Differential cross sections for neutron scattering from the ${}_{}{}^{182,183,184,186}{}_{}{}^{}\mathrm{W}$ isotopes have been measured at an incident energy of 3.4 MeV. Angular distributions have been obtained for elastic scattering and inelastic scattering to the first and second excited levels of the four isotopes. Nuclear deformations have been extracted for these nuclei from a coherent analysis which combines the data presented here with low energy neutron scattering properties and total cross sections over a wide energy range. The coupled-channel and compound nucleus formalisms were used in this analysis. Volume integrals and root mean square radii of the obtained neutron optical model potential are presented and compared to the theoretical predictions of Jeukenne, Lejeune, and Mahaux. In addition, the quadrupole and hexadecapole moments of our potential are compared to the potential moments deduced from deuteron and alpha-particle scattering measurements and to experimental charge distribution moments. Finally, matter rms radii have been estimated for the four isotopes and are compared with new Hartree-Fock-Bogolyubov calculations involving Gogny's D1 effective force.

NUCLEAR REACTIONS ${}_{}{}^{182,183,184,186}{}_{}{}^{}\mathrm{W}\mathrm{}(n,n)\mathrm{}$, ($n,n^{\prime }$), $E_n=3.40\mathrm{}$ MeV; measured $\sigma (E_n,\theta )$, $\theta =20\mathrm{}-160°$. Coupled-channel and statistical model calculations. Deduced optical potential parameters, deformation parameters, potential moments, volume integrals, and rms radii. Estimated rms matter radii.

An effective Coulomb correction term arising from the second order Dirac equation is calculated for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. The optical potential used consists of a mixture of a Lorentz scalar potential and the timelike component of a Lorentz four-vector potential. These calculations show that the real Coulomb correction term resulting naturally from the Dirac equation is in agreement with empirics.

NUCLEAR REACTIONS Relativistic optical potential, mean field theory of nuclear matter; Coulomb correction for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

The level structure of ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ has been studied using the ${}_{}{}^{173}{}_{}{}^{}\mathrm{Yb}(n,\gamma )$ reaction with both thermal and 2-keV neutrons. Measurements of $\gamma$-ray energies and intensities were made using Ge(Li) detectors. From these data a neutron separation energy of 7464.8±0.5 keV has been determined for ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$. A level scheme is proposed for ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ which contains 47 excited states, with identified de-excitation modes, below 2.35 MeV. Features of the proposed level scheme include: the $K^{\pi }=2^{-},0^{-}, \mathrm{and} 3^{-}$ octupole-vibrational bands with band-head energies of 1318, 1710, and 1851 keV, respectively; the $\gamma$-vibrational band at 1634 keV; three excited $K^{\pi }=0^{+}$ bands with band-head energies of 1487, 1885, and 2100 keV; and, several two-quasiparticle bands with band-head energies in keV (and $K^{\pi }$ assignments) of 1660($3^{+}$), 1624($1^{+}$), 2016($3^{+}$), and 2049($3^{-}$). Configuration assignments for these two-quasiparticle bands are discussed. The available data for the $K^{\pi }=3^{+}$ band at 1606 keV are not inconsistent with the assumption that it has collective character; and it is suggested that it, together with the lowest-lying $3^{+}$ band in ${}_{}{}^{172}{}_{}{}^{}\mathrm{Yb}$ (at 1172 keV), might represent, in the framework of the interacting boson approximation model, examples of $g$-boson excitations.

NUCLEAR REACTIONS ${}_{}{}^{173}{}_{}{}^{}\mathrm{Yb}(n,\gamma )$, $E=\mathrm{thermal}$, 2 keV; measured $E_{\gamma }$, $I_{\gamma }$; ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ deduced levels, $J$, $\pi$. Enriched targets, Ge(Li) detectors.

An antisymmetrized second-order microscopic calculation of the imaginary optical potential for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\mathrm{}(n,n)\mathrm{}$ is made using random-phase approximation transition densities to the intermediate excited states. An optical Green's function is used for the intermediate projectile propagator. Both inelastic and ($n,p$) charge exchange intermediate states of the nucleus are included and a finite range effective projectile-target nucleon interaction is used. The local approximation to the calculated imaginary optical potential is surface peaked but at a smaller radius than most of the phenomenological potentials, and the depth is somewhat smaller. Collectivity and intermediate charge-exchange states are shown to play an important role.

