Light ions with $Z=1,2\mathrm{}$ and velocities greater than the beam velocity, produced in collisions between carbon and nickel nuclei, are studied using ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ beams with energies between 7.5 and 16 MeV per nucleon. Energy spectra and angular distributions are reported and excitation functions derived from these data are presented. Integral cross sections for protons with velocities greater than the beam velocity are found to be insensitive to the beam energy. A model in which particles are emitted by an excited source, moving with a velocity approximately one-half that of the beam, is found to be capable of reproducing most of the data.

NUCLEAR REACTIONS ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\mathrm{xp}$), (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\mathrm{xd}$), (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\mathrm{xt}$), (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$x{}_{}{}^3{}_{}{}^{}\mathrm{He}$), (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\mathrm{xd}$), $E=90, 123, 156, 189$ MeV; measured $\sigma (E;\theta )$; deduced integral yields, model parameters.

Excitation functions for the total cross section in various mutual excitation channels have been measured in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system using a $\gamma -\gamma$ coincidence technique in the energy range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=24-41\mathrm{}$ MeV. The inclusive cross section for the production of 6.13 MeV $\gamma$ rays has also been measured using a Ge(Li) detector. Gross structure oscillations are seen in the mutual excitation of the second excited ($J^{\pi }=3^{-}$) state; these oscillations are approximately in phase with those of the single excitation cross section, which has also been extracted from the present data using the combined results of coincidence and singles measurements. The general trend of the data is accounted for by recently published coupled channels calculations, although a detailed fit is not achieved.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$*)${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$* $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=24-41\mathrm{}$ MeV; measured $\gamma -\gamma$ coincidences; deduced reaction mechanism.

The independent yields of ${}_{}{}^{82}{}_{}{}^{}\mathrm{Br}$, ${}_{}{}^{86}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{98}{}_{}{}^{}\mathrm{Nb}_{}^m{}_{}{}^{}$, ${}_{}{}^{128}{}_{}{}^{}\mathrm{Sb}_{}^g{}_{}{}^{}$, and ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$ were determined in the reactor-neutron-induced fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ using radiochemical techniques. Results: (2.3±2.3)×${10}^{-4\mathrm{}}$% for ${}_{}{}^{82}{}_{}{}^{}\mathrm{Br}$, <3.8×${10}^{-4\mathrm{}}$% for ${}_{}{}^{86}{}_{}{}^{}\mathrm{Rb}$, <4.2×${10}^{-5\mathrm{}}$% for ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$, (2.48±0.53)×${10}^{-3\mathrm{}}$% for ${}_{}{}^{98}{}_{}{}^{}\mathrm{Nb}_{}^m{}_{}{}^{}$, (2.34±0.37)×${10}^{-3\mathrm{}}$% for ${}_{}{}^{128}{}_{}{}^{}\mathrm{Sb}_{}^g{}_{}{}^{}$, and (1.70±0.13) ×${10}^{-4\mathrm{}}$% for ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$. Using the extended $\mathrm{Zp}$ model of Wahl with the yield data from this work and the literature the following parameters were obtained for the charge distribution in ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ fission: width of Gaussian dispersion ${\overline{\sigma }}_Z=0.52\mathrm{}\pm 0.01$, $\Delta Z_P (=Z_P-Z_{\mathrm{UCD}})=0.45\mathrm{}\pm 0.02$. The even-odd proton and neutron enhancement factors were found to be small. These parameters and systematics of even-odd proton and neutron effects in low energy fission are discussed.

NUCLEAR REACTIONS, FISSION Radiochemical fission yields ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$($n$,$f$), calculated charge dispersion parameters, and odd-even effects.

Equilibrium shapes and fission barriers of rotating nuclei have been calculated using a macroscopic two-center model, with a finite-range nuclear force and a diffuse nuclear surface. Our model differs from the rotating-liquid-drop model of Cohen, Plasil, and Swiatecki in the shape parametrization and in the calculations of the surface, Coulomb, and rotational energies. We use the two-center-model shape parametrization, which allows for triaxial shape variations and a continuous transition from one-center to two-center shapes with a smooth neck. We calculate the surface energy with the Yukawa-plus-exponential folding function of Krappe, Nix, and Sierk, which incorporates the effects of the finite range of the nuclear force and the diffuse nuclear surface, and calculate both the Coulomb and rotational energies with surface diffuseness described by a Yukawa folding function. The calculation includes beta-stable nuclei up to mass number $A=250\mathrm{}$ and selected nuclei off the line of beta stability. The results are compared with the predictions of the rotating-liquid-drop model and with experimental results statistically deduced from heavy-ion induced reactions.

