Three-body-correlation corrections to the saturation curves of two phase-shift-equivalent potentials have been computed. The corrections for both curves are of the same sign. They are very small at normal densities but increase rapidly with increasing density and defect integral.

A comparative study of the level structure of ${\mathrm{Ca}}^{44}$ is made employing the conventional shell-model and Kuo-Brown matrix elements for the Hamada-Johnston interaction, and Clement matrix elements for the Tabakin interaction. Results on spectroscopic strengths for the reaction ${\mathrm{Ca}}^{43}\mathrm{}(d,p)\mathrm{}{\mathrm{Ca}}^{44}$ and transition rates are also reported. Except for some differences, the two interactions are found to give essentially similar results. Some differences with the earlier calculation of McGrory, Wildenthal, and Halbert are also pointed out.

The correspondence between the recent Letter of the same title by Monahan, Shakin, and Thaler, and the method of "completely orthogonalized plane waves" is pointed out, and the geometrical significance of the corresponding transformation is elucidated. The analysis of Monahan, Shakin, and Thaler is generalized and simplified.

The statistical theory of nuclear reactions is applied to explain the strong tendency for protons to be transferred out of the projectile when heavy targets are bombarded by moderately heavy projectiles. The predictions of the theory for the relative probability of stripping to pickup reactions agree in general with the experimental data, and the degree of agreement increases with increasing number of transferred nucleons.

Differential cross sections for the process ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$ are presented for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ beam energies of 82.1, 64.3, and 49.9 MeV. The measurements were made to test the Barshay-Temmer theorem which requires ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ yields to be independently symmetric about 90° c.m. We find a pronounced deviation from 90° c.m. symmetry which is angle- and energy-dependent. A distorted-wave Born-approximation analysis assuming the reaction mechanism to be a simple $l=0\mathrm{}$ nucleon-pickup process can qualitatively account for the observed deviations.

A calculation of the differential cross section ($\frac{d\sigma }{\mathrm{dEd}{\Omega }^2}$) for the $\mathrm{D}\mathrm{}(p,2p)\mathrm{}$ process at 600 MeV has been carried out using as input the available nucleon-nucleon elastic scattering data and a model deuteron wave function. The calculation includes Glauber double-scattering and final-state-interaction corrections to the plane-wave impulse approximation (PWIA). The calculation agrees favorably with the recent $\mathrm{D}\mathrm{}(p,2p)\mathrm{}$ experimental data at most residual neutron recoil momenta and is an improvement over the earlier PWIA analysis. The recently proposed D* component of the deuteron appears to be unimportant in reactions of this kind.

For many years a 10% discrepancy has existed between theory and experiment for the total radiative thermal $\mathrm{np}$ capture cross section. This process is usually considered to be dominated by a ${}_{}{}^1{}_{}{}^{}S\to d$ transition. Breit and Rustgi have shown that a significant amount of ${}_{}{}^3{}_{}{}^{}S\to d$ transition would be detectable in experiments with polarized $n$ and $p$. We show that the ${}_{}{}^3{}_{}{}^{}S\to d$ transition can be described with a general transition current containing two parameters. On the assumption that the amplitude is large enough to explain the discrepancy, we give angular distributions for the $\gamma$-ray emission from polarized $n$ on polarized $p$. On the other hand, we calculate theoretical values for the parameters which indicate that the ${}_{}{}^3{}_{}{}^{}S\to d$ transition is probably not large enough to explain the discrepancy, and we discuss the correctness of the theory.

Hartree-Fock calculations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically. Skyrme's interaction is described and the general formula for the mean energy of a spherical nucleus derived. Hartree-Fock equations are obtained by varying the mean energy with respect to the single-particle wave functions of occupied states. Relations between the parameters of the Skyrme force and various general properties of nuclear matter and finite nuclei are analyzed. Calculations have been made for closed-shell nuclei using two rather different sets of parameters, both of which give good binding energies and radii for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Both interactions give good binding energies and charge radii for all closed-shell nuclei. Calculated electron scattering angular distributions agree qualitatively with experiment, and for one interaction there is good quantitative agreement. The single-particle energies calculated with the two interactions are somewhat different owing to a different nonlocality of the Hartree-Fock potentials, but both interactions give the correct order and density of single-particle levels near the Fermi level. They differ most strongly in their predictions for the energies of $1s$ single-particle states.

