The multiple-scattering structure of various scattering operators as well as the integral equations they satisfy are investigated for Hamiltonians consisting of terms of definite but arbitrary connectivities. This is done in order to encompass the effective interactions which arise in few-body models of nuclear reactions. The counterparts of the Watson and other kinds of multiple-scattering expansions are developed under these circumstances. Connected-kernel scattering integral equations which have the unique and practical feature of being both partition labeled and possessing a multiple-scattering structure are obtained for the transition operators. These extended versions of both the multiple-scattering expansions and partition-labeled multiple-scattering integral equations are applied to the specific class of few-body Hamiltonian reaction models found by Polyzou and Redish. The concept of a well-structured reaction mechanism is introduced and it is established that for such a reaction mechanism an appropriately modified multiple-scattering picture carries over to the approximate few-body models. It is shown, for example, that for a well-structured reaction mechanism the analogs of the Born and impulse approximations emerge directly from the extended partitionlabeled multiple-scattering equations in contrast to alternative formulations.

NUCLEAR REACTIONS Multiple-scattering theory with many-body forces. Connected-kernel $N$-particle equations with multiple-scattering structure. Few-body models for nuclear reactions and related approximations.

The ${}_{}{}^1{}_{}{}^{}\mathrm{H}(n,\gamma ){}_{}{}^2{}_{}{}^{}\mathrm{H}$ reaction $\gamma$-ray energy was obtained from measurement of the energy difference between it and the 2185-keV $\gamma$ ray emitted in the ${\beta }^{-}$ decay of ${}_{}{}^{144}{}_{}{}^{}\mathrm{Ce}$-${}_{}{}^{144}{}_{}{}^{}\mathrm{Pr}$. Based on the $\gamma$-ray energy value of 2223.247 ± 0.017 keV obtained from this measurement, a value of 2224.564 ± 0.017 keV was determined for the binding energy of the deuteron $S_n\left({}_{}{}^2{}_{}{}^{}\mathrm{H}\right)$. By combining this binding energy value with published mass differences of doublets involving neighboring isotopes and ${}_{}{}^1{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, values of 6257.268 ± 0.024, 4946.329 ± 0.024, 8176.483 ± 0.040, and 10833.297 ± 0.038 keV were obtained for the neutron binding energies of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, respectively, together with a value of 8071.367 ± 0.029 keV for the neutron mass excess $n-1\mathrm{}$.

NUCLEAR REACTIONS ${}_{}{}^1{}_{}{}^{}\mathrm{H}(n,\gamma )$, $E=\mathrm{thermal}$; measured $E_{\gamma }$. Deduced neutron binding energies for ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$; deduce neutron mass. Natural targets, Ge semiconductor detectors.

Photoneutron cross sections involving the emission of one and two neutrons from ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ have been measured over the energy interval 8.5 to 39.7 MeV using monoenergetic photons from positron in-flight annihilation. The 6-MeV wide giant dipole resonance is observed to be centered at 23 MeV and a pygmy resonance is seen at about 13 MeV. Such structure as is apparent in the cross sections is not as pronounced as for the cases of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. Comparison of the total photoneutron cross section with recent ground-state data indicates that much of the pygmy resonance decays to the ground or first excited state of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, but that the giant dipole resonance decays mainly to highly excited states in the daughter. Excellent agreement is observed between the present results and a recent two-particle, one-hole shell-model calculation of the isospin-split giant dipole resonance states for this nucleus. New photoneutron cross-section results for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ up to 39.7 MeV are reported as well.

NUCLEAR REACTIONS ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(\gamma ,n)$, $E_{\gamma }=8.5\mathrm{}-39.7$ MeV and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma ,n)$, $E_{\gamma }=15.9\mathrm{}-39.7$ MeV; measured $4\pi$ neutron yield for monenergetic photons; $\sigma (E_{\gamma },1n)$, $\sigma (E_{\gamma },2n)$, integrated cross sections, isospin splitting of the giant resonance for ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$.

We investigate the problems connected with the incorporation of the Coulomb interaction into the equations which describe reactions involving charged particles. In particular, the formalism of Vesselova and of Alt, Sandhas, and Ziegelmann is considered. Here various Coulomb quantities play a role which all have a so-called essential singularity in the zero-energy point. This singularity has to be taken care of when the total three-particle energy is near the breakup threshold. We use formulas, both for the case of a repulsive and an attractive Coulomb potential, by means of which the essential singularity is split off in a satisfactory way. This allows one to make really exact calculations for simple models. It is shown that a comparison of such exact calculations with known approximations is indeed necessary. We present and discuss exact calculations of the three-dimensional Coulomb $T$ matrix and of its partial wave projections for all real energies.

