A method for separating direct and compound nuclear reaction contributions to inelastic $\alpha$ scattering on spin 0 targets is proposed. It is based on the characteristic behavior of the parameters of the $\alpha -\gamma$ angular correlation function in a distorted-wave Born approximation and a Hauser-Feshbach model treatment. The method is applied to the reaction ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha , {\alpha }^{\prime }\gamma )$.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ($\alpha , {\alpha }^{\prime }\gamma$), $E_{\alpha }=10, 16.5$ MeV. Measured differential cross sections and angular correlations. Determined direct and compound nuclear contributions.

Nuclear levels in ${}_{}{}^{109}{}_{}{}^{}\mathrm{In}$ have been investigated by means of the ${}_{}{}^{108}{}_{}{}^{}\mathrm{Cd}({}_{}{}^3{}_{}{}^{}\mathrm{He}, d){}_{}{}^{109}{}_{}{}^{}\mathrm{In}$ reaction, at incident energies of 19.5 and 21 MeV, using a magnetic spectrograph. Twenty six levels, up to 3 MeV excitation, have been observed. The experimental angular distributions have been compared with distorted-wave Born approximation calculations to assign angular momentum transfers and to determine spectroscopic factors. Total spin assignments have tentatively been made with the help of shell-model predictions. The proton configuration for the ground state of ${}_{}{}^{108}{}_{}{}^{}\mathrm{Cd}$ has been deduced. The results are compared with previous data on ${}_{}{}^{109}{}_{}{}^{}\mathrm{In}$ and with (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $d$) studies on other odd-mass indium isotopes.

NUCLEAR REACTIONS ${}_{}{}^{108}{}_{}{}^{}\mathrm{Cd}({}_{}{}^3{}_{}{}^{}\mathrm{He}, d){}_{}{}^{109}{}_{}{}^{}\mathrm{In}$; $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=19.5, 21.0$ MeV; deduced ${}_{}{}^{109}{}_{}{}^{}\mathrm{In}$ levels; measured $\sigma \left(\theta \right)$; DWBA analysis; deduced $l$, $J$, $\pi$, spectroscopic strengths.

The variation of the total neutron cross section, $\Delta {\sigma }_{\mathrm{align}}$, on ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ due to nuclear alignment of the target has been measured over the energy range from 0.8 to 20 MeV employing a cobalt single crystal with a 34% nuclear alignment. The results show that $\Delta {\sigma }_{\mathrm{align}}$ oscillates from a minimum of -5% at about 2.5 MeV to a maximum of + 1% at about 10 MeV. The data were successfully fitted by optical model coupled-channel calculations. The coupling terms were deduced from a model representing the ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ nucleus as a vibrational ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ core coupled to a proton hole in a ($1f_{\frac{7}{2}}$) shell, without free parameters. The optical model parameters were determined by fitting the total cross section, which was independently measured. The theoretical calculations show that, at lower energies, $\Delta {\sigma }_{\mathrm{align}}$ depends appreciably on the coupling with the low-lying levels.

NUCLEAR REACTIONS ${}_{}{}^{59}{}_{}{}^{}\overrightarrow{\mathrm{Co}}+n$, $E_n=0.8-20\mathrm{}$ MeV; measured ${\sigma }_T$ and deformation effect $\Delta {\sigma }_{\mathrm{align}}$; data analyzed by coupled-channel calculations; deduced optical model parameters; no free parameters used in coupling terms.

An attempt is made to find a satisfactory explanation for the average spin-spin cross section of ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ for neutrons between 0.3 and 2.9 MeV. Calculations with an optical model spin-spin potential obviously fail to reproduce these data. A hybrid model is developed containing elements of compound-nucleus formation and of the optical model. Partial waves with orbital momenta up to $l=4\mathrm{}$ are taken into account. This model yields a good explanation of the ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ data. It also agrees with the spin-spin cross section of ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$, the only other nuclide for which data exist above 0.1 MeV.

