A number of isotopically enriched light targets were bombarded with ${\mathrm{O}}^{16}$ ions of 36- to 48- MeV energy (lab), and ten elastic angular distributions were measured. All cross sections show strongly destructive interference of nuclear and Coulomb scattering at angles above 30 to 60° c.m., and fall orders of magnitude below the Coulomb cross section. The data were fitted reasonably well with conventional optical-model calculations, and $〈{\chi }^2〉$ values between 0.5 and 5.2 could be obtained for all targets. Typically, four-parameter fits were adequate. For the heavier targets the parameter sets are not unique, but were found to have continuous well-depth—geometry ambiguities, which were investigated in some detail. A procedure to produce in situ clean targets of highly reactive elements is described.

The mass of ${}_{}{}^9{}_{}{}^{}\mathrm{C}$ has been measured by counting delayed protons near the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}({}_{}{}^3{}_{}{}^{}\mathrm{He},n){}_{}{}^9{}_{}{}^{}\mathrm{C}$ threshold. The data are consistent with an $s$-wave threshold at $E_{3_{\mathrm{He}}}=8980\mathrm{}\pm 5$ keV, giving a ${}_{}{}^9{}_{}{}^{}\mathrm{C}$ mass excess of 28 907±4 keV, and confirming the reported deviation of the $A=9\mathrm{}$, lowest $T=\frac{3}{2}$ quartet from the quadratic mass formula. The half-life of ${}_{}{}^9{}_{}{}^{}\mathrm{C}$, measured with a multiscaler, is 126.5 ± 2 msec.

States in ${\mathrm{C}}^{12}$ have been studied using the ${\mathrm{B}}^{11}({\mathrm{He}}^3,d){\mathrm{C}}^{12}$ reaction at a ${\mathrm{He}}^3$ energy of 44.0 MeV. Energy spectra were obtained to 26-MeV excitation in ${\mathrm{C}}^{12}$. The results indicate the presence of a positive-parity state at 11.16 ± 0.05 MeV having a width of 550 ± 100 keV. It is suggested to be the $2^{+}$ member of an $\alpha$-cluster band based on the $0^{+}$ state at 7.65 MeV. There is no evidence of a state at 14.7 MeV. The $4^{-}$, ${\left(p_{\frac{3}{2}}\right)}^{-1\mathrm{}}\left(d_{\frac{5}{2}}\right)$ $T=0\mathrm{}$ and $T=1\mathrm{}$ states are located at 18.27 and 19.56 MeV, respectively. In the region of the giant dipole resonance in ${\mathrm{C}}^{12}$, there is a peak at 22.4 MeV.

A method for the calculation of isomer ratios in reactions in which the compound nucleus decays by the emission of a few particles followed by $\gamma$ emission is presented. It is shown that the calculated value of the isomer ratio is sensitive to the spin cutoff parameter, the amount of quadrupole admixture in the $\gamma$-ray cascade, and the presence of discrete levels. In most cases good agreement between experimentally measured and calculated values of isomer ratios is obtained.

The $\pi$-nucleus interaction near the $\pi$-nucleon 3-3 resonance $\Delta \mathrm{}\left(1236\right)\mathrm{}$ is examined by use of multiple-scattering theory. $\pi$-nucleus total cross sections are calculated and are found to be in agreement with experimental data. Multiple-scattering effects are found to be important for this agreement.

Low-energy $n-{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ elastic scattering phase shifts are calculated from potential matrix elements using nuclear-reaction theory. As in bound-state calculations, it is found to be essential to include second-order contributions. When this is done the theoretical calculations which contain essentially no adjustable parameters reproduce the experimental phase shifts reasonably well, the disagreement between theory and experiment being generally no larger than the spread in the theoretical results produced by different two-body forces. A nonlocality of the optical potential arises naturally out of the calculation. We are able to see the effect of this by comparing the internal wave function to that obtained using a Woods-Saxon well with parameters adjusted to give the same phase shift, i.e., we can investigate the Perey effect. The scattering wave function is found to be about 30 to 50% smaller in the potential region than the corresponding wave function calculated from the Woods-Saxon well.

The spectrum of the internal bremsstrahlung accompanying the electron-capture decay of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ has been measured in coincidence with the 477-keV $\gamma$ rays. From the extrapolated endpoint energy of the spectrum, the transition energy to the first excited state of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ was determined to be 395 ± 25 keV. The intensity of the internal bremsstrahlung in the energy range from 120 to 360 keV was determined to be (5.45 ± 1.1) × ${10}^{-5\mathrm{}}$ per ordinary nonradiative $1s$ capture (based on a theoretically predicted $\frac{L}{K}$ ratio of 12.4 × ${10}^{-2\mathrm{}}$) as compared with the value of 7.86 × ${10}^{-5\mathrm{}}$ predicted by the theory of Martin and Glauber.