The 90° yield from the reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(d,{\gamma }_0){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ has been measured between 2.1 and 2.9 MeV to accurately determine the location of the strong resonance previously observed in this region. Two separate measurements were made. It is found that the resonance occurs at $E_d=2.40\mathrm{}\pm 0.05$ MeV, moving it with respect to the dip ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(p,{\gamma }_0){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma ,n_0){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$. This result brings into question interpretations of the fine structure of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ giant dipole resonance made on the basis of earlier experimental work.

The soft-pion theory and the Fubini-Furlan mass dispersion relations have been used to analyze the pion-nucleon scattering lengths and obtain a value for the $\sigma$ commutator term. With this value and using the same principles, scattering lengths have been predicted for nuclei with mass number ranging from 6 to 23. Agreement with experiment is very good. For those who believe in the Gell-Mann-Levy $\sigma$ model, the evaluation of the commutator yields the value $0.26{\left(\frac{m_{\sigma }}{m_{\pi }}\right)}^2$ for the $\sigma$-nucleon coupling constant. The large dispersive corrections for the isosymmetric case imply that the basic idea behind many of the soft-pion calculations, namely, slow variation of matrix elements from the soft-pion limit to the physical pion mass, is not correct.

A variational-bound formulation of the three-body problem based on the Faddeev equations has been derived previously. This method involves a variational calculation of the exact effective potential between the incident particle and the bound two-body target. Variational upper and lower bounds on this effective potential are obtained by constructing approximate separable three-body Green's operators. The eigenphase shifts determined by using the effective potential in the two-body Lippmann-Schwinger equation are upper and lower bounds on the true eigenphases for energies below the three-body breakup threshold. The method is applied to the neutron-deuteron system, and a set of variationally converged phase shifts is obtained.

The particle decays of the first $T=\frac{3}{2}$ state in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ (${}_{}{}^9{}_{}{}^{}\mathrm{B}$) have been studied by the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},pn)$ reaction at $E\left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)=10.0\mathrm{}$ MeV (8.7 and 7.95 MeV). Protons (neutrons) emitted at 0° were detected in coincidence with decay neutrons (protons). Neutron energy was determined by the associated-particle time-of-flight technique. The ratios of partial neutron (proton) widths to the ground and first excited states of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ to the ground-state radiative width ${\Gamma }_{{\gamma }_0}$ are found to be, respectively, 6.4 ± 2.0 and 20.4 ± 4.6 for the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ analog state (<1.5 and 13.9 ± 2.1 for ${}_{}{}^9{}_{}{}^{}\mathrm{B}$). Taking ${\Gamma }_{{\gamma }_0}=10.5\mathrm{}\pm 1.5$ eV, these results give ${\Gamma }_{n_0}=67\mathrm{}\pm 26$ eV, ${\Gamma }_{n_1}=213\mathrm{}\pm 56$ eV, ${\Gamma }_{p_0}<18\mathrm{}$ eV, and ${\Gamma }_{p_1}=147\mathrm{}\pm 30$ eV for the mirror decays.

The "elementary-particle" treatment of nuclear $\beta$ decay is extended to include the effects of final-state Coulomb interactions. The resulting formalism is valid for both allowed and forbidden decays. The Coulomb correction in allowed transitions is considered in detail and compared with the usual impulse-approximation calculation. The spectrum shape factor for the transition ${\mathrm{B}}^{12}\to {\mathrm{C}}^{12}+e^{-}+{\overline{\nu }}_e$ is evaluated as an example.

At a bombarding energy of 24 MeV, angular distributions have been measured for the reactions ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^6{}_{}{}^{}\mathrm{Li},t){}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$. A distorted-wave Born-approximation (DWBA) analysis in the zero-range three-nucleon-cluster-transfer approximation has been performed. The sensitivity of the DWBA calculations on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ parameters was demonstrated, with 160-190-MeV real-well-depth ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ parameters giving the best fits. By using Watson's ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ parameters, it was possible to account for the observed differences between the (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) and (${}_{}{}^6{}_{}{}^{}\mathrm{Li},t$) cross sections. The extracted relative spectroscopic strengths are consistent with the known structure of the final states.

