We have measured angular distributions of the analyzing powers $A_y$, $A_{\mathrm{xx}}$, $A_{\mathrm{yy}}$, and $A_{\mathrm{xz}}$ for the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\overrightarrow{d}$,$p$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$ reaction at deuteron lab energies $E_d$ of 13.39 and 17.00 MeV. These distributions do not show the symmetry or antisymmetry about 90° (c.m.) expected on the basis of a simple direct-neutron-transfer reaction mechanism. In a companion experiment, we have measured the same four analyzing powers for both the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\overrightarrow{d}$,$p$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$ reaction and its charge-symmetric partner ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\overrightarrow{d}$,$n$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at $E_d=15.50\mathrm{} \mathrm{and} 17.00$ MeV in a restricted angular range. These latter data were obtained by simultaneously detecting the tritons and helions. Only small differences were observed in the respective analyzing powers for the two reactions, which suggests a weakening of the mechanism responsible for the larger differences found by others at lower energies.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\overrightarrow{d}$,$p$), $E=13.39, 17.00$ MeV; measured $A_y\left(\theta \right)$, $A_{\mathrm{xx}}\left(\theta \right)$, $A_{\mathrm{yy}}\left(\theta \right)$, $A_{\mathrm{xz}}\left(\theta \right)$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\overrightarrow{d}$,$p$), ($\overrightarrow{d}$,$n$) simultaneously, $E=15.50, 17.00$ MeV; measured $A_y\left(\theta \right)$, $A_{\mathrm{xx}}\left(\theta \right)$, $A_{\mathrm{yy}}\left(\theta \right)$, $A_{\mathrm{xz}}\left(\theta \right)$.

New measurements of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($d$,$p$) reaction cross sections to the ground-, 0.87-, and 5.09-MeV states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ have been performed for eleven angles from 17.5° to 150° at a bombarding energy of 12 MeV. The results are compared with earlier measurements at the same energy. The new measurements are shown to resolve a discrepancy observed for the comparison of the neutron strength of the unbound 5.09-MeV state extracted from earlier ($d$,$p$) studies with that from neutron scattering experiments. These results indicate that the method of Vincent and Fortune for distorted-wave analysis of stripping to unbound states yields a reliable value for the neutron width for this important test case. Measurements of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($d$,$d$) elastic scattering cross sections performed simultaneously are reported.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($d$,$d$) elastic scattering and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($d$,$p$)${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ (0.0, 0.87, 5.09 MeV), $E=12\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $\theta =17.5\mathrm{}°-150\mathrm{}°$, eleven angles; deduced neutron width from the ($d$,$p$) reaction to 5.09-MeV state.

A generalization of the Feshbach projection operator method to include rearrangement in the context of the Baer, Kouri, Levin, and Tobocman many-body scattering theory has been proposed recently. The formalism provides a simplified set of connected kernel equations for an approximate transition operator matrix and an explicit procedure for relating the approximate transition operators to the exact ones. In this paper we extend the flexibility of the aforementioned generalization by making it possible to allow the approximate transition operators to couple fewer partitions than the exact ones. Particular attention is given to the case where the approximate transition operator matrix is the solution of coupled-reaction-channel-type equations for transitions between few cluster configurations of the system. It is also shown that all the equations derived here have connected kernels after iterations.

NUCLEAR REACTIONS Multipartition generalization of the Feshbach projection operator method applied to BKLT many-body scattering theory. Approximate few-cluster-model scattering equations developed.

The elastic scattering cross section for neutrons on oxygen is calculated beginning with a realistic nucleon-nucleon interaction. A soft interaction is employed so that a perturbation expansion is tractable. The results reinforce the conclusions derived from a previous calculation of the $s$-wave scattering phase shift. Namely, it is shown that ab initio calculations such as these can be carried out and that one may thereby gain an understanding of complex reactions between nuclei on a microscopic level.

NUCLEAR REACTIONS Microscopic calculation of elastic cross section for $n$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering.

