The $\alpha$ capture reaction ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(\alpha , \gamma ){}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ was studied in the bombarding energy range of $E_{\alpha }=4.13\mathrm{} \mathrm{to} 5.00$ MeV corresponding to the excitation energy range of $E_x=10.31\mathrm{} \mathrm{to} 11.08$ MeV in ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$. Seven resonances have been located and their resonance strengths determined. Two of the resonances decay predominantly to the ground state while the other five decay predominantly to the first excited state of ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$. Angular distribution measurements of the predominant decay gamma ray have been performed and the spin and parity of all the resonances assigned. The isospin of two of the resonances have been assigned as $T=0\mathrm{}$ while $T=1\mathrm{}$ has been assigned for three others. Evidence has been obtained for the operation of the isospin selection rule for the dipole ($E1\mathrm{}$ and $M1\mathrm{}$) and quadrupole ($E2\mathrm{}$) gamma decay.

NUCLEAR REACTIONS ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(\alpha , \gamma ){}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, $E_{\alpha }=4.13\mathrm{} \mathrm{to} 5.00$ MeV; measured resonance strengths, angular distributions; deduced $J^{\pi }$, $T$ of the resonances, enriched target.

A four-body model is used in studying the four-nucleon system. This model is solvable and can be applied to nuclear reactions involving four nucleons. Intermediate quasiparticle states are used for the two- and three-body scattering leading to $T$ matrices which are separable. The model leads to four-body equations which, by using partial wave decomposition, are reduced to single variable integral equations. Numerical calculations of the differential cross sections of the nuclear reactions ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, p){}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, n){}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, d){}_{}{}^2{}_{}{}^{}\mathrm{H}$ are carried out for different deuteron laboratory energies between 6.1 and 51.5 MeV. Inclusion of the $p$-wave three-body amplitudes is tested. Also, the simultaneous exchange of two nucleons between the incoming deuterons is investigated. The theoretically calculated angular distributions are in good agreement with the experimental measurements. The extracted values of the spectroscopic and normalization factors are reasonable.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, p){}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, n){}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(d, d){}_{}{}^2{}_{}{}^{}\mathrm{H}$; $E_d=6.1-51.5\mathrm{}$ MeV; four-body model. Calculated $\sigma \left(\theta \right)$. Extracted spectroscopic factors.

The approximations made in the statistical multistep direct reaction theory of Feshbach, Kerman, and Koonin are examined. It is shown that these approximations individually produce rather large errors and that, although they sometimes cancel out partially, a significant amount of net error remains in general.

NUCLEAR REACTIONS Multistep direct reaction methods, Feshbach-Kerman-Koonin approximations.

Excitation functions have been measured for the elastic and inelastic scattering of polarized protons from ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ at ${\theta }_{\mathrm{lab}}=120\mathrm{}°, 135°, 150°, \mathrm{and} 165°$ in the energy range $E_{\mathrm{p}}=14.25-18.00\mathrm{}$ MeV. Excellent fits to the elastic scattering data were obtained using a parametrized background and the isobaric analog resonances of 35 states in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ (the "parent states") with $E_x=2.3-5.7\mathrm{}$ MeV; spinparity assignments and resonance parameters were determined for all of these isobaric analog resonances. The data for inelastic scattering to the first excited state ($2^{+}$, 0.803 MeV) were described using a distorted-wave Born approximation background and the same isobaric analog resonances; good fits to the data were obtained by varying only the inelastic partial width amplitudes. A set of spectroscopic amplitudes was then found, for both the single-particle and the particle-core components of the parent states, by comparing the best-fit resonance parameters with those given by model calculations. The internal consistency of this set was verified by using sum rules. The spectroscopic amplitudes are compared with those given by simple weak-coupling model predictions; there is considerable disagreement, probably because too few configurations were used in the theoretical calculations.

NUCLEAR REACTIONS ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}(\overrightarrow{\mathrm{p}}, \mathrm{p})$, ($\overrightarrow{\mathrm{p}}, {\mathrm{p}}^{\prime }$), $E=14.25-18.00\mathrm{}$ MeV; measured $\sigma (E; \theta )$, $A_y(E; \theta )$; deduced isobaric analog resonance parameters. ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ deduced $J$, $\pi$, single-particle and particle-core spectroscopic amplitudes for 35 levels.