NUCLEAR REACTIONS Spin-spin interaction model applied to ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$.

A phase shift analysis of 15 alpha particle elastic scattering angular distributions measured accurately between 30° and 170° center of mass and between 26.13 and 47 MeV by the Basel group has been performed. Perfect agreement between experimental and the calculated differential cross sections is obtained over the full range of energy. The fluctuating behavior of the scattering matrix elements can possibly be explained by the presence of an intermediate-structure resonance phenomenon with contributions from many overlapping resonances.

NUCLEAR REACTIONS Phase shift analysis of 15 angular distributions for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha )$, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=30\mathrm{}°-170\mathrm{}°$, $E_{\alpha }=26-47\mathrm{}$ MeV.

The in plane correlations between alpha particles and various ejectiles were investigated in the reaction of 208 MeV ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ on ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ at ${\theta }_{\mathrm{HI}}=+22\mathrm{}°, +50\mathrm{}°, \mathrm{and} +80\mathrm{}°$. There were three sources of coincident alpha particles: (i) the sequential alpha decay of the excited ejectiles, (ii) the equilibrium alpha emission from the targetlike fragments, and (iii) the nonequilibrium process. Process (i) contributed mainly to the cross sections with the angular range of ${\theta }_{\alpha }$ close to ${\theta }_{\mathrm{HI}}$. Process (ii) contributed to the lowest part of the alpha energy spectra irrespectively of ${\theta }_{\mathrm{HI}}$ and ${\theta }_{\alpha }$. The remaining part was ascribed to process (iii). For this process the differential coincidence cross section of the lower energy part of the alpha particles was approximately factorized as $\frac{d^4\sigma }{d{\Omega }_{\mathrm{HI}}d{\Omega }_{\alpha }d{E}_{\mathrm{HI}}d{E}_{\alpha }}=K{\left(\frac{d^2\sigma }{d{\Omega }_{\mathrm{HI}}d{E}_{\mathrm{HI}}}\right)}_{\mathrm{singles}}{\left(\frac{d^2\sigma }{d{\Omega }_{\alpha }d{E}_{\alpha }}\right)}_{\mathrm{singles}}$ with $K\sim 0.4/\mathrm{b}$, whereas the higher energy part of the alpha particles emitted at the forward angles had a tendency to coincide weakly with the ejectiles emitted at the backward angles (${\theta }_{\mathrm{HI}}=+50\mathrm{}° \mathrm{and} +80\mathrm{}°$) as compared to the lower energy part of the alpha particles.

NUCLEAR REACTIONS ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, \mathrm{HI}\alpha )$, $E=208\mathrm{}$ MeV, ${\theta }_{\mathrm{HI}}=22\mathrm{}°, 50°, 80°$; measured two-dimensional H—$\alpha$ coincident energy and angular correlations; deduced reaction mechanisms.

A very simple estimate is made of the baryon rapidity distribution to be expected from central collisions of high energy nuclei. This estimate is based upon straight-line trajectories and some average rapidity loss per nucleon-nucleon collision. It is found that U + U will become transparent at a beam energy of about 500 GeV/nucleon, or 15 + 15 GeV/nucleon for colliding beams.

NUCLEAR REACTIONS Relativistic nuclear collisions, straight-line trajectories, stopping power, baryon rapidity distribution.

