Resonant photon scattering from ${}_{}{}^{206,207,208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ has been measured from 4 MeV to the neutron thresholds using enriched targets, Ge(Li) detectors and bremsstrahlung beams with end-point energies of 7.0, 7.5, 7.6, 8.0, 8.5, and 10.4 MeV. Energies and values of $\frac{g{{\Gamma }_0}^2}{\Gamma }$ were obtained for many levels not observed in previous photon experiments. Spins of levels in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ were determined from the angular distributions, and ground-state branching ratios were obtained from self-absorption measurements for seven transitions in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The results are compared with earlier spectroscopic studies and with lower resolution average cross-section measurements. The spectra of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ are discussed in terms of the excitations of the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ core.

NUCLEAR REACTIONS ${}_{}{}^{206,207,208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(\gamma , \gamma )$; enriched targets; resonance fluorescence with 7.0, 7.5, 7.6, 8.0, 8.5, and 10.4 MeV bremsstrahlung. Measured $E_{\gamma }$, $I_{\gamma }$ at 90° and 127°, and self-absorption; deduced $\frac{g{{\Gamma }_0}^2}{\Gamma }$, $\frac{{\Gamma }_0}{\Gamma }$, $J$.

Cross sections and effective recoil ranges of nuclei produced in the 80, 136, 153, and 164 MeV proton bombardment of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$ targets have been measured using the conventional thick target recoil catcher technique. The measured ranges increase monotonically with the number of nucleons removed from the target, and only for the lightest of the product nuclei are they comparable to values expected for compound nucleus formation. This trend is consistent with the picture in which the initial proton-nucleus interactions leave a few intermediate nuclei over a broad range of excitation, from which the bulk of the final nuclei are produced by evaporation. Detailed comparisons of the observations with predictions of the cascade model are presented and discussed.

NUCLEAR REACTIONS ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(p, X)$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}(p, X)$, $E=80-164\mathrm{}$ MeV. Measured $E_{\gamma }$, $I_{\gamma }$ of radioactive products; deduced $\sigma (X, E)$, recoil ranges, mass distribution, charge distribution. Enriched targets, Ge (Li) counting.

The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic $T$ matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus $T$ matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear $T$ matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb $T$ matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV $p$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering and compared with experimental data.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p)$, $E=0.8\mathrm{}$ GeV, Kerman, McManus, and Thaler, and Watson multiple scattering theories, Coulomb correction terms, high momentum transfer.

Activation techniques were used to measure more than 30 excitation functions for single and multiple nucleon and/or $\alpha$ particle emission for $d$+${}_{}{}^{64,66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ with $E_d=9-26\mathrm{}$ MeV and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ with $E\left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)=10-44\mathrm{}$ MeV. The excitation functions are generally in agreement with the results of a combined equilibrium and preequilibrium hybrid model calculation applying initial exciton numbers $n_0=3\mathrm{}$ for $d$ and $n_0=4\mathrm{}$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ reactions. The composite system ${}_{}{}^{66}{}_{}{}^{}\mathrm{Ga}$ has been produced via $d$+${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ at excitation energies between 22 and 36 MeV. An entrance channel dependence shows up in the yields for single $p$- and $n$-emission when compared in the double ratio $R=\frac{\left[\frac{\sigma ({}_{}{}^3{}_{}{}^{}\mathrm{He}, p)}{\sigma ({}_{}{}^3{}_{}{}^{}\mathrm{He}, n)}\right]}{\left[\frac{\sigma (d, p)}{\sigma (d, n)}\right]}$. It approaches a value of about 2, indicating enhanced $p$ emission for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-induced reaction. This value disagrees with the equilibrium isospin formalism and is best reproduced by initial particle exciton numbers $n_{0p}=n_{0n}=1.5\mathrm{}$ for $d$ and $n_{0p}=2.5\mathrm{}$, $n_{0n}=1.5\mathrm{}$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ projectiles, indicating conservation of charge asymmetry in the entrance channel. Isomeric ratios have been measured for ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(d, 2n){}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}({}_{}{}^3{}_{}{}^{}\mathrm{He}, xn){}_{}{}^{96-x}{}_{}{}^{}\mathrm{Tc}$ ($x=1, 2, 3$). Calculations with a full statistical model fail to reproduce $\frac{{\sigma }_g}{{\sigma }_m}$ as well as ${\sigma }_g$ and ${\sigma }_m$ for reasonable values of the spin cutoff parameter. Inclusion of a preequilibrium decay mode improves the fit, in particular if the angular momentum depletion of the composite system due to preequilibrium decay is increased over that of the equilibrium decay at the same channel energy.