NUCLEAR REACTIONS ($n,n$) scattering, calculation of optical potential; $E=30\mathrm{}$ MeV.

Recent work by Noble and collaborators has pointed out that wave function orthogonality in bound-state to continuum-state transitions can produce large cancellations in transition amplitudes. In single-channel examples, nonorthogonal wave functions (such as plane waves) were shown to greatly overestimate the exact results even at high energies. In this paper we examine a simple coupled-channel model which can be exactly solved for the many-channel scattering and bound wave functions. In such a model, the exact transition amplitude can be compared with standard plane-wave and distorted-wave approximations. Dispersive corrections are shown to be large and to persist even at high energies.

NUCLEAR REACTIONS Orthogonality constraints on bound-continuum transitions in coupled-channel systems. Dispersive corrections to DWIA.

The level structure of the $N=80\mathrm{}$ nucleus ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ has been studied by the ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}(p,2n\gamma ){}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ reaction using a 30-MeV $p$ beam. We have assigned $37\gamma$ rays deexciting 30 states in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$, placed on the basis of excitation functions and $\gamma -\gamma$ coincidence information. Angular distributions were taken at 90°, 100°, 110°, 125°, 140°, and 155° with respect to the beam direction, yielding the $A_2$ and $A_4$ coefficients. The in-beam experiments tended to excite higher-spin states than those known from existing $\beta$-decay data. Taking the various data together, we could make definite $J^{\pi }$ assignments for most of the states in ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$. Calculations were performed to explain the resulting level structure in terms of a triaxial weak-coupling model for both prolate and oblate deformations. These calculations indicate that ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ has a slight oblate deformation.

NUCLEAR REACTIONS ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}(p,2n\gamma ){}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$, $E_p=30\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coinc, $\sigma (E_{\gamma },\theta )$; deduced ${}_{}{}^{143}{}_{}{}^{}\mathrm{Eu}$ levels $J$, $\pi$; enriched targets, Ge(Li) detectors; triaxial weak-coupling shell-model calculations.

The Boltzmann master equation approach of Harp, Miller, and Berne has been modified to treat the coalescence and equilibration sequence which might be expected in heavy-ion reactions. Assumptions made to accomplish these ends are discussed. Results are presented for sample reactions ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}({}_{}{}^{40}{}_{}{}^{}\mathrm{Ar},X)$ at 240 and 320 MeV projectile energy, and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},X)$ at 214 and 320 MeV. For the latter case, theoretical proton spectra (angle integrated) are compared with experimental yields measured by Symons et al. Very good agreement was found for the shapes of the calculated and experimental precompound spectra. Types of experimental data necessary to rigorously test this model approach are discussed.

NUCLEAR REACTIONS Precompound model for heavy-ion reactions, Boltzmann master equation approach for coalescence plus equilibration phases. Predict $\frac{d\sigma }{d\epsilon }$ for $n$ and $p$ emission for ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},X)$ and ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}({}_{}{}^{40}{}_{}{}^{}\mathrm{Ar},X)$ reactions each at two bombarding energies.

Low- and high-spin states of ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ge}$ are investigated through in-beam $\gamma$-ray spectroscopy via the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},2p)$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}({}_{}{}^7{}_{}{}^{}\mathrm{Li},2n)$, and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}({}_{}{}^{19}{}_{}{}^{}\mathrm{F},p2n)$ reactions. A surprising richness of collective bands is observed in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ge}$ including three even parity bands built on $8^{+}$ levels, the lower two of which are assigned as rotational aligned bands built on both proton and neutron ${\left(g_{\frac{9}{2}}\right)}^2$ configurations, and three odd parity bands built on $\pi$ and $\nu$ configurations that include the $g_{\frac{9}{2}}$ orbit. Details of the multiple bands and other levels observed in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ge}$ are presented. Rotation-aligned model calculations and interacting boson model calculations for ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ge}$ are also described.