From an analysis of the effective potentials and the surface region behavior of quantum mechanical radial wave functions, we find that the most interesting physical phenomena taking place in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering at $E_{\mathrm{lab}}=55\mathrm{}$ MeV is the orbiting mechanism for $l=24, 25, 26$. We find that the orbital amplitude $A_0\left(\theta \right)$ generated by these partial waves acts coherently at large angles with the background amplitude $A_b\left(\theta \right)$ describing the remainder of the full amplitude. The enhanced large angle oscillations are caused by the almost, but not complete, destructive interference between $A_0\left(\theta \right)$ and $A_b\left(\theta \right)$. Using appropriate mathematical techniques, we show that at large angles $\theta \lesssim 180°$, both $A_0\left(\theta \right)$ and $A_b\left(\theta \right)$ are dominated essentially by the same Legendre polynomial. This explains the observation of Takemasa and Tamura that the cross sections generated by exact Regge pole terms behave quite similarly to that generated by the corresponding Regge background terms. Furthermore, our analysis clarifies the underlying reason for the success of the purely parametric Regge pole model at large angles. We also compare the infinite sequence of Regge poles generated by the barrier term in the Wentzel-Kramers-Brillouin formula for the "nuclear" $S$ matrix and the exact quantum mechanical orbiting Regge pole. The oscillatory behavior of the reflection function ${\eta }_l$ of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ system at $E_{\mathrm{lab}}=55\mathrm{}$ MeV as a function of $l$ for $l$ below the orbiting region is also explained.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering at $E_{\mathrm{lab}}=55\mathrm{}$ MeV. Analysis of orbiting phenomena. Regge poles related to orbiting.

Fission product yields for 24 masses were determined for the fission of ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ with essentially monoenergetic neutrons of 0.17, 1.0, 2.0, 3.4, 4.5, 6.1, and 7.9 MeV. Fission product activities were measured by Ge(Li) $\gamma$-ray spectrometry of irradiated ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ targets and by chemical separation of the fission product elements followed by $\beta$ counting. Yields of near symmetric (valley) fission products increase nearly monotonically with incident neutron energy and do not exhibit a break in the slope of the yield versus neutron energy curve in the energy region where second-chance fission begins. This is in contrast to the curves for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ neutron-induced fission.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}(n, f)$, $E_n=0.17, 1.0, 2.0, 3.4, 4.5, 6.1, \mathrm{and} 7.9$ MeV; measured mass yields.

Induced nuclear fission is viewed as a diffusion process of the fission degree of freedom over the fission barrier. We describe this process in terms of a Fokker-Planck equation which contains the fission variable and its canonically conjugate momentum. We solve this equation numerically for several energies (temperatures) of the fissioning nucleus neglecting changes of the fission barrier due to the temperature dependence of nuclear shell effects. We pay particular attention to the time $\tau$ needed for the system to build up the quasistationary probability flow over the fission barrier. The rate of the latter is approximated in terms of the Bohr-Wheeler formula or Kramer's transition state expression; the precise value of the quasistationary current depends on the nuclear friction constant $\beta$. Our results for $\tau$ are consistent with those obtained earlier in the framework of a simplified model: As long as $\beta \le {\beta }_0$, the time $\tau$ is proportional to ${\beta }^{-1\mathrm{}}$. This relationship exhibits the fact that with increasing friction $\beta$, the diffusion process is accelerated, so that it takes the system increasingly less time to attain the quasistationary distribution. The constant ${\beta }_0$ is roughly given by $2{\omega }_1$, where ${\omega }_1$ is the frequency of a harmonic oscillator potential which osculates the potential at the minimum corresponding to the initial configuration of the fissioning nucleus. The condition $\beta \le {\beta }_0$ is roughly equivalent with the motion in that minimum being underdamped. The converse relationship—$\tau$ increases with $\beta$—is found for $\beta >{\beta }_0$. We ascribe this to the fact that now the fission variable executes an overdamped motion. Generalizing Kramers's original derivation, we obtain an analytical expression for the time dependence of the probability current over the fission barrier. For $\beta \lesssim {\beta }_0$, this expression agrees well with our numerical results. We use it to calculate the energy dependence of the fission probability $P_f$ and find that $P_f$ grows much less rapidly with increasing excitation energy than would be predicted by the Bohr-Wheeler formula. This is in qualitative agreement with recent experimental findings and suggests that the energy dependence of $P_f$ deserves further investigation and can be used to determine $\beta$ experimentally. Our analysis does not yet include the additional time delay incurred by the system on its way from the saddle to the scission point: Clearly the time needed to establish the quasistationary situation at the scission point will be larger than $\tau$. This would probably lead to additional modifications of the energy dependence of $P_f$.