NUCLEAR REACTIONS ${}_{}{}^{64,66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(d, \mathrm{xnypz}\alpha )$, $E_d=9-26\mathrm{}$ MeV, ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \mathrm{xnypz}\alpha )$, $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=10-44\mathrm{}$ MeV, $x<~4$, $y<~1$, $z<~2$; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ by activation, enriched targets. Statistical model analysis including preequilibrium decay, deduced reaction mechanism, charge asymmetry conservation, spin depletion.

A study has been made of the energy, angular, and charge distribution of products emitted in the reaction of 166-MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ions with ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$. The first three moments of the $\gamma$-ray multiplicity distribution and the out-of-plane $\gamma$-ray angular correlations have been measured in coincidence with the projectile-like fragments. Relaxation times of 2.6 × ${10}^{-22\mathrm{}}$ s for energy dissipation, 4.1 × ${10}^{-22\mathrm{}}$ s for angular momentum transfer, and a charge diffusion coefficient of 0.58 × ${10}^{22}$ ${\mathrm{}\left(\mathrm{charge}\mathrm{units}\right)\mathrm{}}^2$ ${\mathrm{s}}^{-1\mathrm{}}$ have been deduced from these data. A small $\gamma$-ray anisotropy and a large width of the multiplicity distribution have been observed. These are interpreted in terms of a random component of transferred angular momentum whose magnitude is comparable to that of the aligned component induced by tangential friction. Thermal excitation of collective modes of motion in the equilibrated dinuclear complex can account quantitatively for these experimental results. Other mechanisms for the generation of a random component of angular momentum are also possible.

NUCLEAR REACTIONS ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}, X)$, $X=\mathrm{deeply}\mathrm{inelastic}\mathrm{fragments}$, evaporation residues, $E=166\mathrm{}$ MeV, enriched target; measured $\sigma (E, \theta , Z)$, $\gamma$-ray multiplicity, angular correlations; deduced relaxation times, diffusion coefficients, random angular momentum. ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, X)$, $X=\mathrm{evaporation}\mathrm{residues}$, $E=133\mathrm{}$ MeV, measured $\gamma$-ray multiplicity.

Nuclear charge distributions for projectile-like and fission-fragment-like reaction products were measured as a function of angle and energy loss at each of the three bombarding energies $E_L=505, 610, \mathrm{and} 710$ MeV for the ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ + ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ reaction. The charge distributions at most angles and energy losses are dominated by a peak centered close to the $Z$ of the projectile. The variances of the $Z$ distributions of this component exhibit a different dependence on energy loss at each of the three bombarding energies. A nucleon-exchange model incorporating the effects of the Fermi motion and Pauli Principle is quite successful in accounting for the rate of energy loss per exchange deduced from the charge distribution data. This result suggests that nucleon exchange is the major mechanism for energy dissipation in these collisions. The data are also analyzed in the framework of a phenomenological model from which diffusion constants are obtained. For large energy losses a second peak appears in the charge distribution with a most probable $Z$ equal to one half the sum of the projectile and target $Z$. This component is attributed to fusion-fission. The magnitude of the fusion-fission cross section at 505 and 610 MeV is larger than time-dependent Hartree Fock predictions.

NUCLEAR REACTIONS Nuclear charge distributions measured as a function of angle and energy loss for $E_{\mathrm{lab}}=505, 610, \mathrm{and} 710$ MeV; analysis with nucleon exchange model incorporating Fermi motion and Pauli blocking; transport model diffusion constants extracted; fusion-fission cross sections deduced.

