Data for two-nucleon transfer reactions on even tungsten nuclei are presented. Several systematic features emerge from the data and are discussed in detail. These include the influence of multistep processes on angular distribution shapes. The systematic behavior of excited $0^{+}$ strengths is shown to arise from two types of excitation, one associated with a subshell gap at $N=108\mathrm{}$, the other being of the pairing isomer type.

NUCLEAR REACTIONS ${}_{}{}^{186,184,182,180}{}_{}{}^{}\mathrm{W}$($p$,$t$), $E_p=21\mathrm{}$ MeV; measured $\sigma (E_t,\Theta )$. ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$($t$,$p$); $E_t=15\mathrm{}$ MeV; measured $\sigma (E_p,\Theta )$. ${}_{}{}^{184,182,180,178}{}_{}{}^{}\mathrm{W}$ deduced levels, $L$, $\pi$, $J$. Nuclear structure analysis.

Data for the ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$($p$,$t$)${}_{}{}^{181}{}_{}{}^{}\mathrm{W}$ reaction are presented. States corresponding to the coupling of the odd neutron to collective excitations of the even core are identified and used to test the microscopic structure of these collective excitations. In particular, the proposed nature of the pairing isomers observed in the neighboring even nuclei is confirmed. Information concerning the previously observed anomalous population of $2^{+}$ states in this mass region is also presented.

NUCLEAR REACTIONS ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$($p$,$t$), $E_p=21\mathrm{}$ MeV; measured $\sigma (E_t,\Theta )$. ${}_{}{}^{181}{}_{}{}^{}\mathrm{W}$ deduced levels, $L$, $\pi$, $J$. Nuclear structure analysis.

The ($\alpha$,$p$) reaction at 26 MeV has been used to study ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{79}{}_{}{}^{}\mathrm{As}$ with 12 keV resolution full width at half maximum. The reaction behaves like a simple proton stripping ("spectator" zero coupled neutron pair) and the characteristic shapes of the angular distributions permit assigning new spins and parities. In ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$: $198 \mathrm{keV}\left(\frac{5}{2^{-}}\right)$, $1116 \mathrm{keV}\left(\frac{1}{2^{-}}\right)$, $1494 \mathrm{keV}\left(\frac{9}{2^{+}}\right)$. In ${}_{}{}^{79}{}_{}{}^{}\mathrm{As}$: $\mathrm{g}.\mathrm{s}.\mathrm{}\left(\frac{3}{2^{-}}\right)$, $233 \mathrm{keV}\left(\frac{5}{2^{-}}\right)$, $499 \mathrm{keV}\left(\frac{1}{2^{-}}\right)$, $777 \mathrm{keV}\left(\frac{9}{2^{+}}\right)$, $1806 \mathrm{keV}\left(\frac{9}{2^{+}}\right)$, $1891 \mathrm{keV}\left(\frac{1}{2^{-}}\right)$, $1964 \mathrm{keV}\left(\frac{9}{2^{+}}\right)$. The observed splitting of the $J^{\pi }=\frac{3}{2^{-}}$ strength in ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$, important as compared to the one observed in ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, is attributed to a change of structure between $N=40\mathrm{} \mathrm{and} 42$.

NUCLEAR REACTION ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$($\alpha$,$p$), $E=26\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{79}{}_{}{}^{}\mathrm{As}$ deduced levels, $E$, $j$, $\pi$.

Production cross sections of various final nuclei have been determined using the in-beam gamma rays produced during the 80, 100, 136, and 164 MeV proton bombardment of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$ targets. From the systematics of these cross sections it is concluded that (a) typically, 1-2 nucleons are emitted in the fast pre-equilibrium phase leaving a few nuclei excited over a broad range of excitation energy, (b) the bulk of the final nuclei are produced following nucleon evaporation from the excited nuclear residues of the pre-equilibrium phase, (c) the fraction of the incident energy dissipated through fast emission increases from about $\frac{1}{2}$ to $\frac{2}{3}$ over the above energy range, (d) the average excitation energy of the nuclear residues of the pre-equilibrium phase is estimated to increase by only 10 MeV in going from about 40 to 50 MeV over the above energy range, and (e) no evidence is found for significantly preferred removal of alpha particles from the target nucleus. Detailed comparisons of the observed cross sections are made with the cascade and hybrid models. The cascade model yields better overall agreement with the measured results. A hybrid model which includes both multiple pre-equilibrium emission and geometric surface effects is needed if it is to be equally effective.

