It is pointed out that within the nested doorway model, the approximate Ericson's formula for the variance of cross section fluctuations is valid independently of the number of doorway classes present. Comparison is presented with the experimental values of the variance for the recently analyzed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ reactions, in which multistep compound processes have been found to be dominant.

NUCLEAR REACTIONS ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p)$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha )$; multistep compound; Ericson fluctuations; extracted and calculated reduced variance.

A perturbative calculation is reported for the mixing of Gamow-Teller strength with two-particle two-hole configurations at high excitation energies. We find that roughly 50% of the Gamow-Teller strength is shifted into the region of 10-45 MeV excitation for the nucleus ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$. This would explain a substantial part of the continuum background seen in the 200 MeV ($p, n$) reaction.

NUCLEAR STRUCTURE ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, Gamow-Teller strength function, $E_{\mathrm{ex}}=10-45\mathrm{}$ MeV, theory.

We clarify some aspects of Bryan's recent paper which introduced a new parametrization for the coupled channel $S$ matrix above the inelastic threshold.

NUCLEAR REACTIONS Scattering theory. Parametrization coupled channels nucleon-nucleon scattering above pion production threshold.

The angular distribution of the two $\alpha$-particle coincidence cross sections, measured at 2 MeV incident energy, is interpreted. Since the momentum transferred to the outgoing $\alpha$ particles is high enough to minimize peripheral effects in a quasifree process, the apparent narrowing of the impulse distribution of the $\alpha -d$ motion in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is attributed to Coulomb effects in the entrance channel.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}+{}_{}{}^6{}_{}{}^{}\mathrm{Li}\to 3\alpha$ at 2 MeV. Discussed angular distribution of two $\alpha$-particle coincidence cross section. Proposed subthreshold mechanism.

The effects of the use of a portion of a three-parameter Fermi set of nuclear shape parameters for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ in a two-parameter Fermi shape are demonstrated.

NUCLEAR REACTIONS Hadron-${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ elastic scattering, calculated $\sigma \left(\theta \right)$, effect of nuclear shape parameters, $p=0.8\mathrm{}$ GeV/c.

Energy and angular correlations between $\alpha$ particles and quasielastic projectilelike fragments produced in the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ reaction at 290 MeV show that the $\alpha$ particles are sequentially emitted from long-living states of primary fragments populated in direct reactions such as inelastic scattering and few-nucleon transfer. An analysis of the energy-integrated angular correlation leaves no notable cross section for a direct breakup or uncorrelated particle emission.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, $E_{\mathrm{Ne}}=290\mathrm{}$ MeV, measured energy and angular correlations of $\alpha$ particles in coincidence with ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Deduced reaction mechanism of quasielastic projectile dissociation.

A model is presented for the low energy spectrum of nucleons produced in small impact parameter heavy ion reactions. Special attention is paid to the effects of the Coulomb force which not only gives rise to an energy shift but also to a sideward focusing. Calculated angular distributions are compared with high multiplicity selected events in the Ne on U reaction at 393 MeV/nucleon.

NUCLEAR REACTIONS $\mathrm{U}(\mathrm{Ne}, x)$ at 400 MeV/nucleon, calculated $\sigma \left(\theta \right)$ for emitted neutrons and protons at energies < 50 MeV.

We argue that $3d$ shifts and widths in heavy ${\pi }^{-}$ atoms are probably not anomalous, contrary to recent experimental and theoretical claims. The observed shifts are small because the ${\pi }^{-}$-nucleus interaction is expected to become repulsive in an atom close to ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. No plausible microscopic explanation has been found for the small widths and it is stressed that the experimental evidence for the anomaly, particularly of the widths, is not strong.

NUCLEAR REACTIONS Strong-interaction shifts and widths in ${\pi }^{-}$ atoms; ${\pi }^{-}$-nucleus optical potential.

Photoneutron cross sections involving the emission of one and two neutrons from ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ have been measured over the excitation energy interval from threshold (10.8 MeV) to 38 MeV using monoenergetic photons from the annihilation in flight of fast positrons. A very broad giant dipole resonance extending from about 16 to 30 MeV was observed, with a maximum ($\gamma , n_{\mathrm{tot}}$) cross section of about 11 mb at 23.5 MeV. The magnitude of the measured average photoneutron energies shows that most of the strength below 15 MeV decays to the ground state of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, whereas most of the strength in the giant resonance decays to excited states. Comparison with particle-capture cross-section data indicates that multiparticle-multihole interference effects probably account for some of the pronounced intermediate structure observed above 16 MeV in the ($\gamma , n$) cross section. Comparison with a recent shell-model calculation favors the use of a Tabakin potential over a $\delta$-function force with a Soper exchange mixture, in marked contrast with recent corresponding results for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$. Features of recently measured photoreaction cross sections for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ nuclei are compared as well.

