Consideration is given to the approximation in which an arbitrary potential is replaced by a separable potential. A method is presented which permits the construction of a rank-$N$ separable potential which has the property that the resulting $T$ matrix is exact on the energy shell and half off the energy shell at $N$ selected bound state and/or continuum energies. This construction yields a $T$ matrix that is correct off the energy shell in the vicinity of the $N$ on-shell points.

The moderate strength and smoothness of two-body forces for interparticle distances $r\ge 1$ fm implies that the Hartree-Fock (HF) wave functions are accurate for those separations. The nearly constant density of nuclei inside a surface region of 1-fm thickness implies that even in as light a nucleus as oxygen the nuclear-matter Bethe-Goldstone (BG) wave functions are accurate for most pairs at $r\le 1.5$ fm. The few pairs with c.m. coordinate $R$ in the surface region will be accurately represented on the average only. Accurate BG and oscillator-basis HF calculations using realistic Feshbach-Lomon (FL) interactions show that both wave functions agree well for $1 \mathrm{fm}<r<\mathrm{}1.5\mathrm{} \mathrm{fm}$ as expected. Consequently a configuration-space Jastrow wave function of sufficient accuracy can be constructed. Matrix elements of density and of energy are calculated using the HF functions for $r>\mathrm{}{r}_s$ and the BG functions for $r<\mathrm{}{r}_s$, with $r_s$ chosen anywhere in the region 1-1.5 fm. Values of the off-shell interior boundary condition $b$ of the FL interaction are used which give good nuclear-matter properties and favorable HF results for nuclei from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ to ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. The corrections due to the BG correlations result in accurate binding energies and moderately good single-particle energies for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$.

The breakup of deuterons in the field of gold and lead nuclei was investigated experimentally. Angular correlations were measured at a deuteron energy of 12 MeV and, in the case of gold, also at 10.5 MeV. Furthermore, the energy dependence of the breakup cross section was studied with a gold target in the range lying between 7 and 12 MeV. Comparison of the experimental results with theoretical predictions based on a model which takes only Coulomb forces into account shows large discrepancies, the reason for which is presumed to be due to neglecting the nuclear interaction of the neutron in the final state.

The disintegration effects for deuterons, tritons, and helions (${}_{}{}^3{}_{}{}^{}\mathrm{He}$) on their optical potentials are investigated in the framework of the adiabatic approximation. Using the eikonal approximation for the involved scattering amplitudes, it was possible to get analytic expression for the optical potentials of composite projectiles. The volume integrals of the resulting potentials are evaluated and compared with the corresponding quantities evaluated using the Watanabe model which neglects the disintegration of the projectiles. This comparison suggests that the disintegration of the projectile can be taken into account in the Watanabe model by an appropriate choice of the energy at which the nucleon potentials involved in the calculations are evaluated. An expression of this effective nucleon energy is given in terms of the volume integrals and mean square radii of the nucleon optical potentials. An extensive analysis of the energy and mass- number dependence of the phenomenological optical potentials of proton scattering at medium energies is given and used to evaluate the effective nucleon energy suggested in this work and to draw some conclusions on the validity of the extended optical model of Greenlees, Pyle, and Tang.

One develops a general integrodifferential equation for the transition matrix of nuclear reaction theory in terms of the physical parameters of the nuclear reaction. One derives, as a corollary of the main result, a system of equations which describes the motion of the poles and residues of the collision matrix as a function of the parameters entering in the reaction formalism. Some applications to the study of the potential-scattering problem are also shown.

Some of the recently proposed one-boson-exchange nucleon-nucleon potentials are discussed in the many-nucleon context.

We show by direct calculation that the lowest-order triangle Feynman diagram model of forward elastic $\alpha$-particle scattering, together with the assumption of $\alpha$-cluster structure of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, is capable of explaining the forward angular distribution of the differential cross section in elastic $\alpha$ scattering from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.

Low-lying levels of ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ were populated by the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li}, p){}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ reaction at a bombarding energy of 16.0 MeV. Angular distributions were measured for all states below 3.3 MeV in excitation energy. The shapes of these angular distributions, and the ($2J+1$) dependence of the integrated cross sections are consistent with a compound-nucleus mechanism for the reaction. The measured cross section for the level at 3.235 MeV suggests that it has a spin of $\frac{3}{2}$ rather than ½.