NUCLEAR REACTIONS ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$($p$,$x\gamma$), $E_p=80, 100, 136, \mathrm{and} 164$ MeV; measured $E_{\gamma }$, ${\sigma }_{\gamma }$, $\sigma$ production various final nuclei; results compared with cascade and hybrid exciton models including evaporation.

Lifetimes have been measured by direct timing for the 1582 keV, $\frac{3}{2^{-}}$ level of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$($\tau <38\mathrm{}$ ps) and the 2010 keV, $\frac{3}{2^{+}}$ level of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$($\tau =730\mathrm{}\pm 18$ ps). These levels are members of closely spaced parity doublets. The sensitivity of measurements to determine the parity mixing within these doublets is discussed.

NUCLEAR REACTIONS ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$($p$,$p\gamma$), $E_x=1582\mathrm{}$ keV, measured $\tau$; ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$($d$,$p\gamma$), $E_x=2010\mathrm{}$ keV, measured $\tau$. Direct timing.

Photon absorption by Al, Ta, and Bi between 3 and 30 MeV was measured using as a photon spectrometer a photoneutron time-of-flight detector and a liquid deuterium target. The atomic cross sections of Ta and Bi at the lowest energies (and of Al at higher energies) agree with calculated values appearing in published tabulations but exceed them at 25 MeV by about 2% in Ta and 3% in Bi. Calculations by others using empirical Coulomb corrections and improved screening corrections to the cross section for pair production by the nucleus agree with experiment to within (0.5±0.4)%. Best experimental values of the combined correction for Bi are given.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$; measured total photon absorption ${\sigma }_{\gamma }\mathrm{}\left(E\right)\mathrm{}$; observed GDR; deduced electron pair production ${\sigma }_K\mathrm{}\left(E\right)\mathrm{}$; $E=3.0\mathrm{} \mathrm{to} 30.0$ MeV; resolution 500 keV; deduced experimental values for Bi of the combined Coulomb and screening correction; ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($\gamma$,$n$) L${\mathrm{D}}_2$/TOF spectrometer.

It is shown that the basic quantity of the abrasion-ablation model of nucleus-nucleus collisions, namely the probability of extracting a nucleon from the projectile, is a quasi-universal quantity. It can be given a form which does not depend upon the target and which depends weakly upon the projectile. It is shown how this property is related to the weak factorization of the cross sections.

NUCLEAR REACTIONS Fragmentation in relativistic heavy ion collisions. Factorization of the cross section.

The particle-particle angular correlation method is applied to the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}\to \alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Deuterons were detected at ${\theta }_d^{\mathrm{lab}}=10\mathrm{}$°. Information on the reaction mechanism is obtained by analyzing the shape and the angular shift of the experimental data. A dominant direct transfer mechanism is found for the primary reaction. The ratios $\frac{{\Gamma }_{{\alpha }_0}}{\Gamma }$ and the $\alpha$-reduced widths ${\gamma }_{{\alpha }_0}$ are deduced.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}\to \alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. $E_{{}_{}{}^6{}_{}{}^{}\mathrm{Li}}=34\mathrm{}$ MeV; measured $W({\Omega }_d,{\Omega }_{\alpha })$; confirmed $J^{\pi }$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ levels. Evaluated $\frac{{\Gamma }_{{\alpha }_0}}{\Gamma }$ and ${\gamma }_{{\alpha }_0}$. EFR-DWBA and HF analysis.

The total fusion cross sections for the system ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured in the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ bombarding energy range 30-60 MeV by the detection of evaporation residues in a $\Delta E-E$ ionization-chamber surface-barrier detector telescope. Although the measured ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ fusion cross sections are similar to those in which a similar compound system is formed by heavy-ion ($A\ge 12$) interaction, the ratio of the measured fusion cross section to the total reaction cross section is much smaller than that observed for other systems and is attributed to the structure of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and the ease with which it breaks up into smaller fragments. This view is consistent with the anomalous ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ elastic scattering results.