NUCLEAR REACTIONS Off-shell Coulomb $T$ matrix, three-particle equations, Coulomb effects when two of the particles charged, discussed exact solution for scattering.

The Feshbach-Yennie approximation is applied to calculate the proton-carbon bremsstrahlung cross sections near the resonance at 1.7 MeV. In all but one case, the predicted cross sections are in very good agreement with the experimental data. The calculation includes not only the principal term of the approximation but also the correction term, which is negligible at an energy far from the resonance but becomes very significant in the region of the resonance.

NUCLEAR REACTIONS $p-{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ bremsstrahlung near 1.7 MeV, calculate bremsstrahlung cross section.

The 90° yield curves for the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},{\gamma }_0){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},{\gamma }_1){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reactions have been measured in 200 keV steps for $E_p=6.25\mathrm{} \mathrm{to} 13.6$ MeV and in 100 keV steps for $E_p=13.6\mathrm{} \mathrm{to} 17.0$ MeV. In addition, 50 keV step data were obtained for $E_p$ of 12.6 to 14.55 MeV. Angular distributions of both the cross section and the analyzing power were also obtained for these two reactions at twelve energies which span the giant dipole energy region. The cross section was measured at nine angles between 30° and 154° while the analyzing power was measured at seven angles between 42° and 142°. These data were used to obtain the complex $E1\mathrm{}$ and $E2\mathrm{}$ transition matrix elements in the case of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},{\gamma }_1){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The results are compared to a direct-semidirect calculation. It is found that there is little justification in introducing $E2\mathrm{}$ amplitudes other than a pure direct $E2\mathrm{}$ term.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},{\gamma }_0)$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},{\gamma }_1)$ measured $\sigma \left(\theta \right)$ and $A\left(\theta \right)$, $E_p=8.05\mathrm{}-15.5$ MeV. ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p,{\gamma }_0)$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p,{\gamma }_1)$ measured $\sigma \left(90\mathrm{}°\right)$, $E_p=6.24\mathrm{}-17.0$ MeV. Deduced $E1\mathrm{}$ and $E2\mathrm{}$ $T$-matrix amplitudes and phases. Compared to model calculations.

The capture cross sections of ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{140,142}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ and the capture cross section of ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$ to the 3.68 h isomeric state in ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ have been determined at 30 keV neutron energy using the activation technique. Neutrons were generated via the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}\mathrm{}(p,n)\mathrm{}$ reaction just above the reaction threshold at a 3 MV pulsed Van de Graaff accelerator. The capture cross sections are of importance to stellar nucleosynthesis. With the ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ cross sections the time integrated average neutron flux for the s process was determined to 0.22 ${\mathrm{mb}}^{-1\mathrm{}}$. This result, the capture cross section of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ and the ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$ cross section to the 3.68 h isomeric state in ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ were used to analyze the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ cosmic clock. The mean s process age of solar matter before the solidification of the solar system was estimated to 6 × ${10}^9$ yr. In addition the Hf/Lu abundance ratio was determined.

NUCLEAR REACTIONS ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}(n,\gamma )$, ${}_{}{}^{140,142}{}_{}{}^{}\mathrm{Ce}(n,\gamma )$, ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}(n,\gamma ){}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}_{}^m{}_{}{}^{}$, ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}(n,\gamma )$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}(n,\gamma )$; $E_n=30\mathrm{}$ keV; measured capture cross sections; nucleosynthesis; ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ cosmochronometer, Hf and Zr abundances.