Angular distributions for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ elastic scattering at 73.7 MeV from targets of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been measured. Optical-model parameters for Woods-Saxon real and imaginary volume potentials have been found which describe the data well and exhibit both discrete and continuous ambiguities. For a fixed geometry, the dependence of the optical potentials on $Z$ and $A$ of the target and on the bombarding energy was investigated.

NUCLEAR REACTIONS ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$), $E=73.7\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; deduced optical-model parameters.

Evidence of a spherical (or oblate) to prolate shape transition around $N=40\mathrm{}$ in even-$A$ germanium nuclei has been obtained by measuring the static quadrupole moments of the first $2^{+}$ excited states of ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$, and ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ using the reorientation effect in Coulomb excitation. The measurements yield $Q_{2^{+}}$ values of $(+0.03\mathrm{}\pm 0.06) or (+0.09\mathrm{}\pm 0.06)e$b for ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, $(-0.13\mathrm{}\pm 0.06)e$b for ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$, $(-0.25\mathrm{}\pm 0.06)e$b for ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$, and $(-0.19\mathrm{}\pm 0.06)e$b for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$.

NUCLEAR REACTIONS ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$′), $E=10.5\mathrm{}$ MeV; ${}_{}{}^{72,74,76}{}_{}{}^{}\mathrm{Ge}(\alpha , {\alpha }^{\prime })$, $E=7.0\mathrm{}$ MeV; ${}_{}{}^{70,72,74,76}{}_{}{}^{}\mathrm{Ge}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$′), $E=29.9\mathrm{}$ MeV; measured $\sigma (E, E_{{}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{\prime }{}_{}{}^{}})$ deduced $Q_{2^{+}}$, $B(E2; 0^{+}\to 2^{+})$. Enriched targets.

Elastic and inelastic scattering of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured at incident energies of 63 and 78.7 MeV. The experimental data were obtained over an angular range from ${\theta }_{\mathrm{lab}}=8\mathrm{}° \mathrm{to} 40°$. Optical model parameters have been extracted by fitting the elastic scattering data, and deformation lengths have been obtained for the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$* (0.48 MeV) state and the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$* (4.44 MeV) state. No single parameter set was found that fitted the elastic scattering over a wide range of energies via simple changes in the depths of the potentials.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^7{}_{}{}^{}\mathrm{Li}$) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^7{}_{}{}^{}\mathrm{Li}$′) $E\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)=63\mathrm{} \mathrm{and} 78.7$ MeV; measured $\sigma \left(\theta \right)$; deduced optical model parameters; deduced deformation lengths for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$* and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$*. Natural targets, DWBA analysis ${\theta }_{\mathrm{lab}}=8-40\mathrm{}°$, $\Delta \theta =1\mathrm{}°$.

Semiclassical approximations are used in the distorted-wave Born approximation to derive expressions for expected polarizations in heavy-ion-induced transfer reactions. The signs and magnitudes of these polarizations are shown to depend upon a few crucial, easily estimated, parameters and also upon the specific final states populated. Comparison of distorted-wave Born-approximation calculations to data is made.

NUCLEAR REACTIONS Semiclassical analysis of heavy-ion-induced transfer, calculated polarizations.

A summation of selected graphs in the perturbation expansion for the statistical operator and the operator of state leads to a simplified equation of motion for the nuclear many-body problem. It contains as a special limit the time-dependent Hartree-Fock and the quantum-statistical master equation. In a pictorial way one could label the approach as "Hartree-Fock plus collision terms." The formalism allows one to understand the progression of the nucleus from the boiling of the particle-hole excitations to the collective state of motion. The work is restricted presenting the formalism. Various applications are possible and indicated, but apart from an illustrative example no concrete comparison with the experiment has been performed.

NUCLEAR REACTIONS Formalism developed for unifying collective and single-particle aspects; mean field theory, Hartree-Fock plus collision terms.

