This investigation has a twofold objective, (a) to examine in some detail the effects of various refinements in the input forces on the binding energy (BE) of the triton and the doublet neutron-deuteron scattering length ($a_{\frac{1}{2}}$), and (b) to compare the effects of shape variations in the potentials on the evaluation of the same quantities. For this purpose, we calculate the BE and $a_{\frac{1}{2}}$ with the inclusion of tensor and core effects individually and collectively and give a comprehensive comparison of these results along with those obtained in earlier investigations by various authors. For the second objective, we present the results for an entirely different shape of the separable potentials (viz., form factors of the type $\surd Q_0$ which fulfill certain analyticity requirements on the potentials), and compare these predictions with those based on potentials proposed by Yamaguchi and Yukawa. The effects of the shape variation on the results found from the comparison of these potentials, which agree only approximately on the energy shell, persist even with higher-ranked potentials which agree much more closely on the energy shell as a result of the inclusion of repulsive-core terms. The limitations that the effects of shape variations imply on the reliability of three-body calculations with input two-body forces are discussed.

An energy-dependent phase-shift analysis of 0-20-MeV $n-\alpha$ scattering is attempted. Reasonable fits to the 0-16.4 data are obtained, but the rest of the data up to 20 MeV elude good fits. Single-energy analyses at energies where polarization data are available corroborate the energy-dependent analysis. Our results differe from the Hoop-Barschall phases as follows: $P_{\frac{1}{2}}$ is larger between 3 and 10 MeV; $S_{\frac{1}{2}}$ and $P_{\frac{3}{2}}$ are larger between 10 and 16.4 MeV. We are not able to reliably determine $D$ or $F$ waves in this energy range.

We have measured the normalized $\alpha -\gamma$ angular correlation in the reaction plane for excitation of the 4.44-MeV, $2^{+}$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 22.750 MeV. These data yield the relative populations ${\left(a_m\right)}^2$ of the three magnetic substates referred to the normal to the reaction plane. The ambiguity between ${\left(a_{+2\mathrm{}}\right)}^2$ and ${\left(a_{-2\mathrm{}}\right)}^2$ was resolved by coincidence measurements of the circular polarization of deexcitation $\gamma$ rays emitted near the normal to the reaction plane. The inelastic scattering process can then be dissected into partial differential cross sections ${\sigma }_m$ to the substates. The results show that each ${\sigma }_m$ has a different angular dependence. ${\sigma }_0$ has the most regular and pronounced diffractionlike structure, ${\sigma }_{-2\mathrm{}}$ dominates out to 75°, and ${\sigma }_{+2\mathrm{}}$ dominates thereafter. Thus, the excited nuclei spin in the sense of classical hard-sphere scattering with friction out to ≈ 75°, and in the reverse sense from ≈ 75° to ≈ 170°. The nuclear polarization exhibits an oscillatory character as a function of angle. Comparison of the results with diffraction-model calculations, and with distorted-wave Born-approximation calculations, is poor. In principle, the experimental method, though difficult, could be applied to nuclei which are more accurately described by nuclear models than is ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.

The approximate treatment of the nonlocality of the optical potential describing scattering from a set of $N$ nonoverlapping potentials is shown to lead to erroneous effective local potentials. The difficulty is circumvented by constructing a local two-body $t$ matrix which leads directly to a local potential.

States of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$ have been investigated via the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}(d, p){}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$ reaction, with 11-MeV deuterons and an over-all energy resolution of 30 keV. Proton groups leading to 23 states in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$ have been identified. The angular-distribution data have been analyzed using finite-range distorted-wave Born-approximation (DWBA) calculations to extract spectroscopic information. Spin and parity assignments, excitation energies, and spectroscopic factors for most of the observed levels are presented. Comparisons are made with preliminary data of proton elastic scattering from ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ at isobaric analog resonances.

Analog resonances in ($p, p$) and ($p, p^{\prime }$) excitation functions on ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ have been studied, and previous data have been extended to complete the range from $E_p=4.8\mathrm{} \mathrm{to} 12$ MeV and include residual channels up to $E_x=4.5\mathrm{}$ MeV in the target system. The various reaction mechanisms contributing to the observed structure are assayed. A comparison of the present data with similar experimental results in this mass region has been made, and the empirical evidence for particle-core coupling in the spectra of several odd-$A$ nuclei near $N=50\mathrm{}$ has been stressed. The possible existence of composite particle-core structure involving the $0_1^{+}$ and collective $2_1^{+}$ and $3_1^{-}$ cores is discussed and a consequent means of populating two-phonon $2_1^{+}$×$3_1^{-}$ state is suggested. Evidence for particle coupling to noncollective core excitations is also cited.