NUCLEAR REACTIONS ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ fusion $E=30-60\mathrm{}$ MeV, measured fusion product angular distributions and total fusion cross sections, calculated total reaction cross section using optical model, compared fusion cross section with total reaction cross section and with fusion cross section systematics.

A parametrization based on the distorted-wave Born-approximation (DWBA) formalism, using the diffractional model, is given in order to fit angular distributions and continuum energy spectra of direct transfer reactions induced by heavy ions populating continuum states at incident energy well above the Coulomb barrier. Experimental data analysis of two-proton and alpha-transfer reactions on $1f-2p$ shell nuclei are successful at low incident energies. On the other hand, at high incident energy, alpha stripping induced by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ beam on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ cannot be described by this direct surface reaction model. It turns out that fragmentation is the most likely process.

NUCLEAR REACTIONS DWBA and diffractional model applied to direct reactions induced by heavy ions—continuum states. Analysis of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{78}{}_{}{}^{}\mathrm{Se}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$)${}_{}{}^{213}{}_{}{}^{}\mathrm{At}$ reactions.

High-spin states in ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$ have been studied by using the ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$,$4n\gamma$) and ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$($\alpha$,$4n\gamma$) reactions and by multiple Coulomb excitation with ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ ions. Several positive-parity bands are excited, and two negative-parity bands have been identified. The previously reported backbending behavior of the yrast sequence is demonstrated to result from the intersection of the ground band (seen to spin ${22}^{+}$) with an even-spin "superband" observed from spins ${12}^{+}$ to ${24}^{+}$. The odd-spin yrast superband and the second lowest even-spin superband also have been observed. All the superbands have moments of inertia appreciably larger than the ground band. The observed intersection of these multiple superbands with the $\gamma$ band produces different backbending behavior and a staggering of the energies of the odd- and even-spin members of the $\gamma$ band. $B\left(E2\right)$ values for transitions below and through the band intersection regions of both the ground band and $\gamma$ bands have been deduced from multiple Coulomb excitation yields. In addition, lifetimes have been measured for the ground band by the Doppler-broadened line-shape technique. The level energies and $B\left(E2\right)$ values are consistent with weak interaction matrix elements (≈ 45 keV) between the intersecting bands. The $B\left(E2\right)$ values of the unperturbed band are found to obey the simple rigid-rotor relationship. The $7^{-}$ negative-parity band exhibits a normal rotational sequence, while the $5^{-}$ band exhibits a large odd-even staggering and a larger moment of inertia. Two-quasiparticle-plus-rotor model calculations indicate strong rotation-alignment and reproduce the observed properties of the high-spin states for both the positive- and negative-parity bands in ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$.

NUCLEAR REACTIONS ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$,$4n\gamma$), $E=69.6\mathrm{}$ MeV, ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$($\alpha$,$4n\gamma$), $E=51\mathrm{}$ MeV, ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$(${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$,${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}_{}^{\prime }{}_{}{}^{}\gamma$) $E=547, 612, 620$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin, Doppler-broadened line shapes, multiple Coulomb excitation probabilities; deduced levels, $J$, $\pi$, $\tau$, $B\left(E2\mathrm{}\right)\mathrm{}$ values from lifetimes and yields, compared levels and $B\left(E2\mathrm{}\right)\mathrm{}$'s to theory.

Spin-isospin instabilities corresponding to the onset of ${\pi }^0$ condensation are investigated for the case of central collisions of high-energy heavy ions in the time-dependent mean-field approximation.

NUCLEAR REACTIONS Calculation of pion condensation in heavy-ion collisions. Time-dependent Hartree-Fock calculation for ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$+${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$.