NUCLEAR REACTIONS, FISSION Calculated equilibrium shapes, fission barriers, and critical angular momenta for rotating nuclei. Macroscopic two-center model with triaxial shapes, rotating liquid-drop model, Yukawa and Yukawa-plus-exponential folding, finite range of nuclear force, surface diffuseness, heavy-ion induced fission.

The isotopic distribution of rubidium produced in the proton induced fission of iridium has been measured at 68, 85, and 100 MeV incident beam energies using an on-line mass spectrometer with a surface ionization ion source. The deduced neutron multiplicities are substantially higher and show a steeper energy dependence compared to similar measurements done with a heavy ion beam in this mass region and in the same range of excitation energies. This might confirm an effect of the angular momentum of the fissioning nucleus on the fragment deexcitation mechanism.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{191,193}{}_{}{}^{}\mathrm{Ir}$($p$,$f$), $E_p=68, 85, 100$ MeV; measured independent relative yields of Rb. Deduced total number of neutrons emitted in symmetric fission.

Differential cross sections were measured for the reaction, ${\pi }^{+}d\to \mathrm{pp}$, at seven energies, 80, 100, 140, 182, 230, 323, and 417 MeV. Sufficient data were taken for a 1% statistical uncertainty at eleven different angles for most of these energies. The elastic ${\pi }^{+}p$ reaction was used to normalize the ${\pi }^{+}d\to \mathrm{pp}$ data. Legendre polynomial fits of the data are presented. The increased accuracy and energy of these data require an addition of a ${{cos}^6\theta }^{*}$ term in the traditional low energy form of the differential cross section: $C(A+{{cos}^2\theta }^{*}+B{cos}^4{\theta }^{*})$. The coefficients, $A$ and $B$, are used to compare the present data with a survey of previous experiments and the theoretical work of Niskanen. Agreement is usually within uncertainties, but some diagreement remains even among recent experiments.

NUCLEAR REACTIONS $d(\pi ,pp)$, $E=80-417\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; calculated Legendre polynomial fits; compared to earlier work.

Angular distributions are reported for 0.8 GeV proton elastic and inelastic scattering from ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The data are analyzed with the optical model using a spherical Woods-Saxon potential and the distorted wave Born approximation with collective form factors.

NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$($p$,$p^{\prime }$), $E=0.8\mathrm{}$ GeV; measured $\sigma \left(\theta \right)$; natural targets; resolution 100 to 200 keV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=5.6\mathrm{} \mathrm{to} 32.0°$. Optical model potential, DWBA analysis, inelastic deformation lengths, ${\beta }_{l}R$.

80 MeV positive and negative pions inelastically scattered from targets of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been studied at laboratory angles between 50° and 120°. Angular distributions are presented for scattering from the 4.44 MeV ($2^{+}$) state in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, the 3.7 MeV ($3^{-}$), 13.4 MeV, and 17.5 MeV states in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. The cross sections are compared with distorted wave calculations using potentials obtained from elastic scattering.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($\pi$,${\pi }^{\prime }$), ${}_{}{}^{40}{}_{}{}^{}\mathrm{C}$($\pi$,${\pi }^{\prime }$), $E=80\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ for low lying (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$) and giant resonance (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$) states; DWBA analysis.

Measurements are reported for the elastic and inelastic scattering of 800 MeV protons from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Differential cross sections were measured out to 42° while analyzing powers were obtained out to 30°. The angular distributions are diffractive in character at all angles. Theoretical analysis of the data was carried out in the framework of the diffraction multiple scattering theory. The following results were obtained: (i) Diffraction multiple scattering theory reproduces the data qualitatively out to the large momentum transfers. (ii) For the ground state density distribution ${〈{r_p}^2〉}^{\frac{1}{2}}-{〈{r_n}^2〉}^{\frac{1}{2}}=0.142\mathrm{}\pm 0.075$ fm is obtained and the analysis favors the value of the correlation length ${\xi }_c=-0.5\mathrm{}$ fm. (iii) The excitation of the lowest-lying collective states ($3^{-}$, $5^{-}$, $2^{+}$) was analyzed using one-phonon excitation macroscopic parameters. The values of the ${\beta }_2$, ${\beta }_3$, ${\beta }_5$ parameters obtained agree quantitatively with lower energy ($p$,$p^{\prime }$) scattering results.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{C}$($p$,$p$), ${}_{}{}^{40}{}_{}{}^{}\mathrm{C}$($p$,$p^{\prime }$), $E=0.8\mathrm{}$ GeV, proton elastic and inelastic scattering cross sections and analyzing powers, target ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $E_{\mathrm{lab}}=0.8\mathrm{}$ GeV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=2.5\mathrm{}°-42\mathrm{}°$, Glauber diffraction scattering theory, deduced $\Delta r_{\mathrm{np}}$, transition strengths.