Neutron total and capture cross sections of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ have been measured up to 1100 keV neutron energy [$E_{\mathrm{exc}}\left({}_{}{}^{33}{}_{}{}^{}\mathrm{S}\right)=9700\mathrm{}$ keV]. Spin and parity assignments have been made for 28 of the 64 resonances found in this region. Values of total radiation widths, reduced neutron widths, level spacings, and neutron strength functions have been evaluated for $s_{\frac{1}{2}}$, $p_{\frac{1}{2}}$, $p_{\frac{3}{2}}$, and $d_{\frac{5}{2}}$ levels. Single particle contributions using the valency model account for a significant portion of the total radiation width only for the $p_{\frac{1}{2}}$-wave resonances. A significant number of resonances can be identified with reported levels excited in ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\mathrm{}(d,p)\mathrm{}$ and ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(\alpha ,n)$ reactions. A calculation of the Maxwellian average cross section appropriate to stellar interiors indicates an average capture cross section at 30 keV, $\overline{\sigma }\simeq 4.2\left(2\right)\mathrm{}$ mb, a result that is relatively insensitive to the assumed stellar temperature. Direct (potential) capture and the $s$-wave resonance capture contributions to the thermal capture cross section do not fully account for the reported thermal cross section (530 ± 40 mb) and a bound state is invoked to account for the discrepancy.

NUCLEAR REACTIONS ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\mathrm{}(n,n)\mathrm{}$, $E_n=25\mathrm{}-1100$ keV, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(n,\gamma )$ $E_n=2.5\mathrm{}-1100$ keV; measured ${\sigma }_{n,\mathrm{tot}}\mathrm{}\left(E\right)\mathrm{}$, ${\sigma }_{n,\gamma }$; deduced level properties, $l$, $J$, $\pi$, ($E_0,{\Gamma }_n,{\Gamma }_{\gamma }$); calc avg properties: $〈D_{\mathrm{lJ}}〉$, $〈S_{\mathrm{lJ}}〉$ for $l=0, 1, 2$; calc single particle contribution to ${\Gamma }_{\gamma }$ (Valency model); calc Maxwellian avg cross sections.

The ${}_{}{}^{186,187,188}{}_{}{}^{}\mathrm{Os}(n,\gamma )$ cross sections were measured over the incident neutron energy range 2.6-800 keV. Optimized statistical model fits to the average cross sections were made employing estimates of the ${}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$, and ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$ $p$-wave strength functions 0.29 × ${10}^{-4\mathrm{}}$, 0.45 × ${10}^{-4\mathrm{}}$, and 0.33 × ${10}^{-4\mathrm{}}$, respectively, $d$-wave strength functions 1.3 × ${10}^{-4\mathrm{}}$, 4.0 × ${10}^{-4\mathrm{}}$, and 1.5 × ${10}^{-4\mathrm{}}$, respectively, and gamma ray strength functions ($\frac{{\overline{\Gamma }}_{\gamma }}{D_0}$) 26.8 × ${10}^{-4\mathrm{}}$, 176 × ${10}^{-4\mathrm{}}$, and 20.8 × ${10}^{-4\mathrm{}}$, respectively. A lower bound for the ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ neutron inelastic cross section is estimated as 0.25(20) b at 30 keV. The Maxwellian-averaged capture cross sections are presented as a function of temperature. The ratio of 30 keV Maxwellian-averaged cross sections $\frac{〈{\sigma }_{\gamma }\mathrm{}\left(186\right)\mathrm{}〉}{〈{\sigma }_{\gamma }\mathrm{}\left(187\right)\mathrm{}〉}=0.504\mathrm{}\left(17\right)\mathrm{}$ is reported and the lack of agreement with earlier measurements of this ratio is discussed. The use of this cross section ratio in estimating, via the ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$-${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ beta decay, the duration of galactic nucleosynthesis is discussed. The cross section ratio from this work yields an estimate of 10.4(25) × ${10}^9$ yr for the duration of galactic nucleosynthesis, a result higher than but still consistent with the estimate 7(2) × ${10}^9$ yr derived from U/Th decay.

NUCLEAR REACTIONS Neutron capture, cross section, inelastic cross section, strength functions, nucleosynthesis, Maxwellian-averaged cross section.

The magnetic moments of $2_1^{+}$ states of ${}_{}{}^{102-110}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{106-116}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{130-136}{}_{}{}^{}\mathrm{Ba}$ have been measured by the dynamic field technique. The resulting magnetic moments are compared to the predictions of the vibrational model and to the interacting boson model.

NUCLEAR REACTIONS ${}_{}{}^{102-110}{}_{}{}^{}\mathrm{Pd}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$′) ${}_{}{}^{102-110}{}_{}{}^{}\mathrm{Pd}$ ($2_1^{+}$), ${}_{}{}^{106-116}{}_{}{}^{}\mathrm{Cd}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$′) ${}_{}{}^{106-116}{}_{}{}^{}\mathrm{Cd}$ ($2_1^{+}$), ${}_{}{}^{130-136}{}_{}{}^{}\mathrm{Ba}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$,${}_{}{}^{32}{}_{}{}^{}\mathrm{Ś}$)${}_{}{}^{130-136}{}_{}{}^{}\mathrm{Ba}$($2_1^{+}$) $E_S\sim 72-80$ MeV, enriched targets; measured $W(\theta ,H,\infty )$ through polarized iron; deduced $g\left(2_{}^{+}{}_1{}^{}\right)$.