The lifetimes and magnetic moments of the $J^{\pi }=8^{+} \mathrm{and} 6^{+}$ isomers in ${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}$ have been measured using the gamma-ray perturbed angular distribution technique. The levels were populated with the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(t,p)${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}$ reaction. The $g$ factors of the $8^{+}$ and $6^{+}$ states are found to be -0.312(8) and -0.312(15), respectively. The magnetic moment, $\mu =-1.42\mathrm{}\left(7\right)\mathrm{}$ ${\mathrm{\mu }}_{\mathrm{n}}$, is deduced for the $2g\frac{9}{2}$ neutron orbital. Mean lifetimes are 290(25) ns for the $8^{+}$ state and 71(9) ns for the $6^{+}$ state. We find $〈g\frac{9}{2}\parallel M\left(E2\mathrm{}\right)\mathrm{}\parallel g\frac{9}{2}〉=-39\mathrm{}\left(2\right)\mathrm{}e$ ${\mathrm{fm}}^2$ and an effective charge of $0.88\left(5\right)\mathrm{}e$ for the $2g\frac{9}{2}$ neutron orbital.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(t,p) $E_t=16\mathrm{}$ MeV. For ${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}$ $E_x=1279\mathrm{}$ keV, $J^{\pi }=8^{+}$, measured ${\tau }_m=290\mathrm{}\left(25\right)\mathrm{}$ ns, $g=-0.312\mathrm{}\left(8\right)\mathrm{}$; for $E_x=1195\mathrm{}$ keV $J^{\pi }=6^{+}$, measured ${\tau }_m=71\mathrm{}\left(9\right)\mathrm{}$ ns, $g=-312\mathrm{}\left(15\right)\mathrm{}$. Deduce for $\nu \left(2g\frac{9}{2}\right)$, $\mu =-1.42\mathrm{}\left(7\right)\mathrm{}$ ${\mathrm{\mu }}_{\mathrm{n}}$, and $e_{\mathrm{eff}}=0.88\mathrm{}\left(5\right)\mathrm{}e$.

The ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(\overrightarrow{\mathrm{p}}, \mathrm{d}){}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$ reaction has been studied at $E_{\mathrm{p}}=90\mathrm{}$ MeV. Using analyzing power measurements, gross structures observed between $E_x\sim 3.4$ and $E_x\sim 7.0$ MeV are deduced to arise mainly from the pickup of $1f_{\frac{5}{2}}$ neutrons. Between 7.0 and 19 MeV, the main strength comes from the $1f_{\frac{7}{2}}$ transfer although $1d_{\frac{3}{2}}$ strength has also been observed between 16.0 and 20.0 MeV of excitation energy.

NUCLEAR REACTIONS ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(\overrightarrow{\mathrm{p}}, \mathrm{d}){}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$, $E=90\mathrm{}$ MeV, measured $\sigma (E, \theta )$, duced $J$, $\pi$, and $S$ for ${}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$.

From the results of prompt and $\beta$-delayed $\gamma$-ray singles and $\gamma -\gamma$ coincidence measurements, twenty-four excited states and forty-six gamma transitions are identified in the level scheme of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$. Angular distributions and directional correlations of prompt ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ gamma rays have been measured to obtain the spins of the ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ ground state and excited states at 18.2, 122.7, 243.6, 711.3, and 1019.9 keV. Parities are assigned to the first five states on the basis of $\mathrm{fp}$ shell systematics and observed ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ gamma-ray branching ratios. The 752-keV excitation energy of the first ${\frac{9}{2}}^{+}$ level in ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ is determined from an excitation function for the ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}(\alpha , \mathrm{n}\gamma ){}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ reaction. The angular distribution and correlation measurements also provide $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios for the 104.4, 120.8, 122.7, 243.6, 589.0, and 897.5 keV ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ gamma rays. The level scheme of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ and the corresponding schemes for ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{65,67}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ge}$ are observed to have strong similarities at low excitation. Systematic trends in $E2\mathrm{}$ transition rates are interpreted in the context of shell and collective features of the nuclei. It is found that models based on a single particle coupled to a vibrational or deformed core do not explain the observed systematics, and are an inaccurate representation of these nuclei. The systematics do agree with a many-nucleon shell model emphasizing the short-range pairing interaction and configuration mixing for the valence neutrons.

NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}(\alpha , \mathrm{n}\gamma )$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, 2\mathrm{n}\gamma )$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, \alpha \mathrm{n})$; ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ level scheme, $E\gamma$, $\gamma \left(\theta \right)$, $\gamma \gamma \left(\theta \right)$, $\delta \left(\frac{E2\mathrm{}}{M1\mathrm{}}\right)$, $J^{\pi }$. Directional correlations with an oriented source. Ge(Li) detectors, enriched targets. Nuclear systematics, nuclear deformation.

Projectilelike fragments from reactions of 465-MeV ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ projectiles with targets of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ have been measured as a function of energy loss, and neutron and proton number. The mass and charge of each fragment were uniquely determined with discrete resolution. Data were analyzed as a function of energy loss by fitting a two-dimensional Gaussian function to the neutron-proton distributions. The fit parameters provide a convenient basis for comparison with theoretical predictions. In addition, centroids and variances derived from more detailed onedimensional Gaussian fits to isobaric charge distributions are presented. Results are given for measured data as well as for the primary fragment distributions after correction for the dominant neutron evaporation. The centroid data show that in the asymmetric reactions proton transfer from projectile to target nucleus is preferred while the average fragment neutron number is largely preserved. This produces a charge equilibration process which is dependent on energy loss within the combined systems. The neutron and proton variances indicate an early dominant neutron flow followed by a constant relative neutron and proton exchange rate at energy losses above about 30 MeV. The degree of correlation of the neutron-proton distributions increases with energy loss and is found to be strongly related to the potential energy surface. Consistently observed negative correlation coefficients at low energy losses suggest the possible importance of processes other than particle exchange in the early stages of the interaction. Variances for constant $N$,$Z$, and $A$ are found to saturate at energy losses and with magnitudes dependent on the target nucleus.

NUCLEAR REACTIONS ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ + ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, $E_{\mathrm{lab}}=465\mathrm{}$ MeV; simultaneous energy, mass and charge determination for projectilelike fragments; parametrization in terms of two-dimensional Gaussian functions; neutron and proton distribution centroids, variances, and correlation coefficients; properties of charge equilibration and nucleon exchange.

Energy dissipation during heavy ion nuclear fission has been calculated by employing the one-dimensional time dependent frictional Schrödinger equation. The variation of loss of energy with respect to the shape of the fissioning system follows the same trend as the classical frictional matrix. The dissipative loss of kinetic energy with respect to time is also shown.

NUCLEAR REACTIONS, FISSION Ar + Th, $E_{\mathrm{lab}}=250\mathrm{}$ MeV, onedimensional quantized frictional motion, loss of energy.

We formulate a procedure implicit in the Jost function formulation of the potential scattering in order to investigate the potential ambiguities occurring in two body scattering by a complex potential. The connection between this method and the distorted-wave Born approximation formalism is pointed out. We apply this method to study the potential ambiguities known to exist in heavy ion scattering by taking ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, $\alpha$ + ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ for typical illustrative calculations. Our calculations trace the origin of the potential ambiguities to the Coulomb potential and sizes and masses of the colliding nuclei. The regions of configuration space which contribute strongly to the partial wave $S$ matrix are illustrated graphically.

NUCLEAR REACTIONS Analysis of heavy ion potential ambiguity by calculating region-wise contribution to reaction and scattering.

Proton spectra have been calculated for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(85 MeV/nucleon) + ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ using a three-dimensional hydrodynamical model with viscosity and thermal conductivity and final thermal breakup. The theoretical results are compared to recent data. It is shown that the predicted flow effects are not observable as a result of the impact parameter averaging inherent in the inclusive proton spectra. In contrast, angular distributions of medium mass nuclei ($A>\mathrm{}3\mathrm{}$) in nearly central collisions can provide signatures for flow effects.

NUCLEAR REACTIONS Theoretical fragment spectra, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ $E_{\mathrm{lab}}=85\mathrm{}$ MeV/nucleon + ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$.

