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.

The distorted-wave matrix element for direct reactions leading to three-body final states is written in terms of convergent integrals. The resulting expression can be evaluated in the Butler approximation, which leads to a diffractive model of the competition of, and interference between, direct breakup and sequential decay reaction mechanisms. Using Amado's methods, I demonstrate the general presence of such interference in processes of interest. Moreover, it should be possible to normalize unstable-state spectroscopic factors by measuring this interference.

Taking into account the mixing of 2p-2h components in the ground state, a method is developed to define the odd-parity excited states of ${\mathrm{O}}^{16}$. Using the effective potential given by Gillet, the excitation energies are given, and the components of the wave functions are put in a form which can be readily used for the computation of electromagnetic transition probabilities. The 3p-3h components in these wave functions are found to be important.

The spins of the ${\mathrm{Mg}}^{24}$ states at 12.74-, 12.85-, and 12.97-MeV excitation, which are populated in the ${\mathrm{Na}}^{23}(p, \alpha \gamma ){\mathrm{Ne}}^{20}$ reaction, have been determined to be $2^{+}$, $2^{-}$, and $2^{-}$, respectively, from $\alpha -\gamma$ correlation measurements. The correlation is measured simply by observing the 1.63-MeV $\gamma$ ray at 0°, and analyzing the $\gamma$-ray line shape in terms of the possible spins of the ${\mathrm{Mg}}^{24}$ states.

A formalism for the analysis of Doppler-broadened $\gamma$-ray line shapes observed in ($a, b\gamma$) reactions, has been developed in order to measure nuclear lifetimes. The technique, which is generally applicable to lifetime determinations in the range 5×${10}^{-15\mathrm{}}$ to ${10}^{-13\mathrm{}}$ sec, has been employed to measure the lifetimes of the levels at 4.43 MeV in ${\mathrm{C}}^{12}$ and 6.92 MeV in ${\mathrm{O}}^{16}$. Results of 65±9 and ${6.4}_{-1.6\mathrm{}}^{+1.9\mathrm{}}$ fsec, respectively, were obtained.

The reactions ${\mathrm{O}}^{18}({\mathrm{He}}^3, p){\mathrm{F}}^{20}$ and ${\mathrm{F}}^{19}(d, p){\mathrm{F}}^{20}$ have been used to study levels in ${\mathrm{F}}^{20}$ up to an excitation energy of 6.043 MeV. The energies of the reaction protons were measured with a broad-range magnetic spectrograph. Excitation energies were obtained for 45 levels in ${\mathrm{F}}^{20}$. The ground-state $Q$ values for the above reactions were also measured and found to be 6.8752±0.0015 MeV for the ${\mathrm{O}}^{18}({\mathrm{He}}^3, p){\mathrm{F}}^{20}$ reaction and 4.3777±0.0009 MeV for the ${\mathrm{F}}^{19}(d, p){\mathrm{F}}^{20}$ reaction.

Two pairs of isobaric analog resonances near 4.1- and 4.9-MeV proton bombarding energy, respectively, have been studied in the ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}(p, n){}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ reaction. Differential cross sections were measured at 2.5, 30, and 130° for neutrons which leave ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ in the ground state and 180-keV first excited state in the bombarding energy region from 4.00 to 4.15 MeV. Analog resonances at 4.075 and 4.098 MeV were analyzed according to the Robson theory. Eleven levels in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ up to an excitation energy of 1.088 MeV were identified in time-of-flight spectra. Hauser-Feshbach analyses were done on the angular distributions of neutrons leaving ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ in 4 and 6 residual nucleus states at 4.400 and 4.512 MeV, respectively, an energy region where no analog resonances appear. Excitation functions for seven neutron groups were measured at 100° in the bombarding energy region 4.7 to 5.0 MeV, where two analog resonances, at 4.87 and 4.92 MeV, were seen. An analysis according to the theory of Robson was performed on these resonances in order to obtain spins, parities, and resonance parameters.