The yields of the eleven most abundant nuclides produced in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction were determined in the energy range from 14-31 MeV (c.m.) via $\gamma$-ray techniques. Several reaction channels, including a few which involve only light-particle emission, show strong structure. Some of these anomalies are very narrow, having widths ≲ 250 keV (c.m.). The $3\alpha$ evaporation cross section, as well as the yield of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ via direct inelastic scattering, is determined. Further information is presented on the nature of a process leading to anomalously large $\alpha$-particle yields from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction at low energies. The strong gross-structure features of the fusion and total reaction cross sections are discussed in the context of the optical model, and also with reference to the limiting angular momentum for fusion. The latter analysis leads to some insight into the origin of the gross structure, but also suggests a striking correlation between the fusion cross section and the extended ground state band of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at high energies. This correlation, if it is not coincidental, has interesting consequences with regard to the behavior of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at high angular momentum and energy.

NUCLEAR REACTIONS Complete fusion, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=14\mathrm{}-31$ MeV, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ for production of 11 nuclides; $\gamma$ measurement, Ge(Li) detectors and natural target; deduced total fusion, $3\alpha$ evaporation, and direct inelastic scattering $\sigma$; deduced limiting angular momenta for fusion; discussed anomalous $\alpha$-particle yield from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at low energies.

The static quadrupole moments of the first $2^{+}$ excited states of ${}_{}{}^{96,98,100,102,104}{}_{}{}^{}\mathrm{Ru}$ were measured employing the reorientation effect in Coulomb excitation. For constructive interference via the second $2^{+}$ excited states the determined quadrupole moments are (-0.13±0.09) eb for ${}_{}{}^{96}{}_{}{}^{}\mathrm{Ru}$, (-0.20±0.09) eb for ${}_{}{}^{98}{}_{}{}^{}\mathrm{Ru}$, (-0.43±0.07) eb for ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ru}$, (-0.57±0.07) eb for ${}_{}{}^{102}{}_{}{}^{}\mathrm{Ru}$, and (-0.70±0.08) eb for ${}_{}{}^{104}{}_{}{}^{}\mathrm{Ru}$. These $Q_{2^{+}}$ represent, respectively, 29%, 36%, 67%, 78%, and 84% of the rotational value.

NUCLEAR REACTIONS ${}_{}{}^{96,98,100,102,104}{}_{}{}^{}\mathrm{Ru}(\alpha ,{\alpha }^{\prime })$, $E=8.5\mathrm{}-9.5$ MeV; ${}_{}{}^{96,98,100,102,104}{}_{}{}^{}\mathrm{Ru}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\text{'}$), (${}_{}{}^{16}{}_{}{}^{}\mathrm{O},{}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{\prime }{}_{}{}^{}\gamma$), $E=36\mathrm{}-44.8$ MeV; measured $\sigma (E,\theta )$ deduced $Q_{2^{+}}$, $B\left(E\lambda \right)$, $B\left(M1\mathrm{}\right)\mathrm{}$, $J$, $\pi$, $T_{\frac{1}{2}}$. Enriched targets.

Levels in ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$ ($N=82\mathrm{}$) have been studied using the (${}_{}{}^6{}_{}{}^{}\mathrm{Li},3n\gamma$) and (${}_{}{}^7{}_{}{}^{}\mathrm{Li},4n\gamma$) reactions. Prompt and delayed $\gamma \gamma$ coincidences, excitation functions, angular distributions, and internal conversion electron measurements were used in the in-beam studies. In addition to the well known levels at 329.4(${7/2}^{+}$) and 716.0(${11/2}^{-}$) keV, firmly assigned levels are placed at 1601.2(${11/2}^{-}$), 1844.6(${13/2}^{-}$), 2244.4(${15/2}^{+}$), 2284.1(${15/2}^{-}$), 2573.6(${15/2}^{-}$), 2813.5(${17/2}^{-}$), 2836.4(${19/2}^{-}$), 2862.7(${19/2}^{-}$), 3183.0(${23/2}^{\mathrm{}(-)\mathrm{}}$), 3976.3(${25/2}^{\mathrm{}(+)\mathrm{}}$), and 4122.8(${27/2}^{\mathrm{}(+)\mathrm{}}$) keV. A ${21/2}^{\mathrm{}(-)\mathrm{}}$ level is provisionally placed at 2911.1 keV. These levels may be interpreted in terms of weak coupling of $d_{\frac{5}{2}}$ and $g_{\frac{7}{2}}$ proton holes to the core states of ${}_{}{}^{146}{}_{}{}^{}\mathrm{Gd}$ and an $h_{\frac{11}{2}}$ proton to the core states of ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$.