NUCLEAR REACTIONS, FISSION Diffusion over a potential barrier; transients; deviation from Bohr-Wheeler formula.

After expansion of the vector and axial vector currents in powers of ($\frac{v}{c}$), a heretofore unremarked regularity results. Meson exchange currents can be classified into types I and II, according to the way they satisfy the constraints of special relativity. The archetypes of these two categories are the impulse approximation to the vector and axial vector currents. After a brief discussion of these constraints, the ($\rho \pi \gamma$) and ($\omega \sigma \gamma$) exchange currents are constructed and classified, and used to illustrate a number of important points which are often overlooked.

NUCLEAR REACTIONS Meson exchange currents, classification scheme.

By solving exact three-and four-body equations, we obtain estimates of the binding energies of light nuclei containing one charmed $C_0^{+}$ baryon.

NUCLEAR STRUCTURE Few-body hypernuclei, charmed analogs of hypernuclei, binding energy estimates.

The conventional description of high energy proton-nucleus collisions in terms of an intranuclear cascade and compound nuclear decay (the two-step model) breaks down at projectile energies $E_p>10\mathrm{}$ GeV. Unusual backward enhancements are found in the angular distribution of heavy fragments (Sc, Cu) from uranium targets. This effect is explained in a fast breakup model of deep spallation/cleavage processes. The observed backward emission originates in the competition between (backward-directed) Coulomb repulsion and (forward-directed) momentum components from recoiling nucleons.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(p, x){}_{}{}^{47}{}_{}{}^{}\mathrm{Sc}$; $T_p=40-400\mathrm{}$ GeV, cleavage model to explain double differential cross section.

A procedure is derived for analyzing ($p, {\pi }^0$) reactions near threshold where pions are present in only $s$- and $p$-wave states. The pions, which decay into two gammas, have an angular distribution in the center of mass which can be correlated to the angular distribution of its decay gammas in the laboratory. Functions are calculated which give the laboratory distribution of both gammas in terms of parameters describing the angular distribution of pions in the center of mass. By fitting these functions to the observed gamma distribution, the pion differential cross section is determined.

NUCLEAR REACTIONS Analysis threshold ($p, {\pi }^0$) reactions.

A calculation of the elastic scattering of mesons from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is performed, using a modification of the first-order multiple scattering theory of Kerman, McManus, and Thaler, in which Pauli blocking effects are omitted from the $\tau$ operator. The modified $\tau$ operator is calculated in a three-body model, in which the struck nucleon is allowed to recoil in a Woods-Saxon nuclear shell model potential exerted by the remainder of the nucleus. The interaction between the meson and the struck nucleon is described by a separable potential. A set of coupled differential equations that describe the elastic and the excited channel wave functions is derived by approximating the shell model binding potential in the excited states of the nucleon as a potential for the meson-nucleon center of mass. This approximation is examined in detail. It is found that in the three-body model the bound states and the single particle resonances of the shell model potential alter the results significantly from those obtained in impulse approximation.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\pi , \pi )$, three-body model of $\pi$-nucleon interaction. ${\sigma }_T\mathrm{}\left(E\right)\mathrm{}$ calculated.

Transformations of nucleon-nucleon amplitudes from the center of mass frame to the proton-nucleus Breit frame are developed for use in multiple scattering analyses. As a by product, a matrix equation is given for the invariant $\mathrm{NN}$ amplitudes in Dirac spinor representation. Based on recent $\mathrm{NN}$ phase shifts, Gaussian parametrization of the $\mathrm{pp}$ and $\mathrm{np}$ amplitudes are calculated and some proton-nucleus calculations are presented to illustrate the effects of the Breit frame amplitudes. For ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, these effects are quite small.