NUCLEAR REACTIONS ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},2p)$, $E=39\mathrm{}$ MeV; ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}({}_{}{}^7{}_{}{}^{}\mathrm{Li},2n)$, $E=18\mathrm{}$ MeV; ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}({}_{}{}^{19}{}_{}{}^{}\mathrm{F},p2n)$, $E=50\mathrm{}$ MeV. Measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \left(\theta \right)$, $\gamma -\gamma \left(\theta \right)$, $P$, Doppler line shapes. ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ge}$ levels, $J$, $\pi$, $\delta$, $T_{\frac{1}{2}}$ deduced. IBA calculations, RAL calculations.

The measurement and analysis of the differential cross sections for the elastic and inelastic scattering to the lowest $2^{+}$ states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ using ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ beams in conjunction with ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ targets are reported. The incident beam energies were 145 MeV for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and 162 MeV for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The measured cross sections were analyzed using coupled channels calculations assuming a rotational model description for the low-lying collective states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The coupled channels calculations are compared with polarization potential calculations in which the experimental $B\left(E2\mathrm{}\right)\mathrm{}$ values are used in both cases. The extracted deformation lengths and deformation parameters are compared to those obtained using similar data with light projectiles, although because of strong Coulomb excitation the present calculations are fairly insensitive to the nuclear deformation parameters.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}_{}^{*}{}_{}{}^{}$) $Q=-1.37\mathrm{}$ MeV, $E=145\mathrm{}$ MeV; ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}_{}^{*}{}_{}{}^{}$) $Q=-1.78\mathrm{}$ MeV, $E=162\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, ${\theta }_{\mathrm{lab}}=20\mathrm{}-120°$; optical model calculations including polarization potential, coupled channels calculations, extracted deformation parameters.

Angular distributions have been measured for inelastic scattering of ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at $E_{\mathrm{lab}}=51.5\mathrm{}$ MeV leading to the first ${1/2}^{-}$ state in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ and the first $2^{+}$, $3^{-}$, and $5^{-}$ states in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Distorted-wave Born approximation calculations reproduce the data quite well and are of quality equal to that of coupled channels calculations. Along with the conventional, deformed Woods-Saxon potential, the analysis employed the double-folding model to fit the inelastic data. The nuclear deformation lengths of the double-folding model agree well with the experimental $B\left(\mathrm{EL}\right)\mathrm{}$ values.

NUCLEAR REACTIONS $E=51.5\mathrm{}$ MeV, inelastic (${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${\mathrm{½}}^{-}$, 2.12 MeV; ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $2^{+}$, 3.90 MeV, $3^{-}$, 3.74 MeV, and $5^{-}$, 4.49 MeV). Measured $\sigma \left(\theta \right)$, deduced nuclear deformation lengths. DWBA, CC, double-folding model analysis.

We have used the particle-gamma coincidence method, Coulomb excitation with 12 MeV $\alpha$ particles and 48 MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ion beams, and a thick enriched target to experimentally determine the intrinsic nuclear shapes of the even-even erbium isotopes ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$. The evaluation was carried out using a computer code based on the semiclassical Winther-de Boer code. The intrinsic nuclear shapes of ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$ are found to be prolate, which disagrees with a recent microscopic calculation using the Reid soft-core nucleon-nucleon potential.

NUCLEAR REACTIONS ${}_{}{}^{162,164}{}_{}{}^{}\mathrm{Er}(\alpha ,{\alpha }^{\prime },\gamma )$, $E=12\mathrm{}$ MeV, ${}_{}{}^{162,164}{}_{}{}^{}\mathrm{Er}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},{}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{\prime }{}_{}{}^{},\gamma )$ $E=48\mathrm{}$ MeV; measured particle-$\gamma$ coincidence $\sigma$, deduced intrinsic ground state shapes. Enriched metal target. Ge(Li) detector. Coupled channel semiclassical analysis.

