A general description of subtraction techniques in scattering theory is given. Applications with the objective of achieving reduced integral equations with nonsingular kernels are applied to both the Faddeev and the Alt, Grassberger, and Sandhas forms of the three-particle equations with and without three-body forces. In the Faddeev case a method similar to one recently proposed by Karlsson is found which is analogous to well-known procedures in the two-particle case. This analogy is shown to be fairly weak when three-particle forces are included. In the absence of two-particle bound states phase-space type integral equations are found which permit the generation of approximate 3-to-3 amplitudes which satisfy unitarity and possess the correct representations of the double-scattering poles as well as the proper connectedness structure. A generalization of the so-called structure invariant perturbation theory to include three-body forces is established using the Alt, Grassberger, and Sandhas equations.

NUCLEAR REACTIONS Scattering theory, three-particle scattering, unitary approximations.

Absolute cross sections for ($d,n$), ($d,p$), and ($d,\alpha$) reactions initiated by ∼0.1 to ∼1.0 MeV deuterons on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ have been obtained. Total reaction cross sections, with absolute accuracies of 8-13%, as well as measured differential cross sections are presented. The experimental procedures are discussed and a comparison with previous results is given.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(d,p)\mathrm{}$, ($d,\alpha$), $E_d=0.1-\sim 1.0$ MeV; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(d,n)\mathrm{}$, $E_d=0.2-\sim 0.9$ MeV; enriched target; measured $\sigma (E_d,\theta )$, $\sigma \left(E_d\right)$.

The Amado model of three-body reactions is applied to investigate the $D$-phase anomalies observed in the $p-{}_{}{}^3{}_{}{}^{}\mathrm{H}$ scattering experiment for proton energies below 12 MeV. A perturbation calculation using $s$-wave separable potentials and including the spin-isospin dependence of the interacting particles demonstrates that the coupling of the $p+{}_{}{}^3{}_{}{}^{}\mathrm{H}$ channel to the $d+d$ and other breakup channels is important only in the singlet $D$ state. The calculated inelasticity parameter ${\eta }_{20}^2$ is found to be in good agreement with experiment.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(p,p)\mathrm{}$, $E=4\mathrm{}-12$ MeV; calculated ${\eta }_{20}^2$. Amado model of three-body reactions.

In the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^8{}_{}{}^{}\mathrm{Be}$ ($0^{+}$,$2^{+}$) reaction, the experimental results of the differential cross section and the polarization are fairly well described by a cluster point of view in which, instead of two-nucleon transfer, a deuteron transfer is a dominant process. The optical-model parameters for $p-{}_{}{}^8{}_{}{}^{}\mathrm{Be}$ are also investigated.

NUCLEAR REACTIONS Mechanism of $n-p$ transfer from cross sections and polarizations. Optical model parameters.

A model independent method of obtaining the total reaction cross section as a difference between integrals over solid angle of the Rutherford and measured elastic cross sections is proposed and discussed. The conditions for validity of the method are first that the measured differential cross section be Rutherford within experimental error at forward angles, and second, that the projectile be highly absorbed. Both conditions are fulfilled in a variety of experiments with complex projectiles. The method is applied to $\alpha$-particle scattering by ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{206,208}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. Limitations of the method, comparison with transmission, charge collection, and optical model methods, and applications to heavy ion scattering are discussed.

NUCLEAR REACTIONS ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(\alpha ,\alpha )$, $E=24\mathrm{}$ MeV, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\alpha ,\alpha )$, $E=20, 22, 24, 26$ MeV; $\theta =20\mathrm{}-170°$; $\Delta \theta =5\mathrm{}°$; measured $\sigma (E;\theta )$; deduced optical-model parameters, reaction cross sections.

Consequences of isospin mixing are explored for compound nucleus reactions and statistical cross section fluctuations. This is done in the framework of a theory of transport phenomena. Formulas differing from previously published results are given for average compound nucleus cross sections, and for the correlation function of cross section fluctuations. The extraction of isospin mixing from evaporation spectra is discussed. It is pointed out that external mixing, which so far has been considered only in the theory of isobaric analog resonances, may dominate internal or bound-state mixing. Hence, Coulomb matrix elements deduced from highly excited compound nuclei only represent upper limits.

NUCLEAR REACTIONS Isospin mixing in compound nucleus reactions.

