The nuclear spreading widths of the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ${\mathrm{½}}^{+}$ doorway resonances are calculated in a particle-vibration model. The hallway states are of the particle—two-photon type. The fine structure in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ is essentially due to the availability of many hallways (some with large matrix elements) and their proximity to the doorway. The ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ${\mathrm{½}}^{+}$ doorway spreading widths are found to be in line with the experimental situation.

Excitation functions have been measured at ${\theta }_{\mathrm{lab}}={170}^{\circ }$ for the reactions ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ ($E_{\mathrm{lab}}=56.0\mathrm{} \mathrm{to} 63.0$ MeV), ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ (42.5 to 50.0 MeV), and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{141}{}_{}{}^{}\mathrm{Ce}$ (56.0 to 61.0 MeV) proceeding to low excited states. Analysis has been made using the sub-Coulomb distorted-wave Born-approximation theory of Buttle and Goldfarb with inclusion of Coulomb correction terms in the form factor and the Buttle-Goldfarb approximation for recoil corrections. Good fits are obtained to the excitation functions at the lower energies. Normalization at these energies determines an essentially invariant quantity, namely the joint probability for the transferred nucleon being at radius $R_1$ with respect to the first core nucleus and radius $R_2$ with respect to the second, where $R_1\equiv \alpha \left[\frac{{A_1}^{\frac{1}{3}}}{({A_1}^{\frac{1}{3}}+{A_2}^{\frac{1}{3}})}\right]$ and $R_2\equiv \alpha \left[\frac{{A_2}^{\frac{1}{3}}}{({A_1}^{\frac{1}{3}}+{A_2}^{\frac{1}{3}})}\right]$, $\alpha$ being the distance of closest approach in a head-on collision averaged between incident and final channels. If specific assumptions are made for the geometrical parameters of the bound states, values can be extracted for the product of spectroscopic factors, $S^{\mathrm{}\left(1\right)\mathrm{}} S^{\mathrm{}\left(2\right)\mathrm{}}$; reasonable geometries lead to values of $S^{\mathrm{}\left(2\right)\mathrm{}}$ very close to those previously obtained from light-ion reactions. Above the barrier, the fits to calculations which use nuclear distorted waves are less satisfactory; for optical potentials which give nearly equivalent elastic scattering, the calculations show moderate ambiguity. We believe the leading uncertainty in our analysis is due to the approximate treatment of recoil.

The occurrence of rearrangement terms in the self-consistent potential of ground-state calculations depends critically on the order in which approximations and variation of the energy expectation value are performed.

Although a modified constrained Hartree-Fock procedure has been presented which permits calculations in "inaccessible regions" a misconception has limited its acceptance. The idea underlying this misconception, namely, a relation between energy and single-particle energies, is discussed and is shown, both algebraically and numerically, to be invalid.

The change in the magnetic moment of the deuteron arising from the presence of the spin-orbit potential in the nucleon-nucleon interaction has been estimated for the Yale, Hamada-Johnston, and Reid potentials. The present estimates are more close to experiment than those obtained previously from some old fashioned potentials.

Assuming the existence of a spherical ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core, self-consistent Hartree-Fock, Hartree-Fock-Bogoliubov, and spherical BCS calculations for the even oxygen isotopes are carried out for Kuo-Brown and a number of other effective interactions. In agreement with the finding of Chandra and Rustgi for the even Ca and Ni isotopes, the spherical BCS approximation is found to yield the actual minimum-energy solution for the even oxygen isotopes as well. The present calculation thus adds credibility to the general inferences made by Chandra and Rustgi that for single-closed-shell structures, the self-consistent shape will always be spherical BCS.

The Skyrme-Levinson model for rotations and the oscillator-projection method for vibrations are combined to give a generalized Skyrme-Levinson model in which rotations and vibrations are treated together on an equal basis. Expressions are given for the moment of inertia and the ground-state energy of a vibrational deformed nucleus. They are applied to the prolate and oblate Hartree-Fock solutions for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$.

Angular distributions of $\gamma$ rays from the ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}(n,n^{\prime }\gamma )$ reaction have been measured at an incident neutron energy of 1.41 MeV. Analysis of the distributions yielded a spin assignment of ($\frac{11}{2}$)- for the 1238-keV level. The results support the collective-model description of this nucleus.

Proton spin-flip in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,p_1){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ($2^{+}$, 4.44 MeV) has been measured in the region of the 8.9-MeV ${\mathrm{½}}^{-}$ level in ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$. The inelastic decay is predominately by $f_{\frac{5}{2}}$ waves. The reduced width in the $f_{\frac{5}{2}}$ channel is about equal to the single-particle limit.

Using the Faddeev formalism, a study of the off-energy-shell variation of the triton binding energy ($E_t$) is made. The results are indicative of the insensitivity of $E_t$ to the off-shell differences associated with the various nucleon-nucleon potentials considered, which are equivalent on the energy shell and vary mainly in the shape of their repulsive cores for $r\lesssim 0.5$ fm.

A new expression for the moment-of-inertia parameter has been derived using the method of moments. The relation between the present expression and the Skyrme expression is given and its implications are discussed.

The Low equation, generalized to the case of an energy-dependent potential, is used to define a nucleon-nucleus optical potential. Although this approach is completely equivalent to previous definitions of the optical potential for nucleon-nucleus scattering, it should be easier to adapt this treatment to relativistic, field-theoretic problems.

Neglecting level-level correlations, we show that consistency conditions derived from general properties of the $S$ matrix determine the distribution of resonance parameters. This is also true in the presence of direct reactions. Formulas are given for average cross sections, autocorrelation, and cross-correlation functions.

