A review of the analysis of the $n+{}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ elastic scattering data advances the argument that two states, with $J^{\pi }={\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$, are the dominant levels in ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ near 5.4 MeV excitation. Both states show significant single-particle strengths. The ${\frac{3}{2}}^{+}$ spin assignment is in agreement with the recent shell-model calculations of Halbert et al. The origin of the ${\frac{5}{2}}^{+}$ state is still open.

A second quantized version of the Lane-Robson reaction formalism is applied to the continuum shell-model problem. The dynamical equations have a matrix structure which differs from that encountered in the conventional shell model only through the addition of a relatively small number of states and the presence of complex, energy-dependent boundary-condition parameters. Oscillator basis states may be used throughout. All matrix elements may be evaluated by existing shell-model codes. The equations provide a practical basis for dynamical studies of resonance phenomena in single-nucleon scattering channels. An extension of the model to include cluster channels is suggested.

An equivalent potential is derived by best fitting the Sussex matrix elements. The derived equivalent potential is compared with the equivalent Yale potential obtained in a similar manner and with central effective potentials in widespread current use. Remarks are made about the general nature of the effective nuclear force.

The $\mathrm{T}\mathrm{}(d,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ neutron-source reaction has been reinvestigated utilizing the neutron time-of-flight techniques. This study was motivated by the lack of cross section data above 11 MeV, by large uncertainties in the 0° absolute cross sections, and by the need to improve the accuracy of both the absolute and relative cross-section data. Angular distributions were measured at $E_d=5.0,6.0,7.0,10.0,11.0,12.0,13.0,14.0,15.0,\mathrm{and} 15.7$ MeV using a neutron detector with a well-established relative efficiency. Absolute cross sections at 0° were obtained by normalization to precise charged-particle cross sections obtained for the reaction $\mathrm{D}(t,{}_{}{}^4{}_{}{}^{}\mathrm{He})n$. Below 10 MeV there is good agreement with earlier data.

Absolute branching ratios for the isospin-forbidden particle decays of the lowest $T=\frac{3}{2}$ levels of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ have been measured by populating the levels in (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $p$), (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $\alpha$), or (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $n$) reactions and observing the resulting decay products in coincidence. Branching ratios of 0.070 ± 0.018, 0.261 ± 0.030, and 0.026 ± 0.018 (0.236 ± 0.012, 0.150 ± 0.010, 0.053 ± 0.015) were determined for the neutron (proton) decays of the 15.1-MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$) to the ground state and first two excited states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, respectively. Branching ratios of 0.91 ± 0.15 and 0.05 ± 0.02 (0.088 ± 0.016, 0.23 ± 0.05) were determined for the neutron (proton) decays of the 11.08-(11.20-) MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$) to the ground state and unresolved 6.05- and 6.13- MeV excited states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, respectively. The $\alpha$-decay branching ratios of the 15.1-MeV, $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ to the ground state and first two excited states of ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ were determined to be 0.049 ± 0.027, 0.039 ± 0.039, and 0.072 ± 0.045, respectively. Possible origins of the large asymmetries observed in the nucleon decays of these analog levels are discussed. The value obtained for $\frac{{\Gamma }_{p_0}}{\Gamma }$ for the lowest $T=\frac{3}{2}$ level of ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ may be combined with ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(e,e^{\prime })$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ measurements to determine the ratio $\frac{{\Gamma }_{\gamma }^{M1\mathrm{}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{C}\right)}{{\Gamma }_{\gamma }^{M1\mathrm{}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)}=1.0\mathrm{}\pm 0.2$ for $\gamma$ decay to the ground state. This places an upper limit on the isotensor transition matrix element at 7% of the isovector matrix element.