The lifetime limits ${\tau }_m<34, <12, <11, <8, \mathrm{and} <23\mathrm{}$ fs for the negative parity states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$, at 2000, 4319, 4804, 6478, and 8425 keV, respectively, were determined with the Doppler shift attenuation method through the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($p$,$\gamma$)${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reaction. The analog of the ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ 6478 keV state lies at 6743 keV in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ and was measured to have a lifetime ${\tau }_m=15\mathrm{}\pm 6$ fs using the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$($\alpha$,$\gamma$)${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ reaction. Experimentally obtained correction factors for the nuclear and electronic stopping powers were used in the Doppler shift attenuation analysis. In the calculations the Monte-Carlo method was employed. A new $\gamma$-ray decay scheme obtained for the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($p$,$\gamma$)${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reaction at $E_p=1110\mathrm{}$ keV together with the angular distribution data illustrate that the properties of the resonant state reported to exist at $E_x=9.73\mathrm{}$ MeV in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ are strongly influenced by background processes and that the resonance structure is ambiguous. In the light of the new lifetime values, the transition strengths are discussed in terms of shell model calculations.

NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($p$,$\gamma$), $E=1.11\mathrm{}$ MeV; ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$($\alpha$,$\gamma$), $E=0.96\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }\left(\theta \right)$, Doppler-shift attenuation. ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ levels deduced $\gamma$-ray branching ratios, ${\tau }_m$. ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ level deduced ${\tau }_m$. Ge (Li) detector, enriched targets.

The ${}_{}{}^{194,196,198}{}_{}{}^{}\mathrm{Pt}$($p$,$t$) reactions have been studied at a proton energy of 35 MeV using nuclear emulsion plates and a high-resolution position-sensitive proportional counter. Fifty states were observed in ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ and ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$ and sixty-four in ${}_{}{}^{192}{}_{}{}^{}\mathrm{Pt}$, many for the first time. Angular distributions were measured for many of these levels from 7° to 60° and the results were compared with zero-range distored wave Born approximation calculations. Several new $J^{\pi }$ assignments were made using distorted wave Born approximation and empirical shapes of transitions to well-known levels in Pt and Pb. No new levels, in particular, no new $0^{+}$ levels, were seen below 1.5 MeV excitation. A new $0^{+}$ level at 1.628 MeV was found in ${}_{}{}^{192}{}_{}{}^{}\mathrm{Pt}$, and new levels tentatively assigned to be $4^{+}$ were seen in all three final nuclei near 1.9 MeV with 15% of the ground state strength at 7° in the ${}_{}{}^{196,198}{}_{}{}^{}\mathrm{Pt}$($p$,$t$) reactions. Enhancement factors were calcualted for simple two-neutron pickup configurations. A comparison is made between experimental ($p$,$t$) strengths and those calculated in the O(6) limit of the interacting boson approximation model for $L=0, 2$ transitions.

NUCLEAR REACTIONS ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$($p$,$t$), ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$($p$,$t$), and ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$($p$,$t$), $E_p=35\mathrm{}$ MeV; measured $\sigma (E_t,\theta )$; deduced energies, $J^{\pi }$, and strengths; DWBA calculations, comparison with experiment; enhancement factors. Enriched targets, 7 keV resolution (plates); interacting boson approximation model.

Primary and secondary $\gamma$ rays in ${}_{}{}^{237}{}_{}{}^{}\mathrm{U}$ from resonant neutron capture in ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ have been measured with the fast chopper facility, the neutron monochromator, and 2- and 24-keV neutron beam filters. A level scheme was constructed including 27 levels with spin and parity assignments. Rotational band members of the Nilsson configurations [631↓], [622↑], [624↓], [631↑], [633↓], and [501↓] and of the vibrational bands {[622↑] - $2^{+}$} and {[631↓] + $0^{+}$} were identified. There are more levels below 800 keV, in particular, $K=\frac{1}{2^{-}}$ bands, than expected from comparison with ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$. The neutron binding energy in ${}_{}{}^{237}{}_{}{}^{}\mathrm{U}$ was determined to be 5125.9±0.5 keV.

NUCLEAR REACTIONS ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$($n$,$\gamma$), $E_n=5-125\mathrm{}$ eV, 2 keV, 24 keV measured $E_{\gamma }$, $I_{\gamma }$, deduced ${}_{}{}^{237}{}_{}{}^{}\mathrm{U}$ levels, transitions, $J$, $\pi$, photon strengths, Ge(Li) detector, three crystal spectrometer, enriched targets, nuclear structure, Nilsson model, vibrational excitations.