At 0.6 and 3 GeV, cross sections for the production of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in C and Si were determined, and for the production of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in oxygen. At 33 GeV only ${}_{}{}^3{}_{}{}^{}\mathrm{H}$: ${}_{}{}^3{}_{}{}^{}\mathrm{He}$: ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ production ratios in C and Si could be established due to a fault in the monitoring. The ${}_{}{}^3{}_{}{}^{}\mathrm{H}$/${}_{}{}^3{}_{}{}^{}\mathrm{He}$ yield of 0.85±0.10 embraces the three target materials throughout the energy range investigated. On the other hand, the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$/${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ratios varied with energy and with target material by up to a factor of 2. Most of the previous ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ cross-section determinations in carbon are shown to be low by a factor of 2 or 3, apparently because of tritium diffusion from the thermoplastic materials used in the earlier studies. The majority of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ cross sections at 600 MeV in targets from helium to bismuth fit the equation $\sigma \mathrm{}\left(A\right)=30\mathrm{}\exp \left(\frac{A}{100}\right)$, which should be beneficial in predicting unknown cross sections. A trend in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ cross sections as a function of target mass was discernable, but the scatter of the data does not permit making a more detailed examination; no ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ trend as a function of $A$ is observed.

The program of the algebraic approach to nuclear collective motion is summarized. In essence, it should permit an accurate solution of the many-body problem within a subspace of the many-particle space if the conditions defining collective motion are present. The formulation, containing both dynamical and kinematical aspects, leads to coupled nonlinear algebraic equations for the matrix elements between collective states of fermion pair operators. An explicit set of equations is given for the problem of $N$ (even) particles confined to a single-$j$ shell and described by the conventional pairing plus quadrupole-quadrupole interaction Hamiltonian. This formulation is designed to be nearly exact in the pairing-dominant (seniority) limit and to be accurate enough (based on plausibility arguments) to describe the transition from spherical to deformed shape. That this is so is verified for configurations, the largest being $j^N={\left(\frac{21}{2}\right)}^6$, for which exact solutions are available. The present method can be viewed as an angular momentum conserving alternative to the description of the transition based on the Hartree-Bogoliubov-BCS method. Qualitative and detailed comparisons of the two methods are carried out. In particular, it is shown from approximate analytic results that the two theories predict the transition to occur for almost identical values of the parameters. Over-all agreement with exact results is much better for the algebraic method, however, confirming its status as an approximate method of variation after projection.

The nucleon-deuteron scattering amplitude is investigated on the basis of a Feynmandiagram technique. A superposition of an exchange pole and triangle graphs is considered. With the aid of some reasonable approximations, the triangle amplitude is given in terms of a nucleon-nucleon amplitude. Angular distributions up to 155-MeV proton energy are calculated for $p-d$ scattering using a phase-shift analysis for the nucleon-nucleon amplitude. Good agreement with the experimental results is obtained.

We measured the cross sections of the different inelastic channels for $\alpha +p$ reactions between 135 and 155 MeV. Starting with some simple assumptions, a theoretical description of differential and absolute cross sections has been sought to be applied to some cosmic-ray studies.

It has been noted recently that a local spin-orbit nucleon-nucleon interaction, if taken seriously in the framework of nonrelativistic quantum mechanics, is generally inconsistent with the asymptotic saturation property of nuclear binding energies. This has motivated the conjecture that nuclear aggregates bound essentially by the spin-orbit interaction exist. The present paper constitutes an attempt to subject this conjecture to scrutiny, to the extent possible without abandoning the firm ground of well-understood, and mathematically sound, many-nucleon nonrelativistic theory, with "realistic" interactions mediated by potentials.

The form factors for electroexcitation of the lowest $T=\frac{3}{2}$ levels in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ (14.39 MeV, ${\frac{3}{2}}^{-}$; 16.97 MeV, ${\mathrm{½}}^{-}$) have been measured for momentum transfers between 0.5 and 1.1 ${\mathrm{fm}}^{-1\mathrm{}}$. Results are also presented for levels of unknown $T{J}^{\pi }$ at 16.63 and 17.48 MeV excitation. Radiative widths have been extracted. The form factor of the 16.63-MeV state is compared with simple-spherical and deformed shell-model form factors. The ground-state rms radius and quadrupole moment have been deduced from the elastic scattering data.