The absolute cross sections for the production of ${\mathrm{Sc}}^{44m}$ and ${\mathrm{Sc}}^{44g}$ by the ${\mathrm{Sc}}^{45}({\mathrm{He}}^3, \alpha )$ reaction have been determined at 1-MeV intervals from 6-19 MeV. The experimentally determined isomer-ratio function has only a limited variance over the energy range studied. Calculations of the Huizenga-Vandenbosch type were performed. Spin cutoff parameters of 2 and 4 gave poor fits of the isomer data. Recoil ranges for ${\mathrm{Sc}}^{44m}$ and ${\mathrm{Sc}}^{44g}$ in ${\mathrm{Sc}}^{45}$ were determined. Recoil energies for ${\mathrm{Sc}}^{44}$ were calculated assuming (1) a compound-nucleus mechanism and (2) a pickup-type mechanism. Recoil ranges for ${\mathrm{Sc}}^{44}$ in ${\mathrm{Sc}}^{45}$ were then calculated using the formulation of Lindhard, Scharff, and Schiott. Comparison of the experimental recoil ranges with the calculated values resulted in poor agreement with both calculations. The inability to fit the isomer-ratio data with a spin cutoff parameter of 2, and the poor agreement of the experimental recoil ranges with the compound-nucleus-mechanism calculation, are interpreted as evidence for the occurrence of non-compound-nucleus-type processes.

Energy spectra of internal-conversion electrons following ($p, 2n$) reactions leading to even-even final nuclei in the $Z\simeq 82$ region were measured. $E0\mathrm{}$ transitions leading from the $0^{+}$ member of the two-phonon triplet to the $0^{+}$ ground state were found, and the systematics of their transition rates was studied. They compete poorly with $E2\mathrm{}$ transitions to the first excited ($2^{+}$) state, and the $E0\mathrm{}$ transition rapidly becomes relatively less probable with decreasing $A$ in this region.

Shell-model calculations are performed for bound $0^{+}$ states of ${\mathrm{Ca}}^{42}$ and ${\mathrm{Ni}}^{58}$. The neutron configurations $1f_{\frac{7}{2}}$, $2p_{\frac{3}{2}}$, $2p_{\frac{1}{2}}$, $1f_{\frac{5}{2}}$, and $1g_{\frac{9}{2}}$ are included, as well as states in which one of the neutrons is in the shell-model continuum. These continuum contributions have little effect on energy eigenvalues, but modify the wave functions in the vicinity of the nuclear surface. The calculated wave functions yield one-particle-transfer form factors whose logarithmic derivatives at large radius are consistent with the neutron separation energies. Comparison is made with other procedures for calculating form factors within the framework of the ordinary shell model. It is found that the conventional well-depth procedure underestimates the ($p, d$) cross sections for populating highly excited states, relative to low-lying states, by about 50%. Two-neutron-transfer cross sections are also calculated and are found to be in agreement with those yielded by the well-depth procedure. However, some of our form factors exhibit an extra node at 8 F, showing that they do not decay like a Hankel function.

The quasiparticle Tamm-Dancoff and random-phase approximations have been applied to ${\mathrm{Sn}}^{116}$ and ${\mathrm{Sn}}^{120}$ using realistic shell-model interactions derived from the Tabakin and Yale-Shakin potentials. It is found that the two approximations are very similar for both spectra and nuclear states.

The $\beta -\gamma$ circular polarization $P_{\gamma }$ has been measured as a function of the $\beta$-particle energy for ${\mathrm{La}}^{140}$ and for ${\mathrm{Co}}^{60}$. The ${\mathrm{Co}}^{60}$ results confirm that $P_{\gamma }$ is proportional to $\frac{v}{c}$. The results for the 2.2-MeV transition of ${\mathrm{La}}^{140}$ show that the original prediction for the vector-matrix-element ratio is not correct for this transition. However, the results are consistent with predictions based on the conserved-vector-current (CVC) theory if the approach suggested by Damgaard and Winther is followed. This interpretation yields information on third-forbidden matrix elements.