Isospin impurities in the ground states of some even-even nuclei are calculated in the shell model including the effective residual interactions and in the three-fluid model. It is shown that the residual interactions reduce the calculated impurities by an order of magnitude. The impurities given by the three-fluid model are even smaller. Comparison of the present results is made with those of the two-fluid model.

In the isobaric parabola equation for ground-state energies expressed as $-E(A,Z)=-E^0\mathrm{}\left(A\right)+\beta {(Z-Z^0)}^2$, the magnitude of $\beta$ decreases with increasing $A$, and has superposed irregular deviations at particular values of $A$. Very similar deviations from smoothly decreasing curves are also observed when the excitation energies for nuclei with odd and even mass number are drawn separately against nucleon number for different states of excitation. It is, therefore, believed that the variation of excitation energies from smooth curves is caused by the corresponding variation of the second term in the above equation.

We therefore attempted to formulate relations which would determine the average expected ground-state energies and excitation energies for odd- and even-mass nuclei in the form of isobaric parabolas. It has been possible to obtain these expressions in terms of the hypothetical energy per nucleon ${\mathcal{E}}_n^0\mathrm{}\left(A\right)\mathrm{}$ in nuclei composed of $\alpha$ particles combined in an ideal state. The deviations are obtained by comparing the experimentally determined values with those obtained from the formulated relations, and are correlated to determine the energies of nuclei in different excited states.

The ideal energy per nucleon in a nucleus of actual nuclear size with $A$ nucleons is determined by the hypothesis that even-even nuclei in the ideal condition, without the associated repulsive energy caused by Coulomb forces, would be composed of $\alpha$ particles only. The binding energy in such a symmetric nucleus of prescribed size is considered as the ideal energy of the nucleus. It is obtained by taking the experimental binding energy with the Coulomb and asymmetry energies. It increases systematically with $A$.

The nucleonic composition and nuclear energy in actual nuclei are obtained by replacing some of the protons of the ideal composition by neutrons in order to minimize Coulomb-repulsive effects, and by subtracting the energy decrease due to asymmetry and the repulsive energy caused by Coulomb forces from the energy in the ideal condition. The replaced number of protons or the subtracted amounts of energy are determined by nucleonic forces in the ideal nucleus and hence by the ideal nucleonic energy ${\mathcal{E}}_n^0\mathrm{}\left(A\right)\mathrm{}$.

The possibility of representing the ideal energy of nuclei with different nucleon numbers by such smooth relations suggests that the $\alpha$ particles forming ideal nuclei are statistically distributed in different energy shells corresponding to different nucleon numbers. The occupation and disengagement probabilities of states and the energy associated with these states give us a statistical background for the relations determining nuclear charge and energies for ground and excited states.

A previously developed separable expansion for the two-particle $T$ matrix is applied to calculating the properties of the three-nucleon system, using spin-dependent static central potentials. The force model is identical to one that was previously employed by Brayshaw and Buck. Results are presented for the triton binding energy, the doublet and quartet scattering lengths, and for the doublet and quartet $s$-wave phase shifts below and above the three-body breakup threshold. It is found that two or three terms of the expansion in each two-particle spin state give satisfactory convergence in the doublet state of the three-nucleon system. Only one term is needed for the quartet state. The over-all agreement with experiment is good, but some possibly significant discrepancies are found between the theoretical and experimental quartet phase shifts above the breakup threshold. Also, it is shown that a two-particle $T$ matrix or an approximation to one which satisfies the off-shell unitarity relation and has the correct behavior at the bound-state poles leads to three-particle scattering amplitudes which satisfy the three-particle off-shell unitarity relations. The proof does not depend on the existence of a two-particle energy-independent Hermitian potential.

Neutron-polarization angular distributions have been measured at six $\alpha$-particle energies between 3.36 and 4.80 MeV for the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\alpha ,n_0){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction in order to investigate the level structure of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ between 8.7 and 10.2 MeV. These measurements have been analyzed together with the previous cross-section data of Walton, Clement, and Boreli and Kerr, Morris, and Risser using an $S$-matrix search code to yield a number of $J^{\pi }$ assignments to ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ levels in this energy interval. Although most assignments agreed with previous results, the assignment for the 9.95-MeV state must be changed to ${\frac{5}{2}}^{+}$. The existence of broad states near 8.7 and 9.6 MeV have been confirmed and assigned $J^{\pi }$ values of ${\mathrm{½}}^{-}$ and ${\frac{3}{2}}^{-}$, respectively.

A simple nucleon-nucleon correlation function has been invoked in the independent-particle shell-model (IPSM) wave functions of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. This has been assumed due to a substantial residual two-body interaction in addition to the IPSM Hamiltonian of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. Using the variational principle, the excitation energy of the first excited state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ has been obtained in good agreement with the experimental value. The nuclear form factor for the inelastic electron scattering and the reduced transition probability have been calculated and compared with experimental data and other calculated results.

