Circular $\gamma$ polarization in heavy nuclei (${\mathrm{Ta}}^{181}$, ${\mathrm{Lu}}^{175}$) has been calculated using the two-body parity-nonconserving potential deduced on the basis of several weak-interaction Hamiltonians. Gauge invariance was elucidated by the Feynman-diagram analysis. The relative contributions from various nuclear single-particle states have been analyzed in detail. Short-range correlations have been approximately taken into account. Our calculation is compared with earlier calculations. According to our calculations, the Cabibbo conventional weak-Hamiltonian model seems to disagree with the ${\mathrm{Ta}}^{181}$ experiment. Other models allowing for extra neutral curents, such as d'Espagnat and the Lee model, might agree with experimental results. This conclusion depends on the sign of the theoretical result, which cannot be fixed with absolute certainty. The Oakes model seems to give absolute values which are too large.

Isobaric analog resonances (IAR) observed in the elastic scattering of protons from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ are analyzed in the framework of the shell-model theory of reactions. Parametrization of the energy-averaged $S$ matrix elements given by the shell-model theory is discussed, and the dependence of the spectroscopic factors upon the various optical-model parameters is exhibited. The resonance mixing phases for most of the IAR analyzed here cannot be distinguished from zero. Damping of the single-particle wave functions arising from the nonlocality of the optical potentials is consistently incorporated. The nonlocality length of 0.85 F employed in this analysis leads to an attenuation of the single-particle wave functions by about 15% inside the nucleus. Neutron spectroscopic factors obtained here compare favorably with corresponding results from the study of ($d,p$) and ($t,d$) reactions.

The cluster expansion for the energy for a system with Bijl-Dingle-Jastrow (BDJ) correlation structure is derived in a new form. It is shown how the theory may be related to the Brueckner-Bethe-Goldstone theory with a particular choice for the correlation operator (or wave matrix) appearing in the BDJ wave function. The three-body cluster terms are discussed. It is shown that these clusters contain a limited class of dispersive terms which may be included in the analysis of the two-body clusters. The three-body clusters are also shown to contain terms which correct for violations of the Pauli principle in the correlation operator.

Several aspects of the three-body problem with singular-core interactions given by the boundary-condition model (BCM), are studied. The kernel of the Faddeev equations for these interactions is shown to have an infinite Schmidt norm even if the two-body interactions are confined to a single partial wave. This does not necessarily imply that the Faddeev kernel is noncompact. A proof of the compactness (or noncompactness) of the kernel has not been found. We consider a family of two-body interactions, with square repulsions of strength $V$ for particle separation $r<\mathrm{}{r}_0$ which become the BCM in the limit $V_0\to \infty$. For finite $V_0$ the Faddeev kernel has a finite Schmidt norm (and is hence compact) and standard numerical matrix texhniques may be used for solving the three-body equations. Simplified calculations of the triton binding energy, using two-body $s$-wave interactions of this type, are carried out for a number of choices of $V_0$. The two-body potentials for $r>\mathrm{}{r}_0$ are not varied. It is found that the three-particle binding energy has a simple dependence on $V_0$. The value of the binding energy extrapolated to the limit $V_0=\infty$ is found to be in excellent agreement with the result of a previous calculation based on BCM two-particle interactions and numerical methods predicated on the assumed validity of standard matrix-inversion techniques. Some implications of these results for more realistic calculations on three-body systems with two-body singular-core interactions are discussed.

The ($\alpha ,2\mathrm{}\alpha$) reactions on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ at 42.8 and 49.2 MeV and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at 46.0 and 52.5 MeV have been studied in order to test the validity of the impulse approximation. The experimental data are consistent with this approximation, but the over-all agreement is much worse than in the case of the ($\alpha ,2\mathrm{}\alpha$) reaction on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$.

This paper is devoted to the study of elastic scattering processes with the use of nonlocal separable interactions. An explicit and general expression for the transition amplitude has been given which includes Coulomb effects and possible excitation of the particles involved. As a first application of the formalism it is shown that a striking improvement of Mongan's results can be obtained in $p-p$ elastic scattering just by including Coulomb effects at low energy. We have then studied the nucleon-$\alpha$ elastic scattering below 50 MeV and the $\alpha -\alpha$ elastic scattering below 100 MeV, and the results obtained are in very good agreement with experimental data.

The photoneutron cross section for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured with monoenergetic photons from threshold to 31 MeV. The cross section reaches its maximum value of 1.0 mb from 24.3 to 27.3 MeV and appears to be split into two broad peaks. The integrated cross section is 7.9 MeV mb. The fore-aft asymmetry of the photoneutrons also was measured. This quantity, which is a measure of the interference between the $E1\mathrm{}$ amplitude and the underlying positive-parity contribution, changes from forward to backward peaking at about 27 MeV. The $E2\mathrm{}$-to-$E1\mathrm{}$ amplitude ratio deduced from these data is of the order of 0.04. A comparison of the cross-section results with the considerably larger values for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\gamma ,p)$ reaction measured elsewhere shows appreciable ( 15%) isospin mixing throughout the energy region studied, with indications that this mixing might be increasing with energy above 28 MeV.

