divided by the forward differential cross section. From this quantity we can determine nuclear correlation independently of the correction due to the overlap in the potentials. Range parameters for nuclear correlation functions are obtained from existing data.

The cross sections for production of ${}_{}{}^{39}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{34m}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ from the proton spallation of argon at 310, 425, and 578 MeV are reported. Experimental production rates and experimental production ratios of the various radioisotopes to ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ are compared to theoretical spallation yield calculations. Applications of the cross sections to health physics problems associated with high-energy accelerators and to studies of atmospheric processes are discussed.

Cross sections for the production of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$ have been determined from targets between magnesium ($Z=12\mathrm{}$) and selenium ($Z=34\mathrm{}$) with 100-, 200-, and 300-MeV protons. The main feature of the results is the exponential decrease of the cross sections with increasing target atomic number or neutron number for values up to $Z\simeq 30$ and $N\simeq 37$. This feature has been found to be consistent with the cross-section dependence predicted on the basis of a cascade-evaporation mechanism. Maxima are also observed in the cross-section distributions at atomic numbers greater than $Z=30\mathrm{}$. It appears that these maxima are caused by nonconventional cascade-evaporation events, since they have thresholds below 200 MeV. A major breakup process in which one of the fragments has greater stability is suggested as a possible mechanism.

Angular distributions of $\gamma$-ray spectra from the ${\mathrm{Ti}}^{46}(p, \gamma ){\mathrm{V}}^{47}$ reaction were observed at the resonances $E_p=1095.4, 1127.0, \mathrm{and} 1285.7$ keV. Accurate level energies and a revised $Q$ value of 5167.9±1.5 keV were obtained. Branching ratios and multipolarity mixing ratios for numerous transitions were determined. The 2.175-MeV level was found to have spin $\frac{5}{2}$. The resonance levels at $E_p=1095\mathrm{} \mathrm{and} 1286$ keV [$E_X\left({\mathrm{V}}^{47}\right)=6.241\mathrm{} \mathrm{and} 6.425$ MeV] were found to have spin $\frac{3}{2}$. The resonance at $E_p=1127\mathrm{}$ keV ($E_X=6.271\mathrm{}$ MeV) has been tentatively identified as the isobaric analog state of the 2.163-MeV level in ${\mathrm{Ti}}^{47}$, with $J^{\pi }={\frac{3}{2}}^{-}$.

The $0^{+}$, $T=2\mathrm{}$ states of $A=40\mathrm{}$ nuclei were calculated by diagonalizing representative nuclear forces in the complete $2\hslash \omega$ basis of 80 states. Both a phenomenological force and a realistic force were employed. When the single-particle energies were corrected in a manner suggested by previous calculations, the realistic force made a good fit to the experimental data. The results for the phenomenological force and the traditional single-particle energies did not fit the data. Many more low-lying $0^{+}$ states in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ are predicted than have been seen experimentally.

High-resolution measurements of the differential cross section for elastic proton scattering on ${\mathrm{Si}}^{29}$ have been performed in the energy range $E_p=1.1-2.5\mathrm{}$ MeV, which corresponds to the range $E_X\left({\mathrm{P}}^{30}\right)=6.7-8.1\mathrm{}$ MeV. Twenty-four resonances were observed, including ten previously unreported resonances. For all but two resonances, the proton orbital momenta were determined, and, in many cases, unique spin assignments were made. Partial proton widths or strengths are given for all resonances. Five $1^{-}$ resonances were observed with the unusually large total $p$-wave reduced width ${{\theta }_p}^2=1.14\mathrm{}$ in the elastic channel. Similarly, four $2^{-}$ resonances appear with a total $p$-wave reduced width ${{\theta }_p}^2=0.68\mathrm{}$. For the $1^{-}$ resonances, both $p_{\frac{1}{2}}$ and $p_{\frac{3}{2}}$ elastic scattering contribute strongly. Two definite, and one probable, $4^{-}$ resonances were observed with a total $f$-wave reduced width ${{\theta }_p}^2=0.15\mathrm{}$. The yield of inelastically scattered protons from the first excited state of ${\mathrm{Si}}^{29}$ was measured in the energy range $E_p=1.9-2.5\mathrm{}$ MeV. Eleven resonances were observed, including three previously unreported resonances. The resonance strengths were measured relative to the known strength of the 1302-keV resonance in the ${\mathrm{Si}}^{29}(p, \gamma ){\mathrm{P}}^{30}$ reaction. For the resonances with known spin, the partial inelastic proton widths were obtained.

Employing ${\mathrm{Ca}}^{40}$ as the core, the odd-parity states of ${\mathrm{Sc}}^{43}$ and ${\mathrm{Ca}}^{43}$ are calculated within the shell-model framework using the reaction matrix elements of the Hamada-Johnston nucleon-nucleon potential as calculated by Kuo and Brown. The three extracore particles are considered to occupy the $0f-1p$ orbitals. The effect of including the additional $0g_{\frac{9}{2}}$ orbital is also investigated. The odd-mass calcium isotopes (${\mathrm{Ca}}^{43}$, ${\mathrm{Ca}}^{45}$, and ${\mathrm{Ca}}^{47}$) are then described by the modified Tamm-Dancoff approximation (MTDA) method and the results are compared with the shell-model calculations of Federman and Talmi and of Engeland and Osnes that had been carried out in a much more restricted configuration space. The MTDA calculations are also performed with the reaction matrix elements of the Tabakin interaction for comparison with the Hamada-Johnston results.

${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}(d, p){}_{}{}^{45}{}_{}{}^{}\mathrm{Ca}$ stripping, corresponding to the various excited states of ${}_{}{}^{45}{}_{}{}^{}\mathrm{Ca}$, has been calculated by including the effect of excitation of the $2^{+}$ state of the ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ core in the stripping process. In this calculation, the term appearing in the stripping amplitude from the protoncore residual interaction has been retained, and its effect has been found to be quite important. It has been concluded that in the cases where the stripping cross section is very small, the usual distorted-wave Born-approximation analysis, which ignores the above effect, may lead one to incorrect conclusions. On the whole, our calculated cross sections show some of the so-called nonstripping features which have been recently observed in a large number of stripping experiments.