NUCLEAR REACTIONS Nucleon-nucleon amplitudes, impulse approximation, Breit frame, Wigner rotation, Dirac invariant amplitudes, proton-nucleus elastic scattering.

Angular distribution data for 800 MeV ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p^{\prime })$ (2.61 MeV, $3^{-}$) are analyzed to determine the sensitivity of the analysis to the neutron component of the transition density. The analysis employs the first order Kerman, McManus, and Thaler optical potential model (distorted wave Born approximation together with the impulse approximation). The total error in the multipole moment of the deduced transition density, $M_n\mathrm{}\left(E3\mathrm{}\right)\mathrm{}$, is computed based on uncertainties in (1) the elastic and inelastic scattering data, (2) the geometry of the transition density, (3) the nucleon-nucleon amplitudes, (4) the proton transition density, (5) correlation corrections, and (6) medium modifications to the effective interactions. Under the presumption of an accurate theoretical model, the minimal uncertainty in $M_n\mathrm{}\left(E3\mathrm{}\right)\mathrm{}$ is ±8.5%. Such accuracy permits meaningful comparisons with results from nuclear structure theory.

NUCLEAR REACTIONS Microscopic analysis of 800 MeV ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p^{\prime }){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ (2.61 MeV, $3^{-}$) inelastic angular distribution data; KMT formalism; DWBA. Deduced neutron transition density. Multipole moment error analysis and sensitivity study.

Elastic differential cross sections and analyzing powers for 800 MeV $\overrightarrow{p}$+${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ are analyzed to obtain the isotonic proton density difference. The calculations employ a local, spin-dependent, second order Kerman, McManus, and Thaler optical potential model; care is given to isovector, spin-unsaturated subshell, and phenomenological nuclear medium corrections. The results obtained here are compared with those from electron scattering experiments and theoretical expectations. The results of this analysis provide an overall consistency check on corresponding studies which start with known charge densities and determine neutron isotopic density differences.

NUCLEAR REACTIONS 0.8 GeV polarized proton elastic scattering from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, KMT optical potential, correlations, spin-unsaturated subshell corrections, isovector terms, medium effects, isotonic proton density differences, tests of proton-nucleus interactions.

The one-nucleon contribution to threshold pion production in pion-nucleus collisions is calculated using a Fermi gas model of the nuclear excitation spectrum in order to carry out the sum over final nuclear states. For the one-body input a threshold approximant to the production amplitude from the phenomenological Lagrangian theory is used. The cross sections are found to have an ${\eta }^4$ dependence near threshold, where $\eta =\frac{({\omega }_k-2\mathrm{}{m}_{\pi })}{m_{\pi }}$ for total incident pion energy ${\omega }_k$. In a simple eikonal approach incident pion attenuation is found to lead to a reduction of threshold estimates by a factor of ∼ 10.

NUCLEAR REACTIONS ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}({\pi }^{+}, 2{\pi }^{+})$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}({\pi }^{+}, 2{\pi }^{+})$; threshold pion production cross section calculated in the Fermi gas model with phenomenological Lagrangian input.

The scattering of a hadron on a strongly bound system of two hadrons (a dihadron) is considered in the high-energy limit for the relative hadron-dihadron motion. The dihadron scatterer motion and the internal interaction are included in our consideration. It is shown that only small values of the internal transfer momentum of dihadron particles bring the principal contribution to the three-particle propagator in the eikonal approximation. On the basis of the exact analytical solution of the integral equation for the total Green's function the scattering amplitude is derived. It is shown that the scattering amplitude contains only single, double, and triple scattering terms. Three new terms to the Glauber formula for the total cross section are obtained. These terms decrease both the effective hadron-hadron cross section and the screening correction.

NUCLEAR REACTIONS Generalization of eikonal approximation. Application to three-hadron problem.