NUCLEAR REACTIONS ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(\gamma , n)$, $E_{\gamma }=10.8-38.0\mathrm{}$ MeV; measured $4\pi$ neutron yield for monoenergetic photons; ($E_{\gamma }, 1n$), ($E_{\gamma }, 2n$), integrated cross sections; comparisons of results with other reaction channels and with cross sections for neighboring nuclei; comparison with shellmodel theory.

The (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $n$) reaction has been studied on targets of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ at an incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energy of 15 MeV. For both residual nuclei ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, angular distributions were measured for transitions to known states up to about 3 MeV. In addition transitions to a few strongly excited states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ up to the first $T=\frac{3}{2}$ level at 8.38 MeV were observed. The data have been compared with results of distorted-wave Born approximation calculations produced from the relevant components of shell model transfer configurations used in analyzing the results of (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $p$) reaction studies on these same targets.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n)$ $E=15\mathrm{}$ MeV, enriched target. Measured $\sigma (E, \theta )$; DWBA analysis, deduced $L$ transfers, enhancement factors. Model comparison.

Angular distributions for the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(h, d_0){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(h, d_0){}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ reactions have been measured at $E_h=130\mathrm{}$ MeV in the $9°\lesssim {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\lesssim 40°$ angular range. The data have been analyzed in terms of the distorted-wave Born approximation theory. Finite-range and nonlocality effects are found to be significant and are necessary for a good description of the experimental data. The extracted spectroscopic strengths are $G\left(2\mathrm{}{s}_{\frac{1}{2}}\right)=0.89\mathrm{}\pm 0.18$ and $G\left(1\mathrm{}{d}_{\frac{5}{2}}\right)=0.22\mathrm{}\pm 0.04$ for the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(h, d_0){}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(h, d_0){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reactions, respectively. The former value agrees well with that predicted by a shell-model calculation performed in a full $1d_{\frac{5}{2}}-2\mathrm{}{s}_{\frac{1}{2}}-1\mathrm{}{d}_{\frac{3}{2}}$ basis space; the latter, however, is only about 40% of the predicted value.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(h, d_0)$, $E=130\mathrm{}$ MeV; measured $\sigma (E, \theta )$. DWBA analysis, deduced spectroscopic strengths. Enriched targets.

Elastic electron scattering cross sections for the nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured in a momentum transfer range from 0.25 to 2.75 ${\mathrm{fm}}^{-1\mathrm{}}$. The data were analyzed in a model independent way with a Fourier-Bessel parametrization of the charge distribution. For the rms radius, the value ${〈r^2〉}^{\frac{1}{2}}=(2.464\mathrm{}\pm 0.012)$ fm (no dispersion corrections applied) has been obtained, and agrees with those of other electron scattering experiments and with muonic atom experiments, but disagrees with data obtained from measurements of muonic x-ray transitions with a crystal spectrometer which show a larger rms radius. The extracted distribution disagrees with Hartree-Fock calculations in both the radial dependence and the rms radius. The behavior of the form factor in the diffraction minimum was investigated in detail. The experimentally determined cross sections in the minimum are always larger than those obtained from the Fourier-Bessel analysis. These deviations amounted to 5% for a primary energy of 320 MeV and to 2% for 240 MeV and may be interpreted as an indication of dispersion effects.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; absolute ($e, e$) cross sections measured. Charge distribution and rms radius deduced. Discussion of dispersion effects, comparison with HF calculations.

We investigate the physical half-shell $T$ matrix for scattering by a smoothly screened Coulomb potential. In particular, we study the Kowalski-Noyes half-shell extension function $F_{\mathrm{hs}}^l\mathrm{}(p;k)\mathrm{}$ in the limit that the screening radius $a$ tends to infinity. For the Coulomb potential the half-shell scattering cross section is a discontinuous (step) function of the off-shell momentum $p$ at the on-shell point $p=k$. For the screened Coulomb potential (with screening of the Hulthén form, for $l=0\mathrm{}$) we find that the half-shell cross section exhibits almost a step behavior near $p=k$: Its magnitude varies dramatically in an interval, the width of which is of the order of the inverse screening radius $a$. We discuss physical implications of this result.