The effects of coupling to a harmonic oscillator on the quantum tunneling of a macroscopic motion are studied through the influence functional formalism of Feynman's path integral method for the general coupling form factor. As an example, we consider the model in which the potential barrier is parabolic and the coupling Hamiltonian is linear in both coordinates of the macroscopic motion and of the intrinsic harmonic oscillator. The results are then compared with the exact solution obtained through the canonical transformation into normal coordinates in the limiting cases when the normal coordinates reduce to the original coordinates. We found that: (1) In the adiabatic case, i.e., when the recurrence time $\frac{\pi }{\omega }$ of the oscillator is much shorter than the transmission time through the macroscopic potential barrier, the effect of oscillator coupling can be well represented by an effective potential. The coupling enhances the tunneling probability on the whole. (2) There exists a critical energy, above which the tunneling probability is reduced because of the linear oscillator coupling. In the weak coupling limit and when $\omega \to 0$, the critical energy becomes $-\infty$, so that the coupling to the oscillator always reduces the tunneling probability.

NUCLEAR REACTIONS Quantum tunneling, coupling of macroscopic motion to intrinsic oscillators, semiclassical method, heavy ion fusion.

Inclusive particle spectra are calculated based on a multiple-collision model which fits the negative-pion multiplicity for central collisions using two different prescriptions. In one case pion absorption and in the other case compressional degrees of freedom are considered to effect this. From a comparision with measured proton, deuteron, triton, and negative pion inclusive spectra for the reaction Ar on KCl at 800 MeV/nucleon, no conclusive evidence for strong compression effects can be extracted.

NUCLEAR REACTIONS KCl(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$,p), (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$,d), (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$,t), (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$,${\pi }^{-}$), $E=800\mathrm{}$ MeV/nucleon; calculated $\sigma (E_{\mathrm{p}}, \theta )$, $\sigma (E_{\mathrm{d}}, \theta )$, $\sigma (E_{\mathrm{t}}, \theta )$, $\sigma (E_{{\pi }^{-}}, \theta )$. Pion absorption versus compression.

Elastic scattering of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ from ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ from ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ has been studied for beam energies from 2.0 to 5.5 MeV using very thin films of isotopically separated LiF as targets. A double-folding model optical potential provided a good fit for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$+${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ for the entire energy range, and for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ for energies low enough that the breakup ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +\mathrm{d}$ could not occur. For higher energies, the real part of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ potential falls off rapidly with energy so that by 5.5 MeV the potential well required to fit the data is only about 40% as deep as is predicted by the folding model.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$,${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,${}_{}{}^7{}_{}{}^{}\mathrm{Li}$), $E_{\mathrm{lab}}=2.0-5.5\mathrm{}$ MeV; measured $\sigma (\theta , E)$, calculated double-folding model potentials.

Reaction products from the bombardment of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ gas targets with ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ beams have been measured at five laboratory energies between 70 and 160 MeV. Fusion, deep inelastic, and quasielastic processes were studied. Large deep inelastic yields (${\sigma }_{\mathrm{Di}}\gtrsim 600$ mb) with average $Q$ values of -50 MeV are present at the highest energy. Analysis of the fusion cross sections for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ suggests that the maximum angular momentum in ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ populated via this entrance channel may be as low as $29\pm 2\hslash$.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; $E_{\mathrm{lab}}=80\mathrm{} \mathrm{to} 160$ MeV. Measured elastic scattering, direct processes, deep inelastic processes, and fusion. All products with $Z>\mathrm{}4\mathrm{}$ identified. Measured angular distributions. Monte Carlo simulation of deep inelastic and fusion.

Gamma ray multiplicities and rotational band transition intensities have been measured for the ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, 4n) reaction for bombarding energies between 62.5 and 73.5 MeV. It is shown that centrifugal barrier penetration leads to a fairly broad spin distribution of the compound nucleus even at near-barrier energies. The results are discussed in terms of optical model absorption probabilities and parabolic barrier penetration probabilities.

NUCLEAR REACTIONS Fusion ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, 4\mathrm{n}\gamma )$), $E=62.5-73.5\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, rotational state populations. Deduced barrier parameters and mean compound nuclear spin values.

A complex band crossing of the yrast band has been observed at spin $I=10\mathrm{}$ in ${}_{}{}^{130}{}_{}{}^{}\mathrm{Ba}$ by the reaction ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}({}_{}{}^{13}{}_{}{}^{}\mathrm{C}, 3\mathrm{n}\gamma )$. Two of the three positive parity bands show backbending and may be the rotation aligned bands built upon ${\left(\nu h_{\frac{11}{2}}\right)}^{-2\mathrm{}}$ and ${\left(\pi h_{\frac{11}{2}}\right)}^2$ configurations, respectively. The nature of the bands was deduced from a comparison with a cranking model calculation. A negative parity band and the quasi-gamma band were identified.