The reactions ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\overrightarrow{p},p){}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{n},n){}_{}{}^3{}_{}{}^{}\mathrm{He}$ are analyzed within the framework of the dynamical $R$-matrix methodology. When compared at equal incident energies, measurements indicate that forward angle ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\overrightarrow{p},p){}_{}{}^3{}_{}{}^{}\mathrm{H}$ polarization values are slightly in excess of ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{n},n){}_{}{}^3{}_{}{}^{}\mathrm{He}$ values. The model predicts the proton polarization has a slightly larger magnitude at forward angles than the neutron polarization, although their shapes and magnitudes are in qualitative agreement with experiment. Lisowski's phase shift analysis suggests the existence of a narrow resonance near $E_x=37\mathrm{}$ MeV. The model predicts several resonances in the vicinity of this tentative level.

NUCLEAR REACTIONS Calculated $P\left(\theta \right)$ for ${}_{}{}^3{}_{}{}^{}\mathrm{H}(\overrightarrow{p},p)$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{n},n)$ at 8.0, 12.0, and 17.1 MeV.

NUCLEAR STRUCTURE The $R$-matrix model predicts $J^{\pi }=1^{+}, 2^{+}, 3^{+}, \mathrm{and} 4^{+}$ states near the position of the tentative narrow resonance of Lisowski et al.

Pole Feynman diagrams with heavy particle transfer mechanism are known to explain the anomalous backscattering of $\alpha$ particles by light nuclei. Triangle Feynman diagrams (with the heavy particle transfer mechanism) are used here to explain forward elastic scattering for the same reactions.

NUCLEAR REACTIONS: Forward cross section.

Cross sections for ($n,2n$) and ($n,3n$) reactions have been measured between 14.7 and 24.0 MeV using a large liquid scintillator to detect neutrons. Measurements were made for ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}$, ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$, ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$, ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ samples. The excitation functions are compared with calculations based on a statistical, preequilibrium model using global sets of optical model and level density parameters.

NUCLEAR REACTIONS ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}\mathrm{}(n,2n)\mathrm{}$; ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\mathrm{}(n,2n)\mathrm{}$, ($n,3n$); $E=14.7\mathrm{}-24.0$ MeV, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$. Natural targets.

Results of a high resolution neutron time-of-flight experiment for neutron energies $27\le E\le 240$ keV on the target nucleus ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y} (J^{\pi }={\frac{1}{2}}^{-})$ are presented. The measurement employed a 5 nsec beam burst and a 250 m flight path. A multilevel shape analysis of the data was carried out. The parities of almost all observed resonances were easily determined, and for $s$ wave levels the $J$ values of most resonances were obtained. It was found that the $\Sigma {\Gamma }_n^0$ vs $E$ plot of the $l=0\mathrm{}$, $J=1\mathrm{}$ levels exhibited a significant change in slope over the 240 keV interval, which was interpreted as evidence for a $1^{-}$ doorway state. The analysis yielded an escape width ${\Gamma }^{\uparrow }=0.8\mathrm{}$ keV and a spreading width ${\Gamma }^{\downarrow }=100\mathrm{}$ keV, with the doorway state located at a neutron energy of 70 keV. No effect attributable to nonstatistical behavior was observed in the $p$ wave channel. Since most $s$ and $p$ wave levels were observed a relatively clean test could be made of the expected ratio of $s$ to $p$ wave level spacings. After estimating the number of missed levels (inferred through the use of the Porter-Thomas distribution), the experimental ratio of $s$ to $p$ wave spacings was found to be 2.74. This is in disagreement with the theoretical level density prediction of 2.06. The average $s$, $p$ strength functions and level spacings are $S_0=0.28\mathrm{}\pm 0.05\times {10}^{-4\mathrm{}}$, $S_1=2.64\mathrm{}\pm 0.03\times {10}^{-4\mathrm{}}$, ${〈D〉}_{l = 0}=4.0\mathrm{}$ keV, ${〈D〉}_{l = 1}=1.46\mathrm{}$ keV.

NUCLEAR REACTIONS Neutron total cross section measurement of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, $27<E<\mathrm{}240\mathrm{}$ keV. Multilevel analysis, determined $E$, $J^{\pi }$, ${\Gamma }_n$ of resonances. Deduced $s$ and $p$ wave strength functions, doorway state parameters $E_d$, $\Gamma \uparrow$, $\Gamma \downarrow$.