NUCLEAR REACTIONS Half-shell scattering, Coulomb potential, screening effects, Kowalski-Noyes half-shell extension function.

Nuclear optical model potentials at low energies have been computed utilizing the two (Micro I and Micro II) versions of the microscopic optical model of Jeukenne et al. A comparison has been made of the experimental nucleon-nucleus interaction data for $E<\mathrm{}10\mathrm{}$ MeV with the theoretical predictions obtained using the microscopic optical model.

NUCLEAR REACTIONS Microscopic nucleon optical model potential at low energies; comparison of neutron and proton data with the theoretical predictions.

Using the vector analyzing powers of the ($\overrightarrow{d}, t$) and ($\overrightarrow{d}, p$) reactions the spins of twenty-one states of ${}_{}{}^{99}{}_{}{}^{}\mathrm{Mo}$ have been determined. Below an excitation energy of 1 MeV, these spin assignments agree with those made on the basis of the ratio of $S_{\mathrm{lj}}$ values in ($d, t$) and ($d, p$) reactions leading to the same final states. New assignments have been made for seven states above 1 MeV. The results have been compared with calculations made by Roy and Choudhury for the even parity states. Fair agreement has been obtained.

NUCLEAR STRUCTURE ${}_{}{}^{99}{}_{}{}^{}\mathrm{Mo}$ measured $J$, $\pi$, and spectroscopic factors, for states up to 2.2 MeV using ($\overrightarrow{d}, t$) and ($\overrightarrow{d}, p$) reactions.

Angle-integrated cross-section data in the form of excitation functions from threshold to 2.5 MeV incident (lab) energy, as measured and calculated, are presented for inelastic scattering of fast neutrons on ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, proceeding to higher collective (quadrupole and octupole vibrational) states of these deformed actinide nuclei. The experimental ($n, n^{\prime }$) data were for the most part obtained from corrected $\gamma$-production ($n, n^{\prime }\gamma$) yields. The theoretical data were derived from an incoherent sum of the compound-nuclear and strong-coupling direct-interaction cross sections, computed using the Bruyères set of optical potential and deformation parameters. The relative coupling strength was the sole adjustable parameter. Provision was made for the effect of Moldauer level-width fluctuations and for competing neutron exit channels (but not for radiative capture, charged-particle, or fission competition); the coupled-channels computations permitted up to six levels to be coupled simultaneously. The ensuing "standard" theoretical level excitation functions matched the experimental data fairly closely in most instances, confirming the viability of this conventional method of analysis. However, indications of potentially still better fits were provided by preliminary calculations employing the unified statistical $S$-matrix formalism of Weidenmüller et al. As illustrated for ($n, n^{\prime }$) scattering to the lowest members of the $K=0^{-}$ octupole band in ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, the latter approach reproduces experimental trends closely when the relative coupling strength is optimized. A subsequent paper will present detailed results of the unified analyses and comparisons with evaluated neutron data-file excitation functions for these actinide target nuclei.

NUCLEAR REACTIONS ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(n, n^{\prime })$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n, n^{\prime })$, $E_n=0.8-2.5\mathrm{}$ MeV; measured and calculated $\sigma \left(E_n\right)$. Enriched targets; measured ($n, n^{\prime }\gamma$) $\gamma$ production: deduced $\sigma (n, n^{\prime })$. Calculations with statistical compound nucleus and coupled-channels direct-interaction formalisms. Deduced relative coupling strengths. Preliminary unified statistical $S$-matrix calculations.