The mass dispersion approach of Fubini and Furlan is applied to single-pion production in nucleon-nucleon collisions. The finite-mass correction to the zero-mass limit is exhibited, and it is shown that in a nonrelativistic approximation this correction leads directly to a simple distorted-wave Born approximation for the physical amplitude. The transition operator is determined directly from the nucleon field-chirality equal-time commutation relation and, in the rest frame of the pion, is given by the standard interaction term.

Sasakawa has rewritten Schrödinger's integral equation in such a manner that the inhomogeneous term has the asymptotic behavior of the exact scattering wave function. This paper gives a proof that the iterative solution for the scattering amplitude converges for all local potentials for which the function $\mathrm{rV}\left(r\right)\mathrm{}$ is absolutely integrable. Under very general conditions the kernel of the Sasakawa equation is a Hilbert-Schmidt kernel. The integral equation is convenient for numerical solution in both the radial representation and the momentum representation.

Calculations of the energy splittings between the parallel and antiparallel coupling states of odd neutron and odd proton in deformed nuclei have been made for both zero-range and finite-range nuclear forces. The energy splittings for both types of forces agree with the corresponding experimental energies. Calculations have also been made for the odd-even shift in $K=0\mathrm{}$ bands. Finite-range interactions improve the agreement between experiment and theory for the odd-even shift, but the results are still unsatisfactory. It is shown that a tensor force is important in reproducing the experimental odd-even shift, especially in the case where ${\Sigma }_n+{\Sigma }_p=1\mathrm{}$.

The lifetime of the 981-keV state in ${\mathrm{Li}}^8$ produced in the $\mathrm{D}({\mathrm{Li}}^7,p){\mathrm{Li}}^{8*}$ reaction was measured by the two-backing variant of the Doppler-shift attenuation method. The resulting mean life was ${\tau }_m=10.1\mathrm{}\pm 4.5$ fsec. This result is in agreement with the shell-model prediction of Cohen and Kurath, and also with that of Barker. The large error limits preclude a detailed test of either prediction.

A comprehensive survey of 21 ($p,t$) reactions for a wide range of $1p$-shell nuclei is made using zero-range distorted-wave Born-approximation codes and previously calculated two-particle fractional parentage coefficients. Average optical parameters are used for the proton and triton potentials in an attempt to relate magnitudes of transitions in different nuclei. A reasonable fit is obtained to the experimental data, but there remain discrepancies in strong transitions for target nuclei with $A>~14$. An effect of ($2s-1d$) admixture which acts differently in $L=0\mathrm{}$ and $L=2\mathrm{}$ transfer is proposed as a likely explanation of this difficulty.

Four generalized one-boson-exchange-potential (GOBEP) models are examined. The first is a highly realistic model which includes only well-established mesons and which takes account of the resonance width of the isoscalar scalar $\epsilon$ meson. Two others are adaptions of this model, each containing a phenomenological term to help improve the fits to high-energy phase shifts. The final model does not assume charge independence of the nuclear force. Meson-nucleon form factors derived from a generalized field theory are used throughout, and a new fitting procedure is introduced which makes allowances for the uncertainties in the theoretical model. The models are compared and evaluated in terms of both the $F$ test for a fit to the phase shifts and the second-derivative matrix method for a fit to observable data. Our basic intention is to provide realistic GOBEP models suitable for nuclear-structure and nuclear-matter calculations.

The renormalized random-phase-approximation equations are solved for a density-dependent particle-hole force emerging from the nucleon-nucleon interaction. Migdal's renormalization constants are determined for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ assuming Woods-Saxon states for the quasiparticle and quasihole propagation, and compared with the renormalization constants for a harmonic-oscillator propagation. In both cases the assumption of good isospin is made. Furthermore, we determined the renormalization constants in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ problem in order to test the assumption of a mass-number-independent renormalization constant. For this purpose we used the standard harmonic-oscillator states for the quasi-single-particle (-hole) propagation (no good isospin).

We have completed measurements of the total cross section, for neutrons between 2.5 and 15 MeV, of 78 natural elements and 14 artificial or isotopically enriched samples spanning the range from hydrogen to plutonium. The measurements were made by transmission in good geometry (inscattering <0.3%), using time-of-flight analysis of the continuous spectrum of neutrons from a pulsed $\mathrm{Li}(d,n)$ source. Data were taken with moderate energy resolution (2 to 4%) and moderate precision (1 to 3% at each point) at a density of three or four points per resolution interval, in order to avoid leaving gaps. We believe systematic errors do not exceed 2%, except in particular cases. Our method leads naturally to small samples, so that we were able to include all of the stable elements except the noble gases. The resulting homogeneous set of data supplies a reference surface for the intercomparison of results from other laboratories. We have made detailed comparisons with virtually all previous measurements in this energy range, and we summarize the systematic properties of the major ones. The completeness of the set helps to reveal a number of systematic properties of the interaction of fast neutrons with nuclei over the entire range of masses.