Calculations of particle energy spectra resulting from the photonuclear reactions at energies below the meson production threshold have been carried out in the framework of combining the pre-equilibrium exciton model and the quasideuteron model. A 2p-2h initial state in the exciton model is assumed because the quasideuteron absorption is the dominant process in the energy region above giant resonance. With this combined model the subsequent secondary interactions of the emerging particle with the rest of the nucleus following the initial photon-nucleus interaction are appropriately taken into account. The experimental difference energy spectra of fast photoneutrons from several elements (Al, Cu, In, Sn, Ta, Pb, Bi, and U) at bremsstrahlung energies of 55 and 85 MeV were compared with the theoretical predictions. General agreements in both spectral shapes and cross sections are obtained. The relative yields of the reactions ($\gamma ,xn$) resulting from monoenergetic photons on ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ at 50, 100, and 150 MeV are also predicted reasonably well by the combined model together with the conventional evaporation theory.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\gamma ,x)$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}(\gamma ,x)$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}(\gamma ,x)$, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}(\gamma ,x)$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}(\gamma ,x)$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}(\gamma ,x)$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(\gamma ,x)$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(\gamma ,x)$, $E_{\gamma }=55\mathrm{} \mathrm{and} 85$ MeV bremsstrahlung. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma ,x)$, $E_{\gamma }=110\mathrm{}$ MeV bremsstrahlung. ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}(\gamma ,xn)$, $E_{\gamma }=50, 100, \mathrm{and} 150$ MeV. Pre-equilibrium exciton, quasideuteron, and statistical compound nucleus models analyses.

The ${}_{}{}^{69,71}{}_{}{}^{}\mathrm{Ga}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{68,70}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ reactions have been studied at 26 MeV with an overall resolution of 18-20 keV using a split pole magnetic spectrometer. Spectroscopic factors have been extracted for 16 levels in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, 14 levels in ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$, and 24 levels in ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$. The ratio $R=\frac{\sigma \left(0_2^{+}\right)}{\sigma \left(0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+}\right)}$ shows a singularity at $N=40\mathrm{}$. The small value of $R$ for ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ is consistent with a previously proposed description of the structure of the states involved which is based on a simple mixing of $p_{\frac{3}{2}}$ and $f_{\frac{5}{2}}$ proton configurations. The results for the $\mathrm{Ga}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He})\mathrm{Zn}$ reactions are compared with a recent shell-model calculation.

NUCLEAR REACTIONS ${}_{}{}^{69,71}{}_{}{}^{}\mathrm{Ga}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He})$, ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E=26\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ deduced levels, $J$, $\pi$, $S$.

NUCLEAR STRUCTURE ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$; shell-model calculations.

A new precision measurement of the mass of ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ has been performed by observing ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ events from the reaction ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$)${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ at an incident beam energy of 80 MeV. The $Q$ values and mass excess are determined to be $Q=-31.796\mathrm{}\pm 0.008$ MeV and mass excess = 31.593 ± 0.008 MeV. The new ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ mass allows for a more stringent test of the isobaric multiplet mass equation in the $A=8\mathrm{}$ quintet. A significant deviation from the quadratic mass equation persists.

NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$). Measured reaction $Q$ value and mass excess. Deduced coefficients of IMME for the $A=8\mathrm{}$ isobaric quintet.

The ${}_{}{}^{72,74,76}{}_{}{}^{}\mathrm{Ge}\mathrm{}(p,t)\mathrm{}{}_{}{}^{70,72,74}{}_{}{}^{}\mathrm{Ge}$ reactions have been studied at 26 MeV incident energy with an overall energy resolution of 10 keV using a split-pole spectrometer. Many new levels are found below 5 MeV excitation energy. Angular distributions are obtained and comparison with distorted-wave-Born-approximation calculations allow spin and parity assignments. Several new $J^{\pi }=0^{+}$ levels are observed around 2.5 MeV. The positions of some $2^{+}$, $3^{-}$, $4^{+}$, $5^{-}$, and $7^{-}$ levels are established.

NUCLEAR REACTIONS ${}_{}{}^{72,74,76}{}_{}{}^{}\mathrm{Ge}\mathrm{}(p,t)\mathrm{}$, $E=26\mathrm{}$ MeV; measured $\sigma =\sigma \left(\theta \right)$; ${}_{}{}^{70,72,74}{}_{}{}^{}\mathrm{Ge}$ deduced levels up to 4.5-5 Mev, $J$, $\pi$.

We develop a macroscopic description of heavy ion inelastic scattering in the context of a folding model. Form factors for the single nuclear excitation of either the projectile or target are derived, as well as the mutual excitation form factor. The formalism is applied to several typical examples.