The energy-density functional proposed by Brueckner etal. is used to calculate the average nuclear-binding-energy surface on the $N-Z$ plane at $\beta$ stability ± about 40 units. The equibinding contours are compared with those predicted by recent liquid-droplet models. Normally, some disagreement begins about 15 units away from the region of known nuclei. The deviations towards lower binding are significant for neutron-rich transuranium (superheavy) nuclei. This would seem to indicate a physically important uncertainty in conventional masslaw extrapolations. The semiempirical dependence on neutron excess cannot be established very well, because of the narrowness of the region of known isotopes. The energy-density functional, on the other hand, incorporates the present knowledge about nuclear matter - including recent neutron-matter results. Our disagreement with other extrapolations, therefore, questions the validity of stability and formation (e.g., $r$-process) calculations based on conventional mass formulas.

The contribution of the "induced-tensor" term in allowed nuclear $\beta$ decays is predicted in the impulse approximation. Current experimental results are compared with these predictions and additional experiments are suggested which could verify the existence of such an effect.

The polarization and cross sections for $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering are calculated for $\Lambda$ incident energies 1-20 MeV. A $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential is constructed using a phenomenological $\Lambda N$ Gaussian central potential and the empirical shape for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and a spin-orbit potential obtained from a one-boson-exchange (OBE) model for the $\Lambda N$ interaction. As indicated recently by Downs, the OBE model for $\Lambda N$ forces leads to strong antisymmetric spin-orbit terms due to vector-meson exchange. This means that the $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential depends only on part of the $\Lambda N$ spin-orbit interaction, since it results from summing the latter interaction over the nucleon spin states. Parameters from three quite different OBE calculations are used to predict the $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering, and these three sets of OBE parameters lead to remarkably similar predictions concerning the cross sections and polarization properties for this energy range. However, no $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ resonances are predicted, in contrast to recent Hartree-Fock calculations of $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering. The polarization effects predicted are large, and experimental data concerning them would have interesting consequences for our knowledge of the origin of spin-orbit forces in the baryon-baryon system.

Semileptonic processes between members of a common isotopic multiplet provide a nearly model-independent test for currents with anomalous or "second-class" $G$-parity properties. For such processes the implications of the presence of second-class currents are discussed for $\beta$ decay, muon capture, and elastic neutrino scattering.

The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d)$ reaction has been used to investigate the structure of the low-lying states of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$. Cross sections are small (a few μb/sr) but angular-distribution shapes are consistent with a direct process. The results suggest considerable mixing between low-lying fourparticle and six-particle-two-hole states in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$.

The levels of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Y}$ have been studied with the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(d,\alpha )$ and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ reactions with 30-to 40-keV resolution at 15-MeV incident energy. The ($d,\alpha$) angular distributions for transitions to eight prominent levels below 2.2 MeV have been measured over $15°\le \theta \le 150°$. The reliability of parameters entering distorted-wave Born-approximation calculations was checked in detail. The ($d,\alpha$) calculations include the finite-range correction of Chant and Mangelson. The two-nucleon form factors (f.f.) were generated by the oscillator-expansion technique of Drisko and Rybicki, and the effect of residual interaction on the f.f. and angular distributions was studied. An attempt has been made to determine the ($d,\alpha$) absolute normalization constant based on local zero-range calculations, and limits of $20\le D_0^{}{}_{}{}^2\le 30$ have been set. Two-nucleon f.f. generated by the Bayman-Kallio method were compared with the Drisko-Rybicki f.f. The (${}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha$) angular distributions for eight strongly populated levels below 1.7 MeV were measured over $20°\le \theta \le 125°$. Spectroscopic factors and $l_n$ transfers have been extracted with both local zero-range and nonlocal finite-range calculations. The (${}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha$) results were compared with ($d,\alpha$) results to determine unique parities and narrow $J^{\pi }$ limits for the levels studied. ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and $\alpha$ elastic scattering on ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ have also been measured and optical-model potentials have been determined. Good agreement between this work and the recently reported ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}(\alpha ,n\gamma ){}_{}{}^{88}{}_{}{}^{}\mathrm{Y}$ results is seen for the level energy and $J^{\pi }$ assignments made.

The reactions ${\mathrm{Sr}}^{87}({\mathrm{He}}^3,d){\mathrm{Y}}^{88}$, ${\mathrm{Sr}}^{87}(\alpha ,t){\mathrm{Y}}^{88}$, ${\mathrm{Sr}}^{88}({\mathrm{He}}^3,t){\mathrm{Y}}^{88}$, and ${\mathrm{Y}}^{89}({\mathrm{He}}^3,\alpha ){\mathrm{Y}}^{88}$ were studied and the data were used to construct a level scheme of ${\mathrm{Y}}^{88}$. Spin and parity assignments are suggested for many new states below 2.5 MeV. The principal components of their wave functions are interpreted in terms of particle-hole multiplets. The angular distributions from the (${\mathrm{He}}^3,t$) reaction are not well fitted by distorted-wave calculations. Some systematic patterns of the (${\mathrm{He}}^3,t$) reaction mechanism are noted, but the exceptions indicate that the conventional treatment of the (${\mathrm{He}}^3,t$) reaction may be far from adequate.

