Differential cross sections for the elastic scattering of ${\mathrm{He}}^3$ by ${\mathrm{He}}^4$ have been measured from 21.9 to 155.0° (c.m.) at ${\mathrm{He}}^3$ energies of 17.79, 19.99, 22.00, 23.98, 26.00, 28.00, and 30.00 MeV (lab). The relative standard deviations of the data are typically less than 2.5%, but become larger at angles where the cross section is very low. In addition to relative errors, the over-all error includes a standard deviation of 3% in the cross-section scale. The measurements are compared with theoretical calculations using the resonating-group method in the one-channel approximation. Differences between theory and experiment can be qualitatively understood as being caused mainly by the omission of reaction channels in the theory.

Differential cross sections for ${\mathrm{He}}^3$ + ${\mathrm{He}}^3$ elastic scattering have been measured at 18 angles from 12.5 to 45° (lab) at energies of 17.91, 20.00, 22.00, 24.00, 26.00, 28.00, and 30.00 MeV (lab). In addition, differential cross sections have been measured at intermediate energies from 19.00 to 32.00 MeV (lab) at angles of 20, 28, 36, and 45° (lab). The relative standard deviations of the data are generally less than 2%, and there is an additional standard deviation in the cross-section scale of 3%. The measurements are compared with theoretical calculations using the resonating-group method in the one-channel approximation. A broad resonance in the $l=3\mathrm{}$ partial wave is predicted by the theory, and such a resonance has been observed in the present experiment. Differences between theory and experiment can be qualitatively understood as being caused principally by omission in the theory of reaction channels and noncentral forces. The effect of radial distortion in resonating-group calculations for the ${\mathrm{He}}^3$ + ${\mathrm{He}}^3$ system has also been investigated in an approximate manner. It is found that the effect can be quite significant for calculations of the energies of states in ${\mathrm{Be}}^6$ below the ${\mathrm{He}}^3$ + ${\mathrm{He}}^3$ threshold.

The Faddeev formalism is used to compute the ground-state energy of the triton for a simple model in which the nucleon-nucleon force is given by a spin-independent $s$-wave Herzfeld potential (hard core with outside square well). The effective nucleon-nucleon potential used corresponds to the usual weighted average of triplet and singlet potential strengths. The two-variable Faddeev equation is solved using the complete off-shell $t$ matrix given by: (1) an exact analytic expression, and (2) an integral-equation formalism recently proposed. Three-body calculations based on both evaluations of the two-body $t$ matrix lead to a triton binding energy of 8.13 MeV with about 0.5% accuracy.

The effect of strong final-state interactions on the process $A(e, e^{\prime } p)B$ is investigated. Cross sections for this process are calculated for various bound-state proton wave functions, and an optical-model potential is used to describe the final-state interaction.

An approximation made in previous Brueckner-Hartree-Fock calculations is removed. Both the hole-hole and the particle-hole matrix elements of the single-nucleon potential are now calculated with the correct available energy of the pair. It is shown that, with a given $G$ matrix, the occupied states and energies do not depend on the prescription used for the particle-particle elements. The formalism is easily extended to include Brandow's occupation probabilities.

A method is developed for evaluating self-consistent occupation probabilities in Brueckner-Hartree-Fock calculations of finite nuclei. The method does not involve explicitly the overlaps of defect wave functions but is based instead on the energy dependence of the $G$ matrix elements. Results are presented for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ using a $G$ matrix which shifts only the low-lying intermediate-particle spectrum.

It is shown how one can use the results of a nuclear-structure calculation in the theory of nucleon-nucleus scattering. We restrict ourselves to the simple case of nucleon scattering on a hole nucleus. The correlations of the ground state have been included.

The high-energy elastic scattering of nucleons by nuclei is studied using the optical-potential operator provided by Watson's multiple-scattering theory. The main motivation is to investigate the possibility of detecting two-body correlations in terms of an optical potential. We have obtained an expression for the second-order potential in coordinate space which explicitly exhibits its nonlocality in terms of the two-body correlations arising from the Pauli principle and the repulsive core of the nucleon-nucleon interaction. We have performed a self-consistent analysis of the elastic scattering of 1-GeV protons on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using a reasonable nucleon-nucleon scattering amplitude, the one-body density obtained from elastic electron scattering, and a parametrization for the two-body density consistent with the one-body density and dependent upon a parameter identifiable as a correlation length. We have also attempted to discriminate among several sets of nucleon-nucleon phase shifts at 630 MeV. The scattering of 1-GeV protons by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is studied in order to investigate the relative importance of Pauli and short-range correlations. We also critically compare our work with that of several others.

We introduce a new separable expansion for local potentials. The expansion, called the unitary pole expansion, has real, energy-independent form factors, and satisfies the requirements of two-particle unitarity in all orders. The convergence of the expansion is investigated by comparing expanded and exact $T$ matrices for negative energies, and by performing three-body bound-state calculations. In the latter case, a one-term approximation gives energies accurate to within 2% for potentials containing repulsion of the magnitude indicated by two-nucleon data.

An attempt is made to improve the predictions of the $A$ dependence of giant dipole energies of the two-fluid hydrodynamical models by the introduction of a more realistic surface behavior of the ground-state densities. The Euler-Lagrange equations of motion for the dipole oscillation are obtained by the expansion of the energy functional $\epsilon [\rho , {\left(\overrightarrow{\nabla }\rho \right)}^2, \alpha (\overrightarrow{\mathrm{r}}\left)\right]$, where minimization yields acceptable neutron and proton densities, in quadratic powers of the densities and their derivatives. The equations are solved under certain limiting conditions, but within these limitations a much better $A$ dependence is obtained.