From the standpoint of nuclear theory, the consistency of the unified (statistical $S$ matrix) formalism, even in its most basic form as treated in this paper, represents a fundamental improvement over the standard approach involving the incoherent addition of compound-nucleus and direct-interaction contributions to a net angle-integrated cross section. A previous paper dealt with standard analyses of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(n, n^{\prime })$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n, n^{\prime })$ level excitation functions from threshold to $E_n=2.5\mathrm{}$ MeV, and foreshadowed the successful application of the unified formalism in illustrative analyses of ($n, n^{\prime }$) scattering to triads of $K=0^{-}$ octupole vibrational states in each of the above nuclei. For these deformed actinide nuclei, a coupled-channels treatment is appropriate: The unified approach intrinsically entails this as a central feature. This paper describes the results of such unified computations for the ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ scattering cross sections to each of 21 principal collective (quadrupole and octupole vibrational) states in ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ up to $E^{*}=1208.7\mathrm{}$ keV, and to 17 such levels in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ up to $E^{*}=1269.4\mathrm{}$ keV, using the relative coupling strengths as the only adjustable parameter. When compared with the measured data, the unified fits were generally of equivalent or superior quality to those derived from the standard treatment, with the same (Bruyères) optical potential parameters employed throughout. Comparisons with (composite) evaluated neutron data file values revelas discrepancies which indicate an evident need for reevaluation. Corrections to the basic unified data will be considered in a subsequent paper.

NUCLEAR REACTIONS ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(n, n^{\prime })$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n, n^{\prime })$, $E_n=0.8-2.5\mathrm{}$ MeV; measured, calculated, and evaluated $\sigma \left(E_n\right)$. Theoretical $\sigma (n, n^{\prime })$ computed for vibrational states with unified (statistical $S$-matrix) formalism. Compared with experimental, standard theoretical, and composite evaluated level excitation-function data.

Analogs of the ground state and the $2^{+}$ one-phonon state have been populated in ${}_{}{}^{76,80,82}{}_{}{}^{}\mathrm{Se}(p, n)$ by 19, 20, 22, and 25 MeV protons. The two-phonon triplet in ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}(p, n)$, the $4^{+}$ analog state and the $0^{+\prime }$, $2^{+\prime }$ doublet in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Se}(p, n)$, and the $0^{+\prime }$ analog state and the $2^{+\prime }$, $4^{+}$ doublet in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}(p, n)$, have also been observed. The integrated cross sections for the ground and $2^{+}$ one-phonon states display a smooth energy dependence over this bombarding energy region. $\frac{\sigma \left(0^{+}\right)}{\mathrm{}(N-Z)\mathrm{}}$ and $\frac{\sigma \left(2^{+}\right)}{\left[{\beta }^2\mathrm{}\right(N-Z\left)\right]}$ show an upward trend as a function of $A$, which is a downward trend with increasing collectivity. A coupled-channel analysis has been made using primarily a generalized optical potential deduced from the Ohio University global optical potential for neutrons. The $0^{+}$, $2^{+}$, $0^{+\prime }$, $2^{+\prime }$, and $4^{+}$ states and their analogs in Br are coupled in the harmonic-vibrator model but using experimentally determined deformation parameters ($\beta \text{'}\mathrm{s}$). Optical parameters deduced from fitting $\mathrm{Se}(n, n)$ and ($n, n^{\prime }$) data yield excellent fits to the ${}_{}{}^{76,80,82}{}_{}{}^{}\mathrm{Se}(p, n)$ ground state analog transitions. If allowance is made for the fractionation of the two-phonon strength, good agreement is also obtained for the one-phonon $2^{+}(p, n)$ transitions. Evidence for one-phonon mixing in the $2^{+\prime }$ state is seen from the weakness of the $0^{+\prime }$, $2^{+\prime }$ doublet in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Se}(p, n)$ and of the $2^{+\prime }$, $4^{+}$ doublet in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}(p, n)$ as calculated with the harmonic model. Inclusion of a one-phonon component into the $2^{+\prime }$ state through the use of the measured $\beta$ values brings the calculated cross sections into reasonable agreement with experiment.

NUCLEAR REACTIONS ${}_{}{}^{76,80,82}{}_{}{}^{}\mathrm{Se}(p, n)$ $0^{+}$, $2^{+}$, $0^{+\prime }$, $2^{+\prime }$, $4^{+}$; $E=19, 20, 22, 25$ MeV; measured $\sigma \left(\theta \right)$; coupled-channel analysis; harmonic-vibrator model with experimental deformation parameters.

Deuteron inelastic scattering and inelastic breakup calculations are formulated in the framework of a simple three-body description, by using an adiabatic approximation. Application is then made for 80 MeV deuterons, exciting the first $2^{+}$ state in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$. Similarities and differences between the elastic and inelastic breakup processes are discussed. Comparison with the predictions of the folding model is also made.

NUCLEAR REACTIONS Deuteron, elastic scattering, inelastic scattering, elastic breakup, inelastic breakup, three-body model, adiabatic approximation, proton-neutron coincidence, folding model, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$.