NUCLEAR REACTIONS ${}_{}{}^{142}{}_{}{}^{}\mathrm{Nd}({}_{}{}^6{}_{}{}^{}\mathrm{Li},3n\gamma )({}_{}{}^7{}_{}{}^{}\mathrm{Li},4n\gamma )$, $E=32,34$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $I_{\gamma }\left(\theta \right)$, $I_{\mathrm{ce}}$, ICC, $\gamma \gamma$ coin; ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$ deduced levels, $J\pi$. Enriched target. Ge(Li); Si(Li) detectors.

The high-spin states of ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$ have been studied through observation of $\gamma$ rays emitted from the ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},2n)$ reaction produced with projectile energies of 33-38 MeV. The energies, relative intensities, angular distributions, and linear polarizations of the $\gamma$ rays were measured. Lifetimes of states were obtained from the Doppler broadening of the $\gamma$-ray peaks. Many of the levels appear to belong to one of three bands: (1) the ground-state band with energy spacing between that given by the pure rotational and vibrational models, (2) a band built on a $5^{-}$ state which is ascribed to rotational alignment of two quasiparticles, one of which is in a $g_{\frac{9}{2}}$ orbital, and (3) a $\Delta J=1\mathrm{}$ band which has characteristics of a $\gamma$-vibrational band in a deformed nucleus. There is evidence for the beginning of a fourth band built on a $J=6\mathrm{}$ level.

NUCLEAR REACTIONS ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},2n)$, $E=33\mathrm{}-38$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \left(\theta \right)$, Doppler broadening, linear polarization; deduced ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$ levels, $J$, $\pi$, $\delta$, $\gamma$ branching, $\tau$.

A broad range of heavy-ion-induced fusion excitation functions are classically analyzed. The fusion-barrier parameters are compared with predictions of the proximity potential, a Yukawa-plus-exponential model, and a modified Woods-Saxon potential. The Yukawa-plus-exponential model is found to give the best overall agreement with the data. The proximity potential is too shallow, but would be in closer agreement with data if a necking contribution were added.

NUCLEAR REACTIONS Extracted fusion barriers and radii from fusion data with heavy ions, compared several theoretical models.

${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},X)$ reactions are studied at 88 MeV. The $A$ and $Z$ of reaction products $X={}_{}{}^{16}{}_{}{}^{}\mathrm{O},{}_{}{}^{15,14,13}{}_{}{}^{}\mathrm{N},{}_{}{}^{13,12}{}_{}{}^{}\mathrm{C},{}_{}{}^{11,10}{}_{}{}^{}\mathrm{B},{}_{}{}^{9,7}{}_{}{}^{}\mathrm{Be} \mathrm{and} {}_{}{}^{7,6}{}_{}{}^{}\mathrm{Li}$ are identified. Despite the low bombarding energy, the general features of (i) energy spectra, (ii) the optimum $Q$ values $Q_{\mathrm{eff}}^m$ and (iii) angular distributions in 5 MeV intervals in $Q$ are very similar to those of much higher energy data of heavier systems: i.e., (i) dominance of deep inelastic reactions, (ii) $Q_{\mathrm{eff}}^m$ values well reproduced by the "universal" relations previously found for deep inelastic reactions, and (iii) $\sigma (\theta ,Q)$ of a form $\frac{A\exp [-\mu \mathrm{}(Q\left)\mathrm{}\theta \right]}{sin\theta }$. The variations of $Q_{\mathrm{eff}}^m$ with $\theta$ and of $\mu$ with $Q$ and $n$, the number of transferred nucleons, are discussed in connection with the gradual evolution in reaction mechanisms from quasielastic to deep inelastic to complete fusion.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},X)$, $E=88\mathrm{}$ MeV, $X={}_{}{}^{16}{}_{}{}^{}\mathrm{O},{}_{}{}^{15,14,13}{}_{}{}^{}\mathrm{N},{}_{}{}^{13,12}{}_{}{}^{}\mathrm{C},{}_{}{}^{11,10}{}_{}{}^{}\mathrm{B},{}_{}{}^{9,7}{}_{}{}^{}\mathrm{Be} \mathrm{and} {}_{}{}^{7,6}{}_{}{}^{}\mathrm{Li}$, measured energy spectra, optimum $Q$ values, $\sigma$, $\sigma \left(\theta \right)$, and $\sigma (\theta ,Q)$.