NUCLEAR REACTIONS ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}({}_{}{}^{13}{}_{}{}^{}\mathrm{C}, 3\mathrm{n}\gamma )$, $E=45-58\mathrm{}$ MeV; measured relative $\sigma (E; E_{\gamma })$, $\sigma (E_{\gamma }, \theta )$, $I_{\gamma }$, $\gamma -\gamma$ coin. ${}_{}{}^{130}{}_{}{}^{}\mathrm{Ba}$ deduced levels, $J$, $\pi$. Cranking model calculation.

A spectroscopic investigation of high-spin states in ${}_{}{}^{201,203}{}_{}{}^{}\mathrm{At}$ was performed by means of the reactions ${}_{}{}^{192,194}{}_{}{}^{}\mathrm{Pt}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,5n)${}_{}{}^{201,203}{}_{}{}^{}\mathrm{At}$ with ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ energies between 85 and 100 MeV. In-beam measurements of $\gamma$-ray excitation functions, $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions, and pulsed-beam-$\gamma$ timing were made to determine the decay scheme, level energies, $\gamma$-ray multipolarities, spin-parity assignments, and isomeric lifetimes. The yrast and near-yrast level structures were established up to $J\sim \frac{25}{2}$, and several isomers with mean lifetimes around 20 ns were observed. The systematic trends of level energies of the odd-mass astatine ($Z=85\mathrm{}$) isotopes are discussed in terms of proton-particle configurations of ${}_{85}{}^{211}{}_{}{}^{}\mathrm{At}_{126}^{}{}_{}{}^{}$ coupled to neutron-hole configurations of the corresponding even-mass lead isotones.

NUCLEAR REACTIONS ${}_{}{}^{192,194}{}_{}{}^{}\mathrm{Pt}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,5n), $E=85-100\mathrm{}$ MeV, measured $\gamma -\gamma$ coincidence, excitation functions, $\gamma$-ray angular distributions, pulsed-beam-$\gamma$ timing; deduced ${}_{}{}^{201,203}{}_{}{}^{}\mathrm{At}$ level energies, spins and parities, lifetimes, transition rates.

Two equivalent methods are developed for solving the problem of small oscillations near equilibrium when dissipative forces are included in the dynamical equations of motion. One method relies on the Lagrangian formulation of the equations of motion, and the other method relies on the Hamiltonian formulation. The eigenvalues are in general complex, but for unstable or overdamped motion they are purely real. We use the Lagrangian formulation to calculate the two lowest symmetric eigensolutions at the fission saddle point for nuclei with $\frac{Z^2}{A}$ ranging from 18.0 to 44.6 for ordinary two-body viscosity, one-body wall-formula dissipation, and one-body wall-and-window dissipation.

NUCLEAR REACTIONS, FISSION Nuclei with $18.0\le \frac{Z^2}{A}\le 44.6$; calculated two lowest symmetric eigensolutions at fission saddle point. Macroscopic nuclear model, Yukawa-plus-exponential model, nuclear inertia, nuclear dissipation, ordinary two-body viscosity, one-body dissipation, eigenvalues and eigenvectors of nonsymmetric matrices.

The isotopic yields of Rb, In, and Cs from the 40-100 MeV proton-induced fission of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, and the isotopic yields of Ga from the 80 and 100 MeV proton-induced fission of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ have been measured by on-line mass spectrometry. The yields have been normalized to the independent formation cross sections of selected isotopes measured radiochemically. Total numbers of neutrons emitted per fission event have been deduced from the centroids of the isotopic distributions. The equal charge displacement, minimum potential energy, and unchanged charge distribution mechanisms have been investigated. It is found that the charge-division mechanism is fragment-mass dependent, the minimum potential energy postulate being attributed to asymmetric fission events and the unchanged charge distribution postulate being attributed to near-symmetric fission events.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{233,235}{}_{}{}^{}\mathrm{U}(\mathrm{p},f)$, $E_{\mathrm{p}}=40\mathrm{} \mathrm{to} 100$ MeV: measured independent yields of Ga, Rb, In, Cs. Deduced total numbers of neutrons emitted in asymmetric (Rb, Cs) and near-symmetric (In) fission: charge-division mechanism.