The expression, $\frac{E}{A}={\epsilon }_{\mathrm{vol}}+\frac{1}{2}{\epsilon }_{\tau }\alpha _{\tau }^{}{}_{}{}^2+\frac{1}{2}{\epsilon }_{\sigma }{({\alpha }_n+{\alpha }_p)}^2+\frac{1}{2}{\epsilon }_{\sigma \tau }{({\alpha }_n-{\alpha }_p)}^2$, for the ground-state energy of nuclear matter with an excess of neutrons, of spin-up neutrons, and of spin-up protons (characterized by the corresponding parameters, ${\alpha }_{\tau }=\frac{\mathrm{}(N-Z)\mathrm{}}{A}$, ${\alpha }_n=\frac{(N_{\uparrow }-N_{\downarrow })}{A}$, and ${\alpha }_p=\frac{(Z_{\uparrow }-Z_{\downarrow })}{A}$), contains three symmetry energies: the isospin symmetry energy ${\epsilon }_{\tau }$, the spin symmetry energy ${\epsilon }_{\sigma }$, and the spin-isospin symmetry energy ${\epsilon }_{\sigma \tau }$. General expressions for ${\epsilon }_{\sigma }$ and ${\epsilon }_{\sigma \tau }$ are obtained in terms of the $K$ matrix which depends on four different Fermi momenta. With suitable approximations, numerical values of ${\epsilon }_{\sigma }$ and ${\epsilon }_{\sigma \tau }$ (and also of ${\epsilon }_{\tau }$) are derived using the Brueckner-Gammel-Thaler, the Hamada-Johnston, and the Reid softcore nucleon-nucleon potentials. The most reliable results, obtained with the Reid soft-core potential, are: ${\epsilon }_{\tau }=61\mathrm{}$ MeV, ${\epsilon }_{\sigma }=74\mathrm{}$ MeV, and ${\epsilon }_{\sigma \tau }=73\mathrm{}$ MeV. The possibility of estimating the energies of the spin and spin-isospin modes of collective nuclear excitations is discussed.

We have reexamined the problem of constructing a nuclear ground-state wave function consistent with the requirement of translational invariance, beginning with a wave function which does not have this property. A class of transformations is constructed which transforms the initial-state vector into an eigenstate of total momentum. The particular transformation of this class which leads to the lowest intrinsic energy is given.

The isoscalar magnetic moments and Gamow-Teller $\beta$ decay of the systems $A=11,13,15,17,19, \mathrm{and} 21$ are analyzed in an attempt to extract, in a largely model-independent way, the effective nuclear renormalization of the axial coupling constant: $g_A\to g_{\mathrm{Ae}}$. We find: $\frac{g_{\mathrm{Ae}}}{g_A}=0.920\mathrm{}\pm 0.047$.

An exactly soluble three-body model is constructed which consists of two light particles and an infinitely heavy one having internal degrees of freedom. This model is designed to simulate various phenomena associated with isobaric-analog states, showing up in scattering and transfer reactions. The formulation and solution are done in the framework of Faddeev's theory using nonlocal separable potentials. The cross sections are calculated in the neighborhood of the channel thresholds. The effect of a resonance on the threshold is studied in detail and threshold anomalies are searched.

Some higher-order corrections to renormalized Brueckner-Hartree-Fock calculations are estimated for the nuclei ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The diagrams of interest are the potential insertions in particle lines and the two-body correlation corrections to the rms radii. Studies are made of the sensitivity of these corrections to the shift in the intermediate spectrum used to calculate the $G$ matrix. The correlation corrections to the radii are small and seem to increase somewhat as the intermediate spectrum is lowered, but there is no appreciable change in the over-all saturation properties. The errors involved in estimating the corrections are discussed. "Off-diagonal occupation probabilities" are also calculated and found to be small, thereby justifying ignoring such diagrams as is usually done in renormalized Brueckner calculations.

A generalization of the Hill-Wheeler generator coordinate method is applied to collective deformations. The intrinsic wave function is constrained (as in constrained Hartree-Fock) to be characterized not only by a given deformation, but also by a deformation velocity. This is effected by a simple ansatz which involves operation on the singly constrained wave function by an exponentiated single-particle deformation operator containing an arbitrary function $\beta \left(\alpha \right)$, where $\alpha$ is the collective variable. The expectation value of the energy is minimized with respect to both $\beta \left(\alpha \right)$ and the Hill-Wheeler projection function $f\left(\alpha \right)$. This leads to an integral equation for $f$ which, upon invoking the collective nature of the intrinsic states, may be approximated by a second-order differential equation in the deformation coordinate $\alpha =〈Q〉$. In order to reduce this equation to the Schrödinger form, certain assumptions are introduced with regard to the approximate form of $f$. This procedure leads to two different differential equations for $f$ and to two mass parameters. One is valid in the classical region and one in the classically inaccessible tunneling region. This is to be contrasted to the cranking model where sufficient energy must always be available to drive the system. The expressions for the mass parameter are given in terms of expectation values of few-body operators. The case of uniform translation of the nucleus as a whole is studied in detail. The generalized Hill-Wheeler method as described above produces the correct mass (= total nuclear mass). This rigorous reproduction of a known result allows the study of approximations which become necessary for the general case of deformations. Comments are made about the potential energy of deformation surface, which is expected to lie lower than the expectation value of the Hamiltonian.