The static quadrupole moments of the first $2^{+}$ excited states of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$ were measured utilizing the reorientation effect in Coulomb excitation. Results for $B(E2;0^{+}\to 2^{+})$ and $Q\left(2^{+}\right)$ values were obtained by combining, for each Fe isotope, light heavy ion (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ or ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) and heavier heavy ion (${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ or ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$) Coulomb excitation results. Scattered ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ or ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions or recoiling Fe ions were detected in a quadrupole-dipole-dipole-dipole spectrometer. The results for the $B(E2;0^{+}\to 2^{+})$, $Q\left(2^{+}\right)$ pairs (in ${\mathit{e}}^2$${\mathrm{fm}}^4$ and e${\mathrm{fm}}^2$) are as follows: ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, 676±38, -5±14; ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, 1022±55, -19±8; and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$, 1234±36, -27.3±5.0.

NUCLEAR REACTIONS ${}_{}{}^{56,58}{}_{}{}^{}\mathrm{Fe}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E=22\mathrm{}$ MeV; ${}_{}{}^{56,58}{}_{}{}^{}\mathrm{Fe}$(${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{56,58}{}_{}{}^{}\mathrm{Fe}$)${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, $E=110\mathrm{}-120$ MeV; ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, $E=28\mathrm{}$ MeV; ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$)${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, $E=86\mathrm{}$ MeV; measured relative cross section, deduced $Q\left(2^{+}\right)$ and $B(E2;0^{+}\to 2^{+})$. Enriched targets.

The thick target, thick catcher technique has been applied to determine the average kinematic properties of a number of target-fragmentation products formed in the reaction of 8.0 GeV (400 MeV/A) ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ with ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$. The forward momentum transferred to the target as a function of product mass is larger than that for the reaction of 25 GeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ or relativistic protons with heavy targets, suggesting that limiting fragmentation has not been achieved in the interaction of 8 GeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ projectiles with a ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ target.

NUCLEAR REACTIONS ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, spallation), $E=8.0\mathrm{}$ GeV; measured target residue recoil properties; relativistic heavy ion reactions; thick target, thick catcher technique; Ge(Li) spectroscopy.

Zero-degree excitation functions of evaporation residues formed primarily by neutron boiloff from the ${}_{}{}^{206}{}_{}{}^{}\mathrm{Rn}$ compound nucleus in the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$+${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$ fusion reaction were measured from 148.5 to 186 MeV beam energy. The evaporation residues were identified by their alpha-decay energies. Cross sections associated with $2n$, $3n$, $4n$, $3n1p$, $5n$, and $4n1p$ emission peak at 155, 157, 165, 168, 177, and 182 MeV, respectively. $3n1\alpha$ emission was also observed and shows hints of forward-backward asymmetry. A maximum total evaporation residue cross section of 1.6 ± 0.5 mb was observed at 165 MeV. A comparison of these results to statistical evaporation theory predictions was made, showing fair agreement, except for the $2n$ cross section which was considerably larger than predicted.

NUCLEAR REACTIONS Complete fusion, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$+ ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$, $E=147\mathrm{} \mathrm{to} 185$ MeV lab, excitation functions for evaporation residues.

The properties of high-spin states in ${}_{}{}^{207}{}_{}{}^{}\mathrm{At}$ have been studied with the ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}({}_{}{}^6{}_{}{}^{}\mathrm{Li},3n){}_{}{}^{207}{}_{}{}^{}\mathrm{At}$ reaction. In-beam measurements with Ge(Li) and intrinsic Ge detectors of $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions, pulsed-beam $\gamma$ timing, and perturbed angular distributions with an applied magnetic field were made to determine a decay scheme, level energies, $\gamma$-ray multipolarities, spin-parity assignments, an isomeric lifetime, and a $g$ factor. High-spin states up to $\frac{25}{2\hslash }$ were identified as either proton excitations of the ($N=126\mathrm{}$) ${}_{}{}^{207}{}_{}{}^{}\mathrm{At}$ nucleus coupled to the ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$ $Z=82\mathrm{}$ ground state or neutron excitations of ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$ coupled to the ${\left(\pi h_{\frac{9}{2}}\right)}^3{\frac{9}{2}}^{-}$ ground state of ${}_{}{}^{211}{}_{}{}^{}\mathrm{At}$. Lifetime and $g$-factor measurements of the ${25/2}^{+}$ 2117-keV isomer, which yielded values of $\tau =156\mathrm{}\left(3\right)\mathrm{}$ nsec and $g=0.30\mathrm{}\left(1\right)\mathrm{}$, respectively, strongly support a $|{\left(\pi h_{\frac{9}{2}}\right)}^3{\frac{9}{2}}^{-},{\left(\nu f_{\frac{5}{2}}\right)}^{-1\mathrm{}}{\left(\nu i_{\frac{13}{2}}\right)}^{-1\mathrm{}}{9}^{-};{\frac{25}{2}}^{+}〉$ configuration for this level.