Ge(Li) spectrometry has been used to study the $\gamma$-ray deexcitation of states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ produced in the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(t, \alpha ){}_{}{}^{18}{}_{}{}^{}\mathrm{O}_{}^{*}{}_{}{}^{}$ reaction at $E_t=2.6\mathrm{}$ MeV. Precision excitation energies were determined from both singles and coincidence measurements. Multiparameter data collection techniques were used to store $\gamma$-ray spectra measured at ${\theta }_{\gamma }=0, 45, \mathrm{and} 90°$ in coincidence with $\alpha$ groups populating various final states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. $\alpha$ particles were detected in an annular detector at ${\overline{\theta }}_{\alpha }=180\mathrm{}°$, thus defining a narrow cone of forward-going ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ recoils which stopped in the Ni target backings. The observed Doppler shifts were analyzed, via the Doppler-shift attenuation method, to determine the lifetimes of the initial $\gamma$-emitting states. Resulting excitation energies (in keV) and meanlives (in psec) for the first 15 excited states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ are as follows: 1982.16 ± 0.20 ($\tau ={2.9}_{-0.6\mathrm{}}^{+0.9\mathrm{}}$), 3555.07 ± 0.45 (> 4.0), 3634.50 ± 0.40 (1.33 ± 0.20), 3920.6 ± 0.4 (0.024 ± 0.010), 4456.1 ± 0.5 (0.065 ± 0.015), 5098.5 ± 1.2 (0.062 ± 0.025), 5260.4 ± 1.2 (0.12 ± 0.03), 5336.4 ± 0.6 (0.20 ± 0.04), 5377.8 ± 1.2 (< 0.03), 5530.5 ± 0.6 (< 0.025), 6196.3 ± 1.2 (...), 6351.3 ± 0.6 (< 0.035), 6404.4 ± 1.2 (0.03 ± 0.015), 6881.6 ± 1.2 (< 0.025), and 7116.9 ± 1.2 (<0.025). The angular correlations data for each $\gamma$ transition were fitted, as a function of ${\theta }_{\gamma }$, in order to determine relative intensities and thus branching ratios. An analysis of the correlation data provides confirmation or support for previously reported conclusions on spin-parity assignments, and in addition restricts possible assignments for the 6351-keV state to $J=1\mathrm{} or 2$. These results are compared to previous data on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and to theoretical considerations.

Angular distributions of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ particles from the three-neutron pickup reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{10}{}_{}{}^{}\mathrm{C}$ have been measured for transitions to the two lowest states of ${}_{}{}^{10}{}_{}{}^{}\mathrm{C}$, the $J^{\pi }=0^{+}$ ground state and 3.35-MeV $J^{\pi }=2^{+}$ state. Observed anomalies in the shapes and magnitudes of these distributions cannot be explained theoretically by zero-range distorted-wave Born-approximation calculations.

We consider a projectile scattering elastically from a system of finite-mass constituents via a separable microscopic interaction. In order to reduce the situation to a solvable problem, several standard assumptions are necessary. The validity of these assumptions can be checked in a given model problem. The optical potential is identified by comparing the multiple scattering series we obtain with that obtained in the equivalent one-body problem. The optical potential explicitly exhibits the effects of the Fermi motion and finite mass of the target particles and is a generalization of an optical potential obtained earlier. Our results are in a form suitable for application to intermediate energy projectile many-body target scattering.

An analytically soluble model is given for which an exact numerical solution of the Hill-Wheeler equation in the continuum can be calculated. Properties of this model, which concern in particular the effects of the Pauli principle and the microscopic definition of an optical potential, are considered.

It is shown that the energy-weighted and inversely-energy-weighted (IEW) random-phase-approximation sum rules may be obtained simultaneously by a doubly constrained self-consistent field calculation. Applications of the IEW sum rule are made to the quadrupole-force Hamiltonian, including a case when zero-frequency modes occur. The relevance to certain higher-order sum rules is noted and discrepancies in some calculations of centrifugal stretching effects in spherical and deformed nuclei are pointed out.

Erros on the charge distribution as derived from electron scattering are determined and they depend largely on assumptions about the possible large-$q$ behavior of the form factor (i.e., at larger-$q$ values than have been measured). We use rather general expansions for $\rho \mathrm{}\left(r\right)\mathrm{}$, for example the cosine series or a set of spline functions. We find the charge distribution and its error to be not very dependent on the set of functions used for expansion but dependent instead on assumptions about and knowledge of the errors in $f\left(q\right)\mathrm{}$. Charge densities and their errors for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ based on electron scattering are shown.