The distorted-wave Born approximation (DWBA) cross section is discussed for a reaction of the form $A(d,pn)A$ in which $n$ is not observed. We evaluate the slowly convergent oscillating radial integrals by contour integration in the complex radius plane. This avoids the computation of wave functions out to the large distances that the Huby-Mines technique requires. The present technique is also useful for stripping to very weakly bound states. We find that the DWBA angular distribution for stripping to a resonant $n$ state is closely reproduced by using a form factor for the resonant energy of $n$. The width of the resonance, rather than the spectroscopic factor, is found to be measured by the absolute magnitude of the cross section. The results of calculations with the present method are compared with the results of the Huby-Mines method for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(d,p)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ reaction leading to the resonant 5.08-MeV state of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$.

Plastic scintillators were exposed in the external 920-MeV $\alpha$-particle beam at the 184-in. cyclotron at Lawrence Radiation Laboratory. The beam-flux monitor was Ilford 100-μ L4 pellicles. The cross section for ${\mathrm{C}}^{12}(\alpha ,\alpha n){\mathrm{C}}^{11}$ was found to be 49.4 ± 1.8 mb.

The generalized cranking model is used to study the corrections to the nuclear rotational spectra that cause it to deviate from the $I(I+1\mathrm{})\mathrm{}$ rule. The fourth-order cranking corrections and the Coriolis-antipairing effect are treated as modes of a generalized vibration in the same way as the centrifugal stretching. The new form helps to explain the success of various two-parameter formulas used to fit the experimental energy levels and shows that they are equivalent. The parameters of such formulas are calculated here microscopically in a good- $j$ basis, and they agree reasonably well with experiment.

Experimental $B\left(E2\mathrm{}\right)\mathrm{}$ values are tabulated for transitions in odd-mass spherical nuclei and compared with predictions of the pairing-plus-quadrupole model including up to two phonons. Of the well over 100 cases, agreement within a factor of 2 is obtained for $\approx \frac{2}{3}$, indicating the general validity of the theory and suggesting its use as a guide to yet unmeasured cases.

The three-body breakup reactions induced by 47-MeV protons on a gaseous ${\mathrm{He}}^4$ target have been investigated in a kinematically complete experiment. Protons were observed in coincidence with tritons or ${\mathrm{He}}^{3,}$s at several pairs of coplanar lab angles using two counter telescopes. Data were stored by an on-line computer which serially listed four linear signals from each event on magnetic tape. The proton spectra showed strong enhancements from neutron-proton and proton-proton final-state interactions, in agreement with the predictions of the Watson-Migdal theory. A Chew-Low-type extrapolation procedure was used to extract the $\mathrm{np}$ singlet scattering length, which was in fair agreement with the value from $\mathrm{np}$ free scattering. The triton and ${\mathrm{He}}^3$ spectra showed peaks due to sequential reaction processes via the continuum resonance states in the ${\mathrm{He}}^4$ system. These enhancements could be identified with previously observed ${\mathrm{He}}^4$ levels of known spin and parity assignments.

The $R$-matrix expansion for the ground-state energy of a many-fermion system is carried through fourth order. We evaluate this expansion for a potential modeled after the nucleon-nucleon one. The calculation is described in detail. We find that the "hole-line" approximation seems to underestimate the attraction so that a hard-core force may well be consistent with the experimental binding energy of large nuclei.

A thick-target method has been used to measure absolute differential cross sections for the reactions ${\mathrm{O}}^{16}\mathrm{}(d,n)\mathrm{}{\mathrm{F}}^{17}$ and ${\mathrm{O}}^{16}\mathrm{}(d,n)\mathrm{}{\mathrm{F}}^{{17}^{*}}$ (0.500 MeV) from 2.0 to 4.2 MeV. Excitation functions were taken at 20° intervals from 0-160° in the lab system. Satisfactory fits to the angular distributions required Legendre polynomials of order 6 or higher. The c.m. Legendre coefficients $A_0$ and $A_1$ are presented as a function of lab deuteron energy for the ground-state data. The total cross sections for production of ground-state and first-excited-state neutrons are also given as a function of energy.

The elastic scattering of the $\Lambda$ particle by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been studied in the 0.1- to 10.0-MeV energy range. The calculation was performed using baryon-baryon interactions composed of central potentials previously employed in binding-energy calculations of ${}_{\Lambda }{}^5{}_{}{}^{}\mathrm{He}$ and a derivative spin-orbit $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential. Phase shifts, total cross sections, angular distributions, and polarizations were computed as functions of energy for $l=0,1, \mathrm{and} 2$. The results are sensitive to the potential parameters, implying that even simple measurements would yield interesting information.

Realistic shell-model potentials are used to test Strutinsky's method. It is found that the results are strongly dependent on the shell-smearing parameter as well as the order of the curvature correction for smearing. No unambiguous values can be obtained for the shell correction, even with the effect of the continuum properly included. As a result, the Strutinsky theory should be regarded only as a recipe to be used in combination with Nilsson potentials.

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 ${\mathrm{Na}}^{23}$.