NUCLEAR REACTIONS Heavy ion inelastic scattering; folding model for single and mutual excitation; applied to inelastic excitation of $2^{+}$, $3^{-}$, $5^{-}$ states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 96 MeV; ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 168 MeV, elastic, single, and mutual inelastic.

Energy dependence arising from the Regge-pole contribution to the heavy-ion elastic scattering amplitude is discussed. First it is shown that the pole amplitude generally does not display resonant energy dependence. Then oscillatory energy dependence of the Coulomb-removed total cross section is shown to arise from interference of the pole contribution with the Rutherford amplitude at $\theta =0\mathrm{}$. Finally, it is shown that fixed angle energy dependence can arise from interference involving a pole contribution.

NUCLEAR REACTIONS: Heavy-ion elastic scattering energy dependence, Regge pole, Coulomb optical theorem.

A survey of elastic scattering angular distributions from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ using beams of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ has been carried out for energies near the Coulomb barrier. The projectile bombarding energies used were ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(14, 17 MeV); ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(24, 27, 30 MeV); ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(27, 30, 33 MeV); ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(33, 36, 38 MeV) and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$(36 MeV). Optical model analyses using a previously proposed parameter set have been carried out in order to fit the data in a global manner. Although low energy data cannot completely define the optical model potential, it is interesting that the potential of Cramer et al., which they used to describe ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ +${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering in the energy range from 33-215 MeV, yields a reasonable description of all the angular distributions for all projectiles and energies presented here.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$), $E=14\mathrm{} \mathrm{and} 17$ MeV; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$) $E=24, 27, \mathrm{and} 30$ MeV; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$) $E=27, 30, \mathrm{and} 33$ MeV; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) $E=33, 36, \mathrm{and} 38$ MeV; and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$) $E=36\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$ and performed global optical model analysis.

The ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{34}{}_{}{}^{}\mathrm{P}$ $T=1\mathrm{}$ four-nucleon transfer reaction has been observed and its cross section measured. The mass excess of ${}_{}{}^{34}{}_{}{}^{}\mathrm{P}$ is -24555(40) keV. ${}_{}{}^{34}{}_{}{}^{}\mathrm{P}$ states have been observed at $E_x=0\mathrm{} \mathrm{and} 441\left(20\right)\mathrm{}$ keV. In addition, there is evidence of a state which would correspond to an excitation energy of 667(40) keV.

NUCLEAR REACTIONS ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=24\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, mass excess and levels of ${}_{}{}^{34}{}_{}{}^{}\mathrm{P}$.

A method is outlined within the formalism of the exact finite-range distorted-wave Born approximation to include exchange terms as well as interference terms with the usual direct reaction process. The method is suitable for use with existing finite-range computer codes. An application is presented for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},\alpha ){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reactions for the ground-state and two-excited-state transitions. The exchange component for the three transitions significantly improved the calculated fits with data suggesting the importance of the exchange mechanism for the reactions in question. The reactions were analyzed at a laboratory energy of 33 MeV.

NUCLEAR REACTIONS Exact finite-range DWBA formalism for direct, exchange, and interference components to angular distributions with application to the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},\alpha ){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reactions, at $E=33\mathrm{}$ MeV.

We introduce a degree of freedom to describe the rupture of the neck in nuclear fission and calculate the point at which the neck ruptures as the nucleus descends dynamically from its fission saddle point. This is done by mentally slicing the system into two portions at its minimum neck radius and calculating the force required to separate the two portions while keeping their shapes fixed. This force is obtained by differentiating with respect to separation the sum of the Coulomb and nuclear interaction energies between the two portions. For nuclei throughout the Periodic Table we calculate this force along dynamical paths leading from the fission saddle point. The force is initially attractive but becomes repulsive when the neck reaches a critical size. For actinide nuclei the neck radius at which rupture occurs is about 2 fm. This increases the calculated translational kinetic energy of the fission fragments at infinity relative to that calculated for scission occurring at zero neck radius. With the effect of neck rupture taken into account, we calculate and compare with experimental results fission-fragment kinetic energies for two types of nuclear dissipation: ordinary two-body viscosity and one-body dissipation.

NUCLEAR REACTIONS, FISSION Included neck-rupture degree of freedom and calculated its effect on fission-fragment kinetic energies. Modified liquid-drop model, hydrodynamical model, nuclear viscosity, one-body nuclear dissipation.