The properties of high-spin states in ${}_{}{}^{212}{}_{}{}^{}\mathrm{At}$, including three isomers, have been studied with the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,$3n$)${}_{}{}^{212}{}_{}{}^{}\mathrm{At}$ reaction. In-beam measurements with Ge(Li) and intrinsic Ge detectors of $\gamma$-ray excitation functions, $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions, pulsed-beam-$\gamma$ timing, and perturbed angular distributions with an applied magnetic field were made to establish a decay scheme, level energies, $\gamma$-ray multipolarities, spin-parity assignments, isomeric lifetimes, and $g$ factors. High-spin states up to $15\hslash$ were identified as predominantly three proton [${\left(\pi h_{\frac{9}{2}}\right)}^3$ or ${\left(\pi h_{\frac{9}{2}}\right)}^2$ ($\pi i_{\frac{13}{2}}$)] states of the ($N=126\mathrm{}$) ${}_{}{}^{211}{}_{}{}^{}\mathrm{At}$ nucleus coupled to a neutron in either the $g_{\frac{9}{2}}$, $i_{\frac{11}{2}}$, or $j_{\frac{15}{2}}$ orbitals. The experimental energy levels, $g$ factors, and $B\left(M2\mathrm{}\right)\mathrm{}$ value are compared with shell model calculations.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,$3n$)${}_{}{}^{212}{}_{}{}^{}\mathrm{At}$ $E=32-44\mathrm{}$ MeV; measured $\gamma$ excitations, $\gamma -\gamma$ coin, $\gamma -W\left(\theta \right)$, pulsed-beam-$\gamma$ timing, perturbed angular distributions; deduced levels, $\gamma$ multipolarities, $J^{\pi }$, $T_{\frac{1}{2}}$, $B\left(E1\mathrm{}\right)\mathrm{}$, $B\left(M2\mathrm{}\right)\mathrm{}$, $g$.

Fusion and elastic scattering cross sections were measured for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ bombardments of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ from 44 to 70 MeV. The evaporation residues from the compound nucleus decay were detected by a gas counter telescope. The fusion data were compared to results for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ within the framework of the proximity, the Siwek-Wilczynska and Wilczynski, and the folding model potentials. Although the ratio $\frac{{\sigma }_{\mathrm{fus}}}{{\sigma }_R}$ is appreciably lower for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ than for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, consistent results were obtained for ${\sigma }_{\mathrm{fus}}$ within the experimental uncertainties.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $E=44.1\mathrm{} \mathrm{to} 70.4$ MeV; Measured evaporation residue $\sigma (E,\theta )$. Deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$ total fusion excitation functions. Measured elastic scattering $\sigma \left(\theta \right)$. Natural target. Deduced ion-ion potentials.

Levels in ${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$ ($N=85\mathrm{}$) have been studied using the (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$3n$) reaction. Prompt and delayed $\gamma -\gamma$ coincidences, excitation functions, and angular distributions were used to study the in-beam $\gamma$ rays. Three $\Delta I=2\mathrm{}$ bands are observed: one built on the $\frac{7}{2^{-}}$ ground state with transitions of 775 and 736 keV extending up to the $\frac{15}{2^{-}}$ state, another on a $\frac{9}{2^{-}}$ state at 527.1 keV extending to the $\frac{21}{2^{-}}$ level, and a third on a $\frac{13}{2^{+}}$ state at 968.3 keV extending to the $\frac{25}{2^{+}}$ level. The energy spacings in the $h_{\frac{9}{2}}$ and $f_{\frac{7}{2}}$ bands resemble those in the core nucleus ${}_{}{}^{150}{}_{}{}^{}\mathrm{Dy}$. The two lowest transitions in the $i_{\frac{13}{2}}$ band also resemble those in the ${}_{}{}^{150}{}_{}{}^{}\mathrm{Dy}$ core while the $\frac{25}{2^{+}}\to \frac{21}{2^{+}}$ transition has an energy close to that of the $6^{+}$→$4^{+}$ transition in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Dy}$.

NUCLEAR REACTIONS ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}$ (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$3n\gamma$) $E=60, 62$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin, $\gamma \left(\theta \right)$, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$ deduced levels, $J$, $\pi$. Enriched target. Ge(Li) detectors.

The mechanisms of strongly damped collisions of 237 MeV ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ with ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ have been studied by measurements of the energy distributions and angular distributions of the identified products. Average gamma-ray multiplicities $〈M_{\gamma }〉$ and average gamma-ray energies $〈E_{\gamma }〉$ have been measured for these reactions. Empirical relationships between $〈M_{\gamma }〉$ and the average angular momenta were employed to determine the angular momenta of the primary fragments produced in the reactions. The angular momentum transfer in the strongly damped collisions increases with increasing angle of emission of the projectile-like fragment. Evidence is presented that for the lowest partial waves contributing to strongly damped collisions the condition of rigid rotation is achieved. The use of such reactions to select nuclei of particular $〈J〉$ is discussed.