NUCLEAR REACTIONS ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}({}_{}{}^6{}_{}{}^{}\mathrm{Li},3n\gamma )$, $E_{\mathrm{Li}}=34\mathrm{}$ MeV; measured $\gamma -\gamma$ coin, $\gamma -W\left(\theta \right)$, pulsed-beam $\gamma$ timing, perturbed angular distributions; deduced levels, $\gamma$ multipolarities, $J^{\pi }$, $T_{\frac{1}{2}}$, $B\left(E1\mathrm{}\right)\mathrm{}$, $g$.

Recent measurements of the sub-barrier fusion of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ with isotopes of Sm, which span the transition region from spherical to deformed equilibrium shapes, are analyzed in terms of static and dynamic reaction models. The classical equivalent-spheres method of incorporating the effect of nuclear deformation on heavy-ion fusion is shown to overpredict the experimentally observed differences in the fusion cross sections. An approximate, classical estimate of dynamic effects connected with the rotation of the target before fusion removes part, but not all, of this discrepancy. Coupled-channels calculations, which treat dynamic effects through the excitation of the $2^{+}$ and $4^{+}$ levels, are also presented. An estimate is given of the effects one may expect to observe for fusion with a polarized deformed target.

NUCLEAR REACTIONS Barrier-penetration analysis of ${\sigma }_{\mathrm{fusion}}$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{148,150,152,154}{}_{}{}^{}\mathrm{Sm}$, $E_{\mathrm{lab}}=60\mathrm{}-75$ MeV, including effects of static deformation. Consideration of dynamic effects. Coupled-channels analysis.

A simple but fully three-dimensional cascade approach, appropriate for considering heavy-ion collisions at a few hundred MeV per projectile nucleon, is applied to ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. For impact parameters $b_{\mathrm{NeU}}$ of 0 and 5 fm the calculated results include densities $\rho (\overrightarrow{\mathrm{r}},t)$ of nucleon masses during the collision and energy-angle distributions $\frac{d^{2}n}{\mathrm{dEd}\Omega }$ of scattered nucleon masses emerging from the collision. All of the present calculations use idealized nucleon-nucleon interactions implying cross sections ${\sigma }_{\mathrm{NN}}$ that are purely elastic, isotropic, and independent of the initial $\mathrm{NN}$ state. Some of these calculations also introduce excluded-volume effects, such as those associated with a classical hard core in the $\mathrm{NN}$ interaction. The calculated density $\rho (\overrightarrow{\mathrm{r}},t)$ is quite sensitive to changes in the size of the excluded volume (we tried hard cores of radius 0, 0.5, and 0.9 fm). However, it is only in the case of zero excluded volume that $\rho (\overrightarrow{\mathrm{r}},t)$ shows much sensitivity to changes in ${\sigma }_{\mathrm{NN}}$ (we tried ${\sigma }_{\mathrm{NN}}=15.4, 25.4, \mathrm{and} 53.1$ mb). The distribution $\frac{d^{2}n}{\mathrm{dEd}\Omega }$ is rather insensitive to the excluded-volume feature but does depend sensitively on ${\sigma }_{\mathrm{NN}}$, on the impact parameter $b_{\mathrm{NeU}}$, and on the emitted-nucleon characteristics $E$ and $\Omega$. For one particular set of $\mathrm{NN}$ parameters—hard-core radius = 0.9 fm, ${\sigma }_{\mathrm{NN}}=25.4\mathrm{}$ mb—our cascade calculation reduces to a case in which each nucleon is modeled precisely as a classical frictionless billiard ball (a "hard sphere") of diameter equal to the hard-core radius. For this case our cascade results would be especially suitable for comparison with analogous fluid-dynamic results—these latter to be computed using the known equation of state of a hard-sphere gas.