Neutron spectra from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(p,n)2p$ reaction have been measured at nine proton energies between 16 and 26 MeV. The high-energy portions of the neutron spectra taken at a laboratory angle of 3.5° have been analyzed with impulse approximation calculations of the proton-proton final-state interaction to extract the proton-proton scattering length. The average value of the scattering length determined from these measurements is within approximately 1 fm of the - 7.8-fm result of $pp$ scattering but is not independent of the details of the comparison of experimental and calculated spectra. Experimental requirements for a determination of the neutron-neutron scattering length from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(n,p)2n$ reaction are discussed.

The $\mathrm{D}\mathrm{}(p,2p)n$ reaction has been studied at $E_p=30.3\mathrm{}$ MeV at kinematic conditions where either final-state interactions or quasifree scattering predominate, and at kinematic conditions where the kinematic domains of these two processes are near each other. Data were obtained at 25°-91°, 30°-80°, 37.5°-68°, 25°-25°, 30°-30°, 42.5°-42.5°, 24°-60°, 30°-56°, 35°-43°, 37°-47°, 63°-30°, 55°-40°, and 49.5°-49.5°. The results are compared with predictions of the Amado model and, in general, there is good agreement between the model and the data.

The cross section ($\frac{d^5\sigma }{d{\Omega }_{p}d{\Omega }_{t}d{T}_p}$) for the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,pt)\mathrm{}$ has been measured in a kinematically complete experiment. The energy resolution did not allow for an identification of the final-state residual nucleus. The cross-section data obtained, when analyzed in terms of the recoil momentum of the three-nucleon residual system, has the shape characteristic of an $S$ state for the relative motion of the triton. If the cross section is fitted with a Gaussian the width at $\frac{1}{e}$ is $\Gamma =100\mathrm{}\pm 20\frac{\mathrm{MeV}}{c}$, and the cross section at zero recoil is 490±120 nb/${\mathrm{sr}}^2$MeV. The width observed is twice as large as obtained in previous, lower-energy experiments, but only slightly larger than predicted by ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$-cluster-model calculations.

Isospin mixing in the mass $A=6\mathrm{}$ system is examined by measuring the deuteron decay branch of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ (5.36-MeV; $T=1\mathrm{}$) state. The mixing to be expected due to the Mott-Schwinger part of the Coulomb interaction is calculated. The measured spectra do not show any positive evidence for deuteron decay of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ (5.36-MeV; $T=1\mathrm{}$) state. However, the experimental upper limit for possible isospin mixing is still appreciably larger than that expected from the Mott-Schwinger interaction.

The transition operator corresponding to a separable nonlocal and of a matrix-type potential is studied theoretically. It is shown that the transition operator possesses the same $\overrightarrow{\mathrm{r}}$ (or $\overrightarrow{\mathrm{k}}$) dependence and properties of separability and nonlocality as the potential and that it is also of a matrix type. This transition operator is then explicitly calculated. A numerical application is made to the simple but physically important case of the low-energy pion-nucleon interaction. The behavior of the transition operator coefficients versus the incident energy are discussed in detail for $S$, $P$, and $D$ waves.

Elastic scattering of $190-\frac{\mathrm{MeV}}{c}$ muons has been measured to ∼1% in the angular range $140 \mathrm{mrad}\le \theta \le 590 \mathrm{mrad}$ corresponding to invariant four-momentum transfers $0.016 {\mathrm{fm}}^{-2\mathrm{}}\le q^2\le 0.33 {\mathrm{fm}}^{-2\mathrm{}}$. Magnetostrictive wire spark chambers were used to measure the incident momentum and scattering angle. A comparison is made with electron scattering experiments which extend down in $q^2$ to 0.02 ${\mathrm{fm}}^{-2\mathrm{}}$. A change of slope of the carbon form factor in the range below 0.05 ${\mathrm{fm}}^{-2\mathrm{}}$ would indicate unexpected structure in the outer regions of the nuclear charge distribution. Disagreement with electron scattering where both processes are measured would indicate a breakdown of muon-electron universality. No such effects are observed.

The small-angle (13°-40°) part of the elastic differential cross section for the scattering of low-energy ($T_{\pi }\sim 100$ MeV) positive and negative pions from natural lead was measured. The same quantity was also measured for the scattering of low-energy muons from lead. The muon-lead data were used to determine the rms charge radius of the lead nucleus. Assuming a Fermi shape for the charge density with a skin thickness of 2.21 fm, the result was ${{〈r^2〉}_{\mathrm{ch}}}^{\frac{1}{2}}=5.50\mathrm{}\pm 0.06$ fm. The ${\pi }^{\pm }-\mathrm{P}\mathrm{b}$ data, taken in the region of large Coulomb nuclear interference, were compared with predictions of the pion-nucleus optical model according to Watson and Kisslinger. Excellent fits to the data were obtained by treating the model phenomenologically; however, the best-fit optical-model parameters were not in agreement with the values computed from experimental pion-nucleon phase shifts. Since the ${\pi }^{\pm }-\mathrm{P}\mathrm{b}$ elastic cross sections are sensitive to the neutron density distribution, a determination of the rms neutron-matter radius could be made. Assuming a Fermi shape for the neutron-matter density, with a skin thickness of 2.21 fm, the result was ${{〈r^2〉}_{\mathrm{n}.\mathrm{m}.\mathrm{}}}^{\frac{1}{2}}={5.45}_{-0.25\mathrm{}}^{+0.13\mathrm{}}$ fm.