Further studies of the ${\mathrm{Ne}}^{20}({\mathrm{He}}^3, p){\mathrm{Na}}^{22}$ reaction have been carried out to investigate in particular those ${\mathrm{Na}}^{22}$ states of excitation energy greater than 2.9 MeV. From a measurement of the linear polarization of $\gamma$ rays from ${\mathrm{Na}}^{22}$ states formed in the above reaction, it has been determined that the 3-MeV doublet states at 2.969 MeV ($J=3\mathrm{}$) and 3.059 MeV ($J=2\mathrm{}$) both have even parity. The $\gamma$ decays of higher-lying states were investigated through $p-\gamma$ coincidence measurements which utilized a 30-cc Ge(Li) spectrometer for $\gamma$ detection. Correlation results lead to a $J^{\pi }=3^{-}$ assignment for the 3.521-MeV state. The $p-\gamma$ measurements also determine the principal $\gamma$ decay of 9 of the 13 states previously reported in the region $4 \mathrm{MeV}<E_{\mathrm{ex}}<5.2\mathrm{} \mathrm{MeV}$. Some information is also obtained on the spins of these states. Evidence is presented for the decay of a previously unreported level at an excitation energy of 4.294±0.002 MeV.

The spectrum of $\gamma$ rays following neutron capture at the 1167-eV resonance in ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ has been measured at 90° and 135° to the incident beam. The partial widths for radiative decay have been determined and compared to the Weisskopf estimates. The $M1\mathrm{}$ and $E1\mathrm{}$ $\gamma$-ray strengths are found to be comparable, and a sizable $E2\mathrm{}$ $\gamma$ ray in the resonance has been recorded. On the basis of the $\gamma$-ray measurements at two angles, and from what has been determined from other experiments, the spin and parity of the 1167-eV resonance are shown to be ${\mathrm{½}}^{-}$.

We present a model of deuteron stripping and elastic scattering which treats explicitly the contributions from channels in which the deuteron is broken up into a relative $S$ state and the target is in its ground state. An adiabatic treatment of these channels leads to a description of deuteron stripping which resembles the distorted-wave Born approximation, although a deuteron optical potential plays no role. The adiabatic approximation is shown to give a good account of 21.6-MeV elastic deuteron scattering from Ni, at least for surface partial waves, and is expected to apply to other nuclei in this mass and energy region, as well as at higher energies. The calculations assume that the effective two-nucleon-nucleus interaction is the sum of the nucleon optical potentials evaluated at one-half the incident deuteron kinetic energy. Some possible corrections to this assumption are discussed.

The structure of the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ nucleus is studied using a variational procedure. The method of angular-momentum projection from a deformed intrinsic state is applied, and each $J^{\pi }$ state is projected from a determinant which is variationally "best" for that state. This more general variational procedure includes important vibrational correlations, which in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have hexadecapole character. The level spacings in the energy spectrum improve considerably compared to those in the Hartree-Fock method followed by angular momentum projection, and this leads to a much better agreement with the experimental spectrum. The $E2\mathrm{}$ transition probabilities, except for the $6^{+}$→$4^{+}$ transition, are also in good agreement with the experiments.

The ${\mathrm{Na}}^{23}(d, n)$, the ${\mathrm{Mg}}^{26}(d, n)$, and the ${\mathrm{Al}}^{27}(d, n)$ reactions were used to populate isobaric analog states. Their $\gamma$ decays were measured with a Ge(Li) detector (i) in coincidence with the neutron groups, (ii) in singles arrangements using a bare detector, and (iii) in a three-crystal configuration. The observed branching ratios were compared to the approximate selection rules operating in the rotational and the Hartree-Fock model. It is found that the 4.23-MeV state in ${\mathrm{Mg}}^{24}$ has a wave function with admixtures of angular momentum projection $K=0\mathrm{}$ and $K=2\mathrm{}$. This fact supports the model proposed by Kelson et al. which gives an ellipsoidally symmetric deformation to ${\mathrm{Mg}}^{24}$. The observed transitions in ${\mathrm{Si}}^{28}$ indicate that the analog of the ground-state doublet in ${\mathrm{Al}}^{28}$ has an oblate deformation.

From the microscopic calculation for the W, Os, and Pt nuclei, we obtain semiquantitative relations among the prolate-oblate difference of the potential energy of deformation, the ${2_{\gamma }}^{+}$ and $4^{+}$ level splitting, and the static quadrupole moment ${Q_2}^{+}$. These relations are applied to ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$. The important role of the $\beta -\gamma$ dependence of the mass parameters is demonstrated.