Angular distributions of ${\pi }^{+}$ and ${\pi }^{-}$ elastic scattering on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 64.8 MeV are presented. The data are analyzed using a first-order, nonlocal optical model based on a Kisslinger $t$ matrix with an off-shell form factor. This model is unable to fit the data for any value of the off-shell parameter $\alpha$ unless the nuclear matter radius is allowed to vary from that derived from electron scattering. The resulting best-fit radii are as much as 0.40 fm larger than the electron scattering value for ${\pi }^{+}$ and 0.55 fm larger for ${\pi }^{-}$. For a given $\alpha$ the ${\pi }^{-}$ best fit radius is also consistently larger by about 0.2 fm than that for ${\pi }^{+}$. In addition, the fits show no significant preference for any value of $\alpha$ between 400 and 900 MeV/c. Inclusion of the normally omitted second-order potential terms in the optical model does not significantly alter the results.

NUCLEAR REACTIONS ${\pi }^{+}$ and ${\pi }^{-}$ elastic scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 64.8 MeV; angular distributions, $15°<{\theta }_{\mathrm{lab}}<127\mathrm{}°$; optical model analysis.

After reviewing briefly the point Coulomb scattering problem in the nonrelativistic, Klein-Gordon, and Dirac cases, the form of the ultrarelativistic vector (Coulomb-like) potential scattering amplitude $f_0$ is developed in partial wave form for the "spinor" representation. The latter is one of a variety of different Dirac scattering amplitudes, and arises naturally in perturbation theory as the coefficient of a spinor matrix element. Unlike the traditional amplitudes, $f_0$ is not required to vanish at $\theta =\pi$, which makes it the natural choice for eikonal treatments. This representation is also the one closest to the usual nonrelativistic and Klein-Gordon amplitudes. Summation by parts, a potentially powerful rearrangement technique, is used to verify several previously known relationships among the various amplitudes, and illustrates the problems associated with summing poorly convergent series.

NUCLEAR REACTIONS Electron scattering, phase shift analysis.

In a previous paper we solved the Bethe-Salpeter equation with separable interactions and demonstrated the applicability of the method for the most important nucleon-nucleon partial waves. In this paper we use the Bethe-Salpeter equation for pion nucleon partial waves including the necessary two potential ansatz for the $P_{11}$ wave. A fully relativistic treatment of the $\pi -d$ system can be performed with these amplitudes.

NUCLEAR REACTIONS Separable Bethe-Salpeter kernels applied to pion-nucleon scattering; $E=0-300\mathrm{}$ MeV; $l=0, 1$; $P_{11}$ wave with two potential ansatz.

We have calculated the pion-deuteron elastic, total, and differential cross sections for energies between 100 and 300 MeV, using two forms of the optical potential similar to those used in the theory of pion-nucleus scattering. We have studied the accuracy of the optical potential descriptions, by comparing these cross sections with the exact ones that are obtained by solving the relativistic Faddeev equations. We found that in all cases the optical potential overestimates the multiple scattering corrections. We interpret this result as meaning that the optical potential series may not converge for pion-nucleus scattering.

NUCLEAR REACTIONS $\pi -d$ optical potentials; $E=100-300\mathrm{}$ MeV; calculated ${\sigma }_{\mathrm{tot}}$, ${\sigma }_{\mathrm{el}}$, and $\frac{d\sigma }{d\Omega }$.

We derive a coupled-channel description of pion production and absorption by the many-nucleon system from the field theoretic definition of the reaction matrix. Our result is manifestly consistent with nucleon antisymmetry, pion crossing, and unitarity and is exact, up to the neglect of terms involving at least $2N-2$ antinucleons. Our equation is approximately soluble in the limit of nonrelativistic nucleons, and in that limit we obtain explicit, Hamiltonian independent forms for the one-body operator and for leading terms in the two-body operator for use in distorted-wave Born approximation calculatios.

NUCLEAR REACTIONS Scattering theory, pion production, and absorption by many-nucleon systems.

Deuteron "missing mass' spectra have been measured at 1.46 GeV/c over the complete allowed phase space angular region for the $\mathrm{np}\to d{\left(\pi \pi \right)}^0$ reaction. Strong enhancements, evidence for the Abashian-Booth-Crowe effect, are not observed near momenta corresponding to the two pion missing mass values. A total cross section of 28.5±1.5 μb has been determined for this reaction.

NUCLEAR REACTIONS $\mathrm{np}\to d{\left(\pi \pi \right)}^0$; $E=795\mathrm{}$ MeV; measured $\sigma (P_d,\theta )$; deduced $\sigma$.