Proton-$\gamma$-ray coincidence measurements have been made on the reactions ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}({}_{}{}^3{}_{}{}^{}\mathrm{He},p\gamma ){}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}({}_{}{}^3{}_{}{}^{}\mathrm{He},p\gamma ){}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ at incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energies of 12 and 13 MeV. The protons were detected at 0° to the beam direction, thereby preferentially selecting $L=0\mathrm{}$ transfers of neutron-proton pairs. A Ge(Li) detector at 90° detected the $\gamma$ rays with good energy resolution. Angular distributions for the ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ reaction were measured with a magnetic spectrograph. These, together with previous results on the ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ reaction, gave precise information on the intensities of the states excited, as well as their energies. The main purpose of the experiments was to measure the $\gamma$ decay of the lowest-lying isobaric analog states in ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$. The analog state in ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ was found to decay primarily (85%) to the 842-keV level and secondarily (15%) to the ground state. The analog state in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ decays in a more complex fashion to several states. The strongest transition (55%) is to the 4091-keV state. $\gamma$-ray decay schemes for several other low-lying even-parity levels in ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ were also measured. The observation that the 4091-keV level of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ decays (34%) to the ${\frac{7}{2}}^{-}$ ground state and (58%) to the ${\frac{3}{2}}^{+}$ level at 2009 keV suggests a ${\frac{5}{2}}^{+}$ assignment. The implications of the measurements are discussed, particularly with reference to the structure of low-lying two-particle-one-hole states in these nuclei.

The ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}\mathrm{}(d,p)\mathrm{}{}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$ reaction leading to three strong low-lying states in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}(d_{\frac{5}{2}}\mathrm{g}.\mathrm{s}.\mathrm{}, 0.53 \mathrm{MeV}{s}_{\frac{1}{2}}, \mathrm{and} 1.47 \mathrm{MeV}{d}_{\frac{3}{2}})$ has been studied as a function of energy from 5.0 to 10.5 MeV at 100, 120, 140, and 160° laboratory angles. The strong, unusually shaped threshold cusp observed in the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}\mathrm{}(d,p)\mathrm{}{}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$($d_{\frac{5}{2}}$ g.s.) excitation curve near 7.56 MeV, threshold of the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}\mathrm{}(d,n)\mathrm{}{}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^A{}_{}{}^{}$ ($d_{\frac{5}{2}}$ isobaric analog resonance) reaction, is discussed in terms of its position in a systematic study and classification of such threshold effects, using simple quantitative physical considerations. The ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ data are fit with coupled-channel Born-approximation calculations.

A gridded ionization chamber was used to detect charged particles produced when ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ was bombarded with 14.4-MeV neutrons. The energies of the $\alpha$ particles so produced yielded levels in ${}_{}{}^{37}{}_{}{}^{}\mathrm{S}$ of 0.59 ± 0.10, 1.39 ± 0.09, 2.20 ± 0.05, and 2.83 ± 0.09 MeV. The $Q$ value for the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}(n,\alpha ){}_{}{}^{37}{}_{}{}^{}\mathrm{S}$ reaction was determined to be -2.41 MeV. Cross sections calculated for the reaction to the ground state and the four excited states are 2.1 ± 0.4, 0.3 ± 0.1, 3.1 ± 0.6, 3.5 ± 0.7, and approximately 0.3 mb. The total cross section for the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}(n,\alpha ){}_{}{}^{37}{}_{}{}^{}\mathrm{S}$ reaction was determined to be 9.4 ± 1.0 mb. Comparisons between the results herein reported, other work, and theoretical predictions are made.

Energy levels in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ have been observed in the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(n,\alpha )$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\mathrm{}(n,p)\mathrm{}$ reactions using a gridded ionization chamber. In the reaction ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(n,\alpha ){}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, cross sections to the ground state and four excited states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ at 0.83, 3.18, 3.90, and 4.63 MeV were determined to be 6.6 ± 2.5, 1.0 ± 0.4, 1.5 ± 0.4, 2.0 ± 0.4, and 1.3 ± 0.3 mb, respectively. The total cross section for the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(n,\alpha )$ reaction is 12.4 ± 4 mb. The ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}(n,2\mathrm{}\alpha ){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ reaction was observed and the $Q$ value and cross section to the ground state of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ were found to be -7.00 ± 0.02 MeV and 41.8 ± 8.1 mb, respectively.

Comparison of the results of the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},p)$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}\mathrm{}(d,p)\mathrm{}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}(d,\alpha )$ reactions leads to an assignment of $J^{\pi }=1^{+}$ for the state at $E_x=3.489\mathrm{}$ MeV in ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$. These results, together with previous information, lead to the identification of the 3.531-MeV state as the only $0^{+}$ state predicted below 6 MeV. Recent information for the low-lying levels of ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ is reviewed and compared with predictions of recent shell-model calculations.