We have measured the intensities of $2p-1s$ pionic x-ray transitions in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ using an absolute-efficiency technique. A pion-cascade calculation which was constrained to reproduce the observed yields predicted population probabilities for the mesonic levels and gave values for the strong-interaction level widths. The $2p$-level broadenings are 0.015 ± 0.005 eV for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, 0.16 ± 0.03 eV for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, 2.1 ± 0.6 eV for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and 12 ± 4 eV for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Comparisons are made with results obtained by others and with predictions based upon a semiphenomenological optical potential. Empirical capture schedules for ${\pi }^{-}$ in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are also presented.

The Jastrow method has been extended to the treatment of tensor forces by the incorporation of suitable spin and isospin dependence into the correlation operators. Here the three-body contributions to the factor-cluster expansion of the energy expectation value are evaluated for nuclear matter, supplementing the evaluation of the one- and two-body contributions already reported in the first paper of this series. Complete numerical results are presented for three semirealistic hard-core potentials containing differing mixtures of central and tensor components. The three-body corrections result in a distinct improvement of the saturation behavior of the approximate energy per particle. Nevertheless, these calculations should be regarded as still exploratory rather than final in the sense that the most intelligent (i.e., a suitably restricted) choice of radial dependence has not yet been determined for the correlation functions.

Current descriptions of ($p,2p$) reactions, nucleon-nucleon bremsstrahlung, and low-energy pion production use the half-off-shell two-nucleon $T$ matrix in the neighborhood of the on-shell point. We present a method for expanding the amplitude $t_0(p,k,;k^2)$ in powers of $p-k$. After explicitly extracting the contributions arising from the long-range part of the interaction, we obtain a power series with an infinite radius of convergence. The coefficients of this series are expressed in terms of weighted integrals of the difference function, thus permitting us to determine precisely how variations of the interior wave function affect the near off-shell behavior of the half-shell $T$ matrix. This allows treatment of a large class of models for the two-nucleon interaction, including wave-function models as well as local, nonlocal, and energy-dependent potentials. As an example, we apply this method to a wave-function model of the two-nucleon ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ $T$ matrix constructed by the authors in a previous paper. We find that the expansion converges rapidly and that the inclusion of more terms extends the representation farther off the energy shell. The expansion coefficients are smooth, rapidly decreasing functions of energy. The even coefficients and the odd coefficients each form a family of similar functions which fall off rapidly with index. The $T$ matrix arising from this model is very similar to those obtained with realistic potentials. Since the coefficient functions can be tabulated or parametrized quite simply, this expansion should provide a compact, useful method of expressing and comparing the near off-shell behavior of the two-nucleon half-shell $T$ matrices arising from different models while permitting one to maintain both a fixed phase shift and the correct long-range behavior of the potential.

A search has been made for double positron-electron pair creation by photons of 6.13 MeV. $\gamma$ rays from the reaction ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(p,\alpha ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ were incident on Ge(Li) detectors of either 15- or 4-${\mathrm{cm}}^3$ volume and the pulse-height spectra were examined for the presence of a four-escape peak. Such a peak was, in fact, observed using the 15-${\mathrm{cm}}^3$ detector, but is accounted for by secondary effects, namely, the production of a second pair by bremsstrahlung from the first pair and the direct production of a second pair by the members of the first pair. These secondary effects are evaluated in the appendixes. An upper limit on the cross section for the genuine production of two pairs (${\sigma }_2$) in one photon-nucleus encounter at 6.13 MeV relative to the formation of a single pair (${\sigma }_1$), is represented by the experimentally determined ratio $\frac{{\sigma }_2}{{\sigma }_1}=-(2\mathrm{}\pm 5)\times {10}^{-5\mathrm{}}$; this is consistent with the theoretical expectation of order ${\left(\frac{\alpha }{\pi }\right)}^2$.