Direct modifications are made to the off-shell two-body $t$ matrices which are used as input to the Faddeev-Lovelace equations for the three-body bound state and for scattering below breakup. The $t$ matrices are modified when either momentum argument exceeds a particular value, in a manner which will maintain off-shell unitarity when it is important. In this way, we are able to test the dependence of these three-body properties on different regions of the off-shell momenta. We find a strong sensitivity for both momenta less than 2 ${\mathrm{fm}}^{-1\mathrm{}}$; weak, potential-dependent sensitivity when either argument is between 2 and 5 ${\mathrm{fm}}^{-1\mathrm{}}$, and essentially no dependence if either argument exceeds 5 ${\mathrm{fm}}^{-1\mathrm{}}$.

Eigenvalues and eigenvectors for all low-lying positive- and negative-parity nuclear states of $A=18,19, \mathrm{and} 20$ are calculated in a shell-model basis of all Pauli-allowed $0p_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}$ configurations outside an inert ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core. Two different effective Hamiltonians are used. One is based on a reaction matrix treatment of the Hamada-Johnston potential. The second one is obtained by varying the 33 effective Hamiltonian matrix elements to reach a least-squares fit between 153 experimental level energies in nuclei in the $A=13-22\mathrm{}$ region and the corresponding shell-model eigenvalues. The energy level spectra and single-nucleon spectroscopic factors from these calculations are compared to the available experimental data in this region. The calculations are also examined for the existence and characteristics of sequences of levels which might be called "rotational bands."

The experimental cross section for radiative $n-p$ capture at thermal energies is 10% larger than the theoretical cross section calculated from the impulse terms (free-nucleon isovector magnetic moment). In the present work the pion-exchange contribution is evaluated using the Chew-Low static model amplitude for the photopion process. We demonstrate how the various pieces of the photopion amplitude contribute to the exchange current. The results for Hamada-Johnston, Reid-hard-, and soft-core potentials are 10.5, 10.9, and 11.5% increases, respectively, to the impulse cross section from pion processes. This work verifies the earlier paper of Riska and Brown demonstrating that the 10% discrepancy can be accounted for as a one-pion-interaction effect.

The two-body scattering formalism is developed in a manner that makes it clear where the assumption of a "smooth" potential enters. Particular attention is paid to the modifications necessary if the scattering states do not form a complete set, as is the case for the pure hard-core (HC) potential and the pure (i.e., no external potential) boundary-condition model (BCM). As examples, the fully-off-shell $t$ matrices for HC and BCM are developed without treating them as the limits of finite-potential models. A general expression is derived for the fully-off-shell $t$ matrix, which can be applied to the general HC or BCM with external potential, and which involves only the solution to the Schrödinger equation in the external potential.

By the simultaneous measurement of the magnetic rigidity of the ${\alpha }_0^{++}$ and ${\alpha }_2^{+}$ groups from the ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(p,\alpha ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction, using a double-focusing spectrometer, the excitation energy of the second excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is found to be 7654.2± 1.6 keV.

A theory of the optical potential for scattering of nucleons from nuclei is presented. A development appropriate for intermediate- and high-energy scattering is given in this paper. For low energies the theory provides the leading term of the optical potential which must then be supplemented by the effects of compound-nucleus formation and inelastic scattering to low-lying states of the target. Particular attention is paid to the Pauli principle, and it is shown how standard multiple-scattering theories must be modified if the projectile is identical to the target particles. The development proceeds in the spirit of the many-body theory of finite nuclei, but deals with the problem of the addition of a (continuum) nucleon to an already known strongly correlated nuclear state. The manner in which the correlations between target and projectile nucleons develop is explicitly displayed. It is the consideration of these additional two-body correlations which allows us to introduce the Bethe-Goldstone type of reaction matrices for the scattering problem.

In phenomenological descriptions of nuclear vibrations a close connection is implied or expressed between the most-collective transition operator and the harmonic-oscillator (boson) variables which are introduced to describe the collective motion. With the help of a widely used example - the monopole vibration model of Meshkov, Lipkin, and Glick - it is shown how this relationship suggests, for the microscopic case, a new and flexible class of boson representations. As shown, these are capable of yielding accurate descriptions of the system not only in the extremes of weak and strong coupling, but in the usually more inaccessible intermediate regions as well.