NUCLEAR REACTIONS ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$,$X$), $E=237\mathrm{}$ MeV, deep inelastic collisions; Measured angular distributions, energy spectra and average gamma-ray multiplicities, deduced primary fragment angular momenta.

We develop a unified nuclear potential for the description of large-scale nuclear collective motion and find that it satisfactorily reproduces experimental data for heavy-ion elastic scattering, fusion, fission, and ground-state masses. Obtained by generalizing the modified liquid-drop model so that two semi-infinite slabs of constant-density nuclear matter have minimum energy at zero separation, this potential is given in terms of a double volume integral of a Yukawa-plus-exponential folding function. For heavy nuclear systems the resulting heavy-ion interaction potential is similar to the proximity potential of Swiatecki and co-workers. However, for light nuclear systems our potential lies slightly below the proximity potential at all nuclear separations. For heavy nuclei fission barriers calculated with our Yukawa-plus-exponential model are similar to those calculated with the liquid-drop model. However, for light nuclei the finite range of the nuclear force and the diffuse nuclear surface lower the fission barriers relative to those calculated with the liquid-drop model. Use of a Wigner term proportional to $\frac{\mathrm{}|N-Z|\mathrm{}}{A}$ in the nuclear mass formula resolves the major part of the anomaly between nuclear radii derived from elastic electron scattering on the one hand and from ground-state masses and fission-barrier heights on the other.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; calculated heavy-ion interaction potential. ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, $E=37.7, 81.0, 215.2$ MeV; calculated elastic-scattering angular distribution. ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$+${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$+${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; calculated compound-nucleus cross section. Calculated fission-barrier heights and ground-state masses for nuclei throughout Periodic Table. Nuclear potential energy of deformation, liquid-drop model, droplet model, modified liquid-drop model, Yukawa-plus-exponential model, proximity potential, Woods-Saxon potential, double-folding potential, optical model, ingoing-wave boundary condition, single-particle corrections, Strutinsky's method.

The cross sections of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$($\gamma$,$d_0$)${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($d$,${\gamma }_0$)${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ have been measured. A resonance was observed at $E_x\simeq 21.9$ MeV in the ($\gamma$,$d_0$) channel. Vector polarized deuterons were used to measure the angular distribution of gamma rays at this resonance and the results were analyzed assuming the two $S=\frac{1}{2}$ $E1\mathrm{}$ transition matrix elements are dominant.

NUCLEAR REACTIONS ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$($\gamma$,$d_0$)${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($d$,${\gamma }_0$)${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$; measured $\sigma \left(\theta \right)$, $A\left(\theta \right)$ and $\sigma \left(\mathrm{tot}\right)$. Deduced $E1\mathrm{}$ $T$-matrix elements and phases at $E_x\approx 21.9$ MeV.

The amount of isospin mixing in the region of the giant dipole resonance was determined by a comparison of $\alpha$-capture reaction cross sections in self-conjugate and nonconjugate nuclei. For the two nuclei ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ Coulomb matrix elements $〈V_c〉=11\mathrm{} \mathrm{and} 4$ keV at mean excitation energies of 17.6 and 15.7 MeV, respectively, were found.

NUCLEAR REACTIONS ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}$($\alpha$,${\gamma }_0$),${}_{}{}^{28,30}{}_{}{}^{}\mathrm{Si}$($\alpha$,${\gamma }_0$), $4<~E_{\alpha }<~16$ MeV; deduced Coulomb matrix elements.

An $s$-wave two-body separable potential may give rise to several phenomena which are absent for nonsingular local potentials. We examine the physical implications of a well known example of such phenomena, the continuum bound state, as well as of two lesser known anomalies, the so-called positive energy spurious state and negative energy bound states with improper long-range behavior. By examining these anomalies in light of Levinson's theorem, Wigner's phase shift inequality, and the effect of a perturbation on the anomalous states by their insertion in a three-body scattering situation, we find in agreement with previous studies that the continuum bound state acts as a resonance of negligible width. However, we find it difficult to see how the presence of a spurious state can be detected experimentally.

NUCLEAR REACTIONS Scattering by a nonlocal potential, continuum bound states, spurious states, wave functions with improper long-range behavior. Levinson's theorem. Three-particle scattering.