Measurements of elastic scattering were made for ${\pi }^{+}$ and ${\pi }^{-}$ beams at 30 MeV on a carbon target and ${\pi }^{+}$ on oxygen at 30 MeV. A magnetic spectrometer utilizing wire spark chambers was used to measure the momenta of the scattered pions over the angular range 40-120 deg. The energy resolution was about 4 Me V full width at half maximum at 30 MeV, which is sufficient to resolve the first excited states of carbon and oxygen. Inelastic scattering from the lower excited states has been estimated. Fits of the Kisslinger optical model to the data have been made.

The electron-momentum-neutron-spin correlation coefficient was found to be $A=-0.115\mathrm{}\pm 0.008$, and the antineutrino-momentum-neutron-spin correlation coefficient was found to be $B=1.00\mathrm{}\pm 0.05$. The value of $A$ leads to $\left|\frac{G_A}{G_V}\right|=1.26\mathrm{}\pm 0.02$ for the ratio of Gamow-Teller-to-Fermi coupling constants in $\beta$ decay, and $B$ is consistent with zero scalar or tensor interaction.

Energy levels of ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ have been studied with the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(d, \alpha ){}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ reaction at deuteron energies of 4.75 to 11.5 MeV. No evidence was found for levels between 0.4- and 3.3-MeV excitation energy. Eleven levels were identified or tentatively identified between excitation energies of 8.4 and 10.3 MeV in addition to 32 previously observed levels below an excitation energy of 8.4 MeV. The fourth, sixth, and seventh excited states at 3.36, 3.96, and 4.32 MeV appear to be populated partially via a two-nucleon pickup reaction at $E_d=10.0, 10.6, \mathrm{and} 11.2$ MeV; and tentative $L$ values are obtained.

States of ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ have been observed whose excitation energies appear to be correlated with thresholds for neutron emission to excited states of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. It is pointed out that similar correlations occur in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and the correlation is discussed in terms of known threshold effects.

An empirical spacing distribution is always based on a finite, and usually small, number of observed levels. Thus, even if the spacing of levels were described exactly by the random-matrix model, the observed distribution would necessarily fluctuate about the theoretical mean-the Gaudin-Mehta distribution. A statistic $\Lambda \mathrm{}\left(n\right)\mathrm{}$ is defined to enable one to judge whether the magnitude of the observed fluctuations about the Gaudin-Mehta distribution is compatible with the random-matrix model. It is found that the correlations between the spacings implied by the model tend to reduce the expected fluctuations significantly. The statistical properties of $\Lambda \mathrm{}\left(n\right)\mathrm{}$ are studied by means of a Monte Carlo calculation with matrices of order 100 sampled from the Gaussian orthogonal ensemble. An illustrative analysis of the published neutron resonances observed in ${\mathrm{U}}^{239}$ by Garg et al., reveals no obvious discrepancy between theory and experiment up to neutron kinetic energies of about 2 keV.

The intermediate-coupling version of the unified model has been used to calculate the properties of the low-lying levels of ${\mathrm{Bi}}^{203,205,207,211}$. In each case, the quadrupole oscillations of the doubly even core have been coupled to the $h_{\frac{9}{2}}$ and $f_{\frac{7}{2}}$ single-particle states. Energy levels, transition rates, and magnetic dipole and electric quadrupole moments have been calculated for these four nuclei. Agreement between calculated nuclear properties and available experimental data is good for ${\mathrm{Bi}}^{205,207,211}$, but ${\mathrm{Bi}}^{203}$ does not appear to fit within the framework of the intermediate-coupling model.

The shell-model calculations have been performed for the $E2\mathrm{}$ decay rate of ${}_{\Lambda }{}^7{}_{}{}^{}\mathrm{He}_{}^{*}{}_{}{}^{}$. It is shown that the inclusion of nucleon-nucleon correlation in the usual independent-particle shell-model (IPSM) charge-density distribution of the core nucleus ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ provides an adequte description and leads to an identification of ${}_{\Lambda }{}^7{}_{}{}^{}\mathrm{He}_{}^{*}{}_{}{}^{}$ as an isomeric state. It also provides a method of studying the effect of core polarization. The treatment of the core nucleus can be applied with confidence to other nuclear systems. It would be particularly useful for those nuclei which cannot be well described by simple IPSM wave functions-e.g., ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$.

An analytic formula is derived for quasi-elastic electron scattering from a compound nucleus. The nucleus is treated as a finite-temperature Fermi gas, although the formula can be used for any nuclear momentum distribution. Many-body correlations can be included by the use of an effective nucleon mass. The formula is good in the high-energy (several BeV) region, and can be used for estimating background. The Drell-Walecka form factors are calculated assuming the finite-temperature Fermi gas distribution.

The experimental $n-d$ differential elastic-scattering cross section has been fitted by a two-term, five-parameter analytic equation in the energy region 1-21 MeV. This equation resembles the direct and exchange terms resulting from a Born-approximation treatment. A least-squares method was utilized to fit this equation, to within 1%, to the tabulated cross sections of Horsley and Stewart. Smooth energy dependences, describable in simple functional forms, have been found for the five parameters. The formula has been shown to interpolate well to fit new elastic-scattering data in this energy region.