Angular distributions and excitation functions for the elastic and inelastic ($2^{+}$, 1.81 MeV) scattering of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions by ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ have been measured in the energy range from 22 up to 50 MeV. The data were analyzed in the coupled channel scheme with different potentials. The inelastic scattering data are found to be important to distinguish between optical model parameter sets. The deformation parameter ${\delta }_n={\beta }_{n}R$ is extracted and found to be potential dependent. It is compared to the Coulomb deformation ${\delta }_{\mathrm{C}}$.

NUCLEAR REACTIONS ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$′). Measured: excitation functions 22-50 MeV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=55\mathrm{}° \mathrm{to} 140°$, angular distributions for g.s. and $2^{+}$, 1.81 MeV in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$. Coupled channel analysis, deduced $\beta R$. Enriched target. Kinematic coincidence.

We have measured the mass and kinetic-energy distributions for fragments from the spontaneous fission of 1.2-s ${}_{}{}^{246}{}_{}{}^{}\mathrm{Fm}$ and 38-s ${}_{}{}^{248}{}_{}{}^{}\mathrm{Fm}$. The mass distributions are highly asymmetric and the average total kinetic energies of 199±4 MeV and 198±4 MeV, respectively, are consistent with systematics for lower $Z$ actinides. Their properties are in contrast to those of ${}_{}{}^{258}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{259}{}_{}{}^{}\mathrm{Fm}$, whose spontaneous fission results in narrowly symmetric mass distributions accompanied by unusually high total kinetic energies.

RADIOACTIVITY, FISSION ${}_{}{}^{246}{}_{}{}^{}\mathrm{Fm}$ (SF) ${}_{}{}^{248}{}_{}{}^{}\mathrm{Fm}$ (SF); measured fragment-fragment kinetic energies; total kinetic energy; deduced fragment mass distributions.

A superprolate structure for nuclei with $A\sim 240$ proposed in 1965 on the basis of the polyspheron theory leads to the value 0.66 for the deformation parameter $\beta$. This value agrees well with a recently reported experimental value, 0.66±0.04 for the spontaneous-fission isomer ${}_{}{}^{240}{}_{}{}^{}\mathrm{Am}_{}^m{}_{}{}^{}$, obtained by Bemis et al. from their measurement of the optical isomer shift. This agreement provides additional support for the proposed superprolate structure.

NUCLEAR STRUCTURE ${}_{}{}^{240}{}_{}{}^{}\mathrm{Am}_{}^m{}_{}{}^{}$; deformation parameter of superprolate shape predicted by cluster theory agrees with experimental value.

The intermediate state in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ($e, e^{\prime }f$) has been studied in a variational alpha-cluster-model calculation with projection onto the experimental spin, parity, and $K$ values. The resulting state has a distinct ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ structure in accord with the observed fragmentation, and its energy is reasonably close to the measured peak of the fission yield. An explanation for the peculiar experimental fragment excitation is given in terms of the overlaps between intermediate and final states.

NUCLEAR STRUCTURE ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$; alpha-cluster model of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($2_1^{+}$) + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($0_1^{+}$) fission. Soft-core forces. Calculated energy, density, overlaps for intermediate state.

Energy spectra and angular distributions have been measured for isotopically separated Li and Be and elementally separated B to Na fragments produced in reactions of 210, 300, and 480 MeV protons with Ag. These data are analyzed in terms of evaporative and nonevaporative processes. A two-parameter self-consistent evaporation calculation, normalized to ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ emission, indicates a major fraction of the cross section to be nonevaporative. An analysis of the data in terms of rapidity and relativistically invariant cross section substantiates this finding. The evaporative component is weakly forward peaked and is a strongly varying function of which isotope of a given element is considered; the nonevaporative component is strongly forward peaked but varies more slowly as a function of fragment mass. Both components show behavior indicative of Coulomb barrier effects appropriate to emission from nuclides near the target. Energy integrated and total cross sections are calculated.