Fractional independent or cumulative chain yields of 35 fission products were determined for the photofission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 20-MeV bremsstrahlung, using direct $\gamma$ spectrometry of irradiated uranium samples, $\gamma$-ray spectrometry of fission product catcher foils, and chemical sparation techniques. For the mass chains 131-136 the width parameter $c$ of the charge distribution was obtained. An average value of 0.93 ± 0.06 was deduced for $c$. A comparison of this $c$ value with the results for other low-energy fissioning systems indicates that the width of the charge distribution is practically independent of the excitation energy of the compound nucleus. Using the average $c$ value, the most probable charges $Z_p$ (20 MeV) were calculated for 8 light and 12 heavy mass chains. A comparison of the deduced $Z_p$ (20 MeV) behavior with the expectations of the unchanged charge density hypothesis shows the higher charge-to-mass ratio of the light fragments compared to the heavy ones and the influence of the closed 50-proton shell on the charge distribution. The $Z_p$ (20 MeV) values determined are very well reproduced by the empirical relation of Nethaway except in the vicinity of the $Z=50\mathrm{}$ line.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\gamma ,F)$, $E_{\gamma max}=20\mathrm{}$ MeV; measured: fragment $\gamma$-ray spectra; deduced: charge distributions, width and most probable charges.

Prompt neutrons in coincidence with the fission fragments from the spontaneous fission of ${}_{}{}^{250,252,254}{}_{}{}^{}\mathrm{Cf}$ and ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$ were measured inside a 75-cm-diameter, Gd-loaded liquid scintillation counter having a neutron-detection efficiency of about 78%. Measurements for ${}_{}{}^{256}{}_{}{}^{}\mathrm{Fm}$ were done just outside the counter with an efficiency of 31%. The kinetic energies of both fission fragments and the number of neutrons for each fission event were recorded. From these data, the fragment kinetic energies and masses and the neutron multiplicity distributions were determined for ${}_{}{}^{250,252,254}{}_{}{}^{}\mathrm{Cf}$ and ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$. Variances of neutron multiplicity distributions as a function of total fragment kinetic energy and the ratio of fragment masses have been calculated and are presented for all the nuclides studied.

RADIOACTIVITY, FISSION ${}_{}{}^{250,252,254}{}_{}{}^{}\mathrm{Cf}$, ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$; measured neutron multiplicity distributions as a function of total kinetic energy and mass ratio. ${}_{}{}^{256}{}_{}{}^{}\mathrm{Fm}$; measured average and variance of neutron multiplicity distributions as a function of total kinetic energy and mass ratio.

We obtain a closed form asymptotic approximation to the eikonal amplitude in hadron-nucleus scattering which agrees remarkably well with numerical evaluation of the full eikonal amplitude. The characteristic features of the scattering are dominated by the nuclear edge—its radius and thickness. The radius determines the oscillations and the thickness the exponential decrease with momentum transfer of the cross section. By developing systematic corrections to our asymptotic approximation we can separate the effects of "hard" and "soft" collisions in the multiple-scattering sense.

NUCLEAR REACTIONS Closed form eikonal amplitude for hadron-nucleus scattering.

We performed a measurement of the $\gamma +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\to {\pi }^{+}+{}_{}{}^{12}{}_{}{}^{}\mathrm{B}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ reaction up to 4 MeV above threshold relative to the $\gamma +p\to {\pi }^{+}+n$ reaction. The resulting cross section is in agreement, at the accuracy level of ±5% with the available theoretical predictions and with another experimental result.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,{\pi }^{+}){}_{}{}^{12}{}_{}{}^{}\mathrm{B}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$, $E_{{\pi }^{+}}:0\mathrm{}-4$ MeV, measured $\sigma$ relative to proton.