NUCLEAR REACTIONS High-energy heavy-ion reactions. Intranuclear cascade calculations. ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ collisions at laboratory energies of about 200-400 MeV per nucleon of the projectile. Density of nuclear matter. Energy-angle distributions of emitted nucleons.

The radiative capture reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at low energies has been analyzed on the basis of the direct capture model in order to provide a theoretical estimate of the stellar reaction rate. The scattering wave functions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ by $\alpha$ and the bound state wave functions of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ were constructed by the empirical model, the phenomenological Woods-Saxon potential model, and the orthogonality condition model; these models account for the measured elastic scattering and excitation energies of the low-lying states of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$. The total cross section factors $S\left(E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\right)$ of the $E1\mathrm{}$, $M1\mathrm{}$, and $E2\mathrm{}$ capture from the $l=0\mathrm{}-3$ partial waves clearly show a rising behavior as the incident energy goes lower, which agrees with the experimental data. The negative scattering phase shifts, which can be associated with the presence of almost energy-independent inner oscillations in the relative wave function between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and $\alpha$ due to the Pauli exclusion principle, seem to be responsible for this behavior.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at low energies; direct capture model analysis; othogonality condition model; calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, $S\left(E\right)\mathrm{}$, and branching ratios.

Absolute yields have been determined for 105 gamma rays emitted in the decay of 95 fission products representing 54 mass chains created during thermal-neutron fission of ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$. These results include 17 mass chains for which no prior yield data exist. Using a Ge(Li) detector, spectra were obtained of gamma rays between 30 sec and 0.3 yr after very short irradiations of thermal neutrons on a 1 μg sample of ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$. On the basis of measured gamma-ray yields and known nuclear data, total chain mass yields and relative uncertainties were obtained for 51 masses between 84 and 156. The absolute overall normalization uncertainty is <8%. The measured $A$-chain cumulative yields make up 81% of the total light mass ($A\le 121$) yield and 92% of the total heavy mass yield. The results are compared with fission-product yields previously measured with generally good agreement. The mass-yield data have been compared with those for thermal-neutron fission of ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ and for ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}(\mathrm{s}.\mathrm{f}.\mathrm{})\mathrm{}$; the influences of the closed shells $Z=50\mathrm{}$, $N=82\mathrm{}$ are not as marked as for thermal-neutron fission of ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ but much more apparent than for ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}(\mathrm{s}.\mathrm{f}.\mathrm{})\mathrm{}$. Information on the charge distribution along several isobaric mass chains was obtained by determining fractional yields for 12 fission products. The charge distribution width parameter, based upon data for the heavy masses, $A=128\mathrm{} \mathrm{to} 140$, is independent of mass to within the uncertainties of the measurements. Gamma-ray assignments were made for decay of short-lived fission products for which absolute gamma-ray transition probabilities are either not known or in doubt. Absolute gamma-ray transition probabilities were determined as (51 ± 8)% for the 374-keV gamma ray from decay of ${}_{}{}^{110}{}_{}{}^{}\mathrm{Rh}$, (35 ± 7)% for the 1096-keV gamma ray from decay of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Sb}$, and (21.2 ± 1.2)% for the 255-keV gamma ray from decay of ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ba}$.

RADIOACTIVITY, FISSION ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}\mathrm{}(n,f)\mathrm{}$ $E_n=\mathrm{thermal}$; measured $\sigma (E_{\gamma },T_{\frac{1}{2}})$; deduced mass, charge yields.

The isobar-doorway model for pion-nucleus interaction is extended to coherent ${\pi }^0$ photoproduction. The modifications to the transition operator due to many-body effects are shown to be the same as those in the optical potential. Nonlocality associated with isobar propagation, recoil corrections, and an off-shell extrapolation of the $\pi N\Delta$ vertex are included. The calculated cross sections are found to be in good agreement with the existing data.

NUCLEAR REACTIONS Coherent ${\pi }^0$ photoproduction; isobar doorway; optical potential model. Many-body modifications of the transition operator.