NUCLEAR REACTIONS $\mathrm{Ag}(p, x)$; measured $\sigma (E, E_x, \theta )$, $E=210, 300, 480$ MeV, $x={}_{}{}^{6,7,8}{}_{}{}^{}\mathrm{Li}, {}_{}{}^{7,9,10}{}_{}{}^{}\mathrm{Be}$, B to Na, $\theta =20, 90, 160°$. Deduced $\sigma (E, \theta )$ and $\sigma \mathrm{}\left(E\right)\mathrm{}$. Calculated evaporative and deduced nonevaporative components; invariant cross section, rapidity analysis. Spallation, fragmentation.

Prompt $\gamma$ rays from the interaction of 720-MeV $\alpha$ particles with ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ were detected and analyzed to identify residual nuclei and to determine cross sections for production of specific levels. No $\gamma$-ray transitions were detected from nuclei heavier than the target. From Doppler broadening, the momentum of the residual nuclei was estimated. The results are compared with previous results for 140- and 1600-MeV $\alpha \text{'}\mathrm{s}$ on ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ∼200-MeV ${\pi }^{\pm }$ on ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and fitted to a spallation-yield formula.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\alpha , X\gamma )$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha , X\gamma )$, $E_{\alpha }=720\mathrm{}$ MeV; detected $\gamma$ rays, Ge(Li); measured $E_{\gamma }$, $90°\sigma$ for specific levels in residual nuclei, Doppler broadening for recoil momentum.

Starting from the eikonal approximation to the scattering amplitude an analytical approximation is obtained, including Coulomb effects. The amplitude is characterized by three numbers, one of which is a radius parameter $b_1$. These numbers are related in a simple way to the optical potential $U\left(r\right)\mathrm{}$ for $r\simeq b_1$. The quality of the analytical result is assessed by comparing it to the exact eikonal amplitude for a model of $U$ which is linear in density. It reproduces accurately the position and depth of the first minimum, the magnitude of the first secondary maximum, and the differences of the ${\pi }^{+}$ and ${\pi }^{-}$ cross sections. It is furthermore shown that at 180 MeV the analytical approximation reproduces semiquantitatively the magnitude and shape of the "model exact" solution of the Klein-Gordon equation at forward angles. An application to scattering by the calcium isotopes is taken as an example to show the sensitivity to the neutron distribution as the $f_{\frac{7}{2}}$ shell is filled.

NUCLEAR REACTIONS Pion elastic scattering; analytical formulas for angular distributions.

We present a complete set of eight differential cross sections of the reactions ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, n){}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, p){}_{}{}^3{}_{}{}^{}\mathrm{H}$ in the 0-60° c.m. angular range for incident deuteron momenta between 1.1 and 2.5 GeV/c. A simple phenomenological interpretation of the energy dependence of the total cross section ${\sigma }_T$ and of $\frac{d\sigma }{\mathrm{dt}}$ at fixed $t$ shows, in the reaction, the contribution of a nucleon exchange process to which we must add a mechanism implying the ${\Delta }_{33}$ resonance excitation in the direct channel.

NUCLEAR REACTION ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, n){}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, p){}_{}{}^3{}_{}{}^{}\mathrm{H}$; $E_d=0.3-1.25\mathrm{}$ GeV; measured $\sigma (E_d, \theta )$; intermediate energy; phenomenological analysis of the baryonic exchange mechanisms.

Using a time ordered diagrammatic method, we derive a set of linear integral equations that couple the $N-N$ to the $\pi -d$ channel and satisfy two- and three-body unitarity. The resultant equations have dressed propagators for the nucleons, and dressed form factors for the $\pi \mathrm{NN}$ vertex. The inclusion of the full $\pi -N$ amplitude in the $P_{11}$ channel leads to a dressing of both the $\pi \mathrm{NN}$ vertex and $N-N$ propagator without changing the basic structure of the equations.

NUCLEAR REACTIONS Nucleon-nucleon and pion-deuteron scattering. Derived coupled equations for $\mathrm{NN}$, $N\Delta$, $\pi d$ with dressed nucleons and $\pi \mathrm{NN}$ vertex.