Results from $K^{\pm }$ elastic and inelastic scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are reported. The data were all taken at an incident momentum of 800 MeV/c over an angular range from 2° to 38°. The elastic data are compared to first-order optical model calculations in coordinate and momentum space; good qualitative agreement is obtained. The inelastic data (from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ only) are compared to distorted-wave Born approximation calculations, and good agreement is found if "realistic" inelastic transition densities are used. Although a first-order optical potential description does not describe the data fully, there are strong indications of the increased penetrability of $K^{+}$ over $K^{-}$ in this energy range.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($K^{\pm }$,$K^{\pm }$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$($K^{\pm }$,$K^{\pm }$)${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $E=442\mathrm{}$ MeV (800 MeV/c), measured $\sigma \left(\theta \right)$ for elastic and inelastic scattering, compared to optical model and DWBA calculations, deduced optical potential parameters; $\theta =2\mathrm{}°-38\mathrm{}°$, $\Delta \theta =1\mathrm{}°$.

The semiclassical trajectory model of Benioff, which treats the nuclear structure of the target by means of the harmonic oscillator model, has been adapted to the ($\pi$,$\pi N$) reaction in the (3,3) resonance region. Excitation functions have been calculated for comparison with the experimental results on the following reactions: ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$(${\pi }^{\pm }$,${\pi }^{\pm }p$), and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$(${\pi }^{\pm }$,${\pi }^{\pm }n$). The nucleon charge exchange probability $P$ was treated as an adjustable parameter and found to decrease from ∼0.2 for light elements to ≲0.05 for heavy elements. The value of $P$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is supported by a parameter-free estimate on the basis of a modified free nucleon-nucleon scattering model. The decrease in $P$ with increasing target $A$ is attributed to nuclear size and structure effects. The calculated excitation functions are in good agreement with the experimental results for both light and heavy target nuclei. Experiments that would constitute a more stringent test of various aspects of the model are proposed.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$(${\pi }^{\pm }$,${\pi }^{\pm }p$), ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$(${\pi }^{\pm }$,${\pi }^{\pm }n$), $T_{\pi }=100-300\mathrm{}$ MeV; calculated excitation functions and and nucleon charge exchange probability.

Measurements were made of $\frac{d\sigma }{d\Omega }$ [${\theta }_{\pi }=90\mathrm{}°\left(\mathrm{lab}\right)$] for ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($\gamma ,{\pi }^{+}$)${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ (g.s.) at $T_{\pi }=17, 29, \mathrm{and} 42$ MeV, for ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($\gamma ,{\pi }^{+}$)${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ ($E_x=3.37\mathrm{}$ MeV) at $T_{\pi }=29\mathrm{} \mathrm{and} 42$ MeV, and for ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($\gamma ,{\pi }^{-}$)${}_{}{}^{10}{}_{}{}^{}\mathrm{C}$ (g.s.) at $T_{\pi }=29\mathrm{}$ MeV. The results disagree significantly with several recent distorted-wave impulse approximation calculations.

NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($\gamma ,{\pi }^{+}$)${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ ($E_x=0, 3.37$ MeV), ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\gamma ,{\pi }^{-}){}_{}{}^{10}{}_{}{}^{}\mathrm{C}(E_x=0)$, ${\theta }_{\pi }=90\mathrm{}°$ (lab), $E_{\pi }=17, 29, 42$ MeV, measured $\frac{d\sigma }{d\Omega }$, compared with DWIA calculations.

We have developed an analytic eikonalized amplitude for the intermediate energy ($p$,$d$) reaction based on the distorted wave Born approximation. Eikonalization of the distorted waves naturally separates the important dynamical quantity, the momentum transfer, into longitudinal and transverse components. Upon evaluation of the amplitude using techniques similar to those employed by Amado, Dedonder, and Lenz for elastic scattering, we find the dependence of the transverse momentum transfer to be dominated by distortion effects. Consequently the shapes of the angular distributions are similar to those for elastic scattering. The geometry of the binding well of the picked-up neutron determines most of the dependence of the longitudinal momentum transfer. This fixes the dependence on bombarding energy. Many simple systematic features of these reactions are predicted using the analytic eikonalized amplitude and are observed in full partial wave calculations.

NUCLEAR REACTIONS Analytic eikonalized amplitudes for intermediate energy stripping and pickup reactions.

Predictions of the eikonalized strong-absorption model for the small-angle excitation of isovector giant-resonance states, as well as for analog states, are given for pion-nuclear single-charge-exchange reactions. Spin-flip excitations are treated, particularly in connection with the recent observation of the giant dipole resonance in (${\pi }^{\pm }$,${\pi }^0$) on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. The results trivially generalize to excitation of isoscalar resonances.

NUCLEAR REACTIONS Pion single-charge-exchange; strong-absorption model. Excitation of giant-resonance states.