The strength function constructed as the Lorentz-weighted average of the reduced widths of the Wigner-Eisenbud $R$ matrix (or of a reactance $K$ matrix) is a continuous and well-defined function of energy for a fragmented doorway state (isobaric analog resonance, fission isomer, etc.) in both weak and strong coupling. If the half-width $I$ of the Lorentz weighting function is chosen appropriately, this strength function itself approximates a Lorentzian whose width is the spreading width ${\Gamma }_I^{\downarrow }$ of Feshbach, Kerman, and Lemmer. An ensemble of 400 doorway systems characterized by coupling strengths ranging from strong to weak is used to study properties of ${\Gamma }_I^{\downarrow }$ and to determine the accuracy with which it can be determined for a particular doorway by a least-squares fit to the strength function. The results of this numerical study show that (1) ${\Gamma }_I^{\downarrow }$ is a characteristic of each doorway state system, and that (2) its value can be determined from experimentally measured resonance energies and widths with an uncertainty which is less than the fluctuations in its value from one system to another and which decreases as the coupling strength decreases.

NUCLEAR REACTIONS spreading of doorway states, fine structure, isobaric analog states.

A common approximation in atomic, molecular, and nuclear rearrangement processes is to neglect $n$-body breakup contributions ($n\ge 3$) by replacing the full wave function by (sums of) product wave functions, each of which is related to a specific asymptotic arrangement channel. We test this bound-state approximation in a simple three-body model of nuclear stripping by comparing bound-state approximation calculations with exact and distorted-wave Born-approximation-type calculations. Calculated are the stripping and elastic amplitudes and cross sections for deuteron energies $E_d=1.78, 6.7, 11.2, \mathrm{and} 15.12$ MeV. The bound-state approximation is best below the breakup threshold ($E_{\mathrm{BU}}=2.225\mathrm{}$ MeV), where it provides an excellent fit in the forward direction and a qualitative fit over the whole angular range. For $E_d=6.7\mathrm{}$ MeV the breakup cross section is still very small; however, the intermediate continuum states already play an important role and the bound-state approximation becomes quite poor. At this energy the distorted-wave Born approximation-type calculation, which is based on exact elastic wave functions and therefore accounts partly for the continuum, is still quite good. For the two higher energies both continuum and multistep effects appear to be very important, rendering both distorted-wave Born approximation and bound-state approximation poor approximations outside the forward region. The qualitative features of the elastic cross sections are explained in terms of the momentum dependence of the bound-state wave functions and two-body $T$ matrices.

NUCLEAR REACTIONS Quality of DWBA and bound-state approximations; Three-body methods; Model ($d$,$p$) calculations at $E_d=1.7-15\mathrm{}$ MeV; Multistep effects

It is shown that the ratio of the cross sections of quasifree ($p$,$2p$) and ($p$,$\mathrm{pn}$) reactions in complex nuclei for identical and suitable geometries can be reliably calculated in the distorted wave impulse approximation. A comparison with preliminary experimental results supports the validity of the impulse approximation for the medium energy scattering of nucleons.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,$2p$), ($p$,$\mathrm{pn}$), $E=400\mathrm{}$ MeV, checked DWIA.

Legendre polynomial coefficients are derived and compared with the results of other authors for the angular distributions encountered in gamma reactions initiated by the capture of vector or tensor polarized or unpolarized particles of arbitrary spin. Attention is given to phase conventions and the consequences of using different angular momentum coupling schemes. Results are given for both the channel spin and the total-$j$ representations. Correction factors for use with other author's results are included. Some potentially useful sum rules are deduced and illustrated.

NUCLEAR REACTIONS Rederived expressions for $\gamma$ ray angular distributions resulting from capture of vector or tensor polarized and unpolarized particles of arbitrary spin. Compared with previously published results.

Ground-state $\alpha$-spectroscopic factors for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been determined via the ($d$,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) reaction at $E_d=80\mathrm{}$ MeV. The results are compared with theoretical shell-model predictions. Relative spectroscopic factors for the excited $2^{+}$ and $4^{+}$ states in ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ are also presented.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$($d$,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$)${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$, ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$($d$,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$)${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, $E_d=80\mathrm{}$ MeV, measured $\sigma (E_{{}_{}{}^6{}_{}{}^{}\mathrm{Li}},\ominus )$, finite-range DWBA calculations.