The neutron-proton bremsstrahlung cross section between 14 and 208 MeV is calculated by including the external radiation terms to all orders in the momentum of the photon, $K$, and by using the low-energy theorem to compute the internal scattering contribution to order $K^0$. These calculations, which employ a simple off-shell calculations of the elastic phase shifts, are in good agreement with the data at 208 MeV. These off-shell calculations are also compared to calculations using the corresponding on-shell phase shifts in order to determine the strength of the off-shell terms. In coplanar scattering where ${\theta }_p+{\theta }_n\le \sim 60°$, these off-shell effects constitute as much as 50% or more of the cross section, while for $60°\le {\theta }_p+{\theta }_n\le 90°$, the offshell contributions are much smaller.

Finite-range stripping calculations are made for heavy-ion reactions which involve nucleon transfer. Three reactions have been studied, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, which span energy regions below, near, and above the Coulomb barrier, respectively. At the low energies, there is quantitative agreement with experimental angular distributions and total cross sections. At higher energies, the agreement with experiment deteriorates as the results become more sensitive to the optical-model parameters used in the calculations. The effects of a repulsive core are noted, and attempts are made to fit some ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ elastic scattering data.

The Hankel-transform (inpact-parameter representation) method is used to simplify the derivation of the diffraction model of direct nuclear reactions. Both first- and second-order processes (represented by pole, triangle, and box diagrams) are discussed, and relatively simple formulas for the corresponding diffraction-model amplitudes are given. Inclusion of Coulomb effects and the extension to backward-peaked processes are also discussed.

The electrodisintegration of the deuteron near threshold has been investigated by inelastic electron scattering at momentum transfers $q=0.35\mathrm{}$ ${\mathrm{F}}^{-1\mathrm{}}$ and $q=0.66\mathrm{}$ ${\mathrm{F}}^{-1\mathrm{}}$ and scattering angles $\theta =125\mathrm{}°, 140°, \mathrm{and} 155°$. The longitudinal and transverse matrix elements to the final ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ states have been compared with the Jankus-Durand theory using repulsive-core wave functions. The repulsive-core parameter, corresponding to a radius of about 0.2 F, has been adjusted to fit the elastic deuteron form factors up to $q=6\mathrm{}$ ${\mathrm{F}}^{-1\mathrm{}}$. The computed inelastic cross sections give a statisfactory description of the existing data in the whole momentum-transfer range experimentally investigated: ($0.35 {\mathrm{F}}^{-1\mathrm{}}\le q\le 3{\mathrm{F}}^{-1\mathrm{}}$).

We report extensive differential cross-section measurements for ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\alpha , {\alpha }_i){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ over the energy range $10.2\le E_{\alpha }\le 18.24$ MeV. The ${\alpha }_0$ and ${\alpha }_2$ exit channels are isospin-allowed, while ${\alpha }_1$ is isospin-forbidden. Except for the Coulomb elastic scattering contribution to ${\alpha }_0$, compound-nucleus formation dominates all three channels. The ${\alpha }_1$ channel displays relatively isolated resonances which imply ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ states with large isospin impurities. These ${\alpha }_1$ data, when expanded in partial waves, fix $J^{\pi }$ for many of the ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ levels (∼20). Comparison of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\alpha , {\alpha }_1){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ with ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d, {\alpha }_1){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ data (some old and some new data) suggests that the same ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ states are usually involved. The estimated isospin impurities are ∼10-25% and are still present at $E_x\left({}_{}{}^{18}{}_{}{}^{}\mathrm{F}\right)\sim 18$ MeV. Our data suggest that the isospin-impure levels in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ tend to occur as doublets, and that for low partial waves isospin may be rather well conserved at our higher excitation energies. Our data do not support Noble's suggestions concerning the importance of direct reactions in isospin-violating reactions.

An approximate procedure which makes use of the spherical Hartree-Fock method and the perturbation approximation is described for generating the correlated ground state. This procedure is compared with an exact shell-model method and with the projected Hartree-Fock (PHF) method, with or without time-reversal constraint, by studying the octupole correlations in ${\mathrm{O}}^{16}$. It is shown that the results given by the present simple method are comparable with the more difficult PHF method with no time-reversal constraint.

It is well known that the random-phase approximation (RPA) overestimates correlation effects. This shows that the RPA assumptions are at least partially violated, and constitutes a serious difficulty. In order to understand the origin of this difficulty, we have performed a calculation of the correlation energy of the electron gas by a version of the RPA dealing only with collective excitations. As expected, it was found that the modified RPA is free of the error of the conventional RPA, showing that this error is connected with the noncollective RPA modes.

As a preliminary to studying three-body problems involving local two-particle potentials with singular core interactions, we derive and numerically study an integral equation for the complete off-energy-shell $t$ matrix for the associated two-particle scattering. The core interaction is described by the boundary-condition model (specified energy-independent logarithmic derivative of the radial wave function at the core radius). Numerical solutions of the integral equation for the special case of the Herzfeld potential (hard core with a square well outside) are found to agree well with the exact $t$ matrix.