The elastic scattering of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ has been measured at laboratory energies of 121.0 and 201.6 MeV. These data have been combined with existing lower energy ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ data in order to carry out a global optical model analysis. Calculations employing Woods-Saxon potentials yield good fits to the data without requiring explicitly energy-dependent parameters. In contrast, using a proximity form for the real potential requires an explicitly energy-dependent Woods-Saxon imaginary potential in order to achieve comparable quality fits. Notch perturbation calculations have been utilized to locate the radial region of the potential to which the scattering is sensitive. At all energies the imaginary potential is stronger than the real potential at the radius of maximum sensitivity. This dominance of the absorptive potential greatly limits the amount of information which can be gained about the real potential. Comparison of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ system with other light heavy ion systems such as ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ suggests that the weak binding of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ may be responsible for the strong absorption in this case.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$), $E_L=121.0\mathrm{} \mathrm{and} 201.6$ MeV, measured $\frac{d\sigma }{d\Omega }$; optical model analysis; deduced Woods-Saxon and proximity model optical parameters, $\frac{V}{W}$ ratios, fusion barriers. Comparison with ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ behavior.

Direct-reaction calculations for heavy ions require special computational techniques that take advantage of the physical peculiarities of heavy-ion systems. This paper is the first of a series on quantum-mechanical coupled-channels calculations for heavy ions. It deals with the problems posed by the long range of the Coulomb coupling interaction. Our approach is to use the Alder-Pauli factorization whereby the channel wave functions are expressed as products of Coulomb functions and modulating amplitudes. The equations for the modulating amplitudes are used to integrate inwards from infinity to a nuclear matching radius (≈ 20 fm). To adequate accuracy, the equations for the amplitudes can be reduced to first order and solved in first Born approximation. The use of the Born approximation leads to rapid recursion relations for the solutions of the Alder-Pauli equations and hence to a great reduction in computational labor. The resulting coupled-channels Coulomb functions can then be matched in the usual way to solutions of the coupled radial equations in the interior region of $r$ space. Numerical studies demonstrate the reliability of the various techniques introduced.

NUCLEAR REACTIONS HI coupled-channel inelastic scattering. Treatment of long-range Coulomb potential.

Measurements of the cross section for fusion of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ with ${}_{}{}^{148,150,152,154}{}_{}{}^{}\mathrm{Sm}$ have been made in the range $60\le E_{{}_{}{}^{16}{}_{}{}^{}\mathrm{O}}\le 75$ MeV. Evaporation residues trapped in a carbon catcher foil were observed off line by means of the $K$ x rays emitted by radioactive Yb nuclei and their daughters. Absolute cross sections varying in magnitude from 0.1 to 400 mb were determined with an uncertainty of ±10%. The cross sections for individual $x-n$ channels were also determined. At high energies, the fusion cross sections for all isotopes are similar, whereas at lower bombarding energies the cross sections for the more deformed targets are larger than those for the spherical targets.

NUCLEAR REACTIONS Measured ${\sigma }_{\mathrm{fusion}}$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{148,150,152,154}{}_{}{}^{}\mathrm{Sm}$, $E_{\mathrm{lab}}^{{}_{}{}^{16}{}_{}{}^{}\mathrm{O}}=60-75\mathrm{}$ MeV. Observation of x rays from radioactive evaporation residues.

This paper, the second in a series on techniques for heavy-ion coupled-channels calculations, compares various iterative methods for the solution of the coupled radial equations in the interior region of configuration space. We consider the Born-Neumann series, sequential iteration, the method of moments, and Austern's modification of the Sasakawa method. The use of Padé approximants is shown to eliminate convergence problems with Born and sequential iteration. We conclude that sequential iteration with Padé acceleration is the most rapidly convergent and most efficient way of carrying out coupled-channels calculations for heavy-ion inelastic scattering; 0.5% accuracy in cross sections can be achieved with three or four interations in each partial wave.

NUCLEAR REACTIONS HI coupled-channels inelastic scattering. Iterative solution of radial equations.

The projected ranges, angular distributions and range distributions at each laboratory angle have been measured for one-, two-, and three-proton transfer reactions induced in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ by various heavy ions from ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ to ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$. The products observed were ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{211}{}_{}{}^{}\mathrm{At}$, and ${}_{}{}^{211}{}_{}{}^{}\mathrm{Rn}$. They were identified by their radioactive decay characteristics. Some complementary experiments have been performed using T1 and Au targets. The angular and energy distributions have been used to identify the most probable reaction paths leading to the observed isotopes. At low incident energy, these reaction paths appear to be those which correspond to the most favorable energetics, for all incident ions. At higher energies, more complex reaction channels have a significant contribution to the production of the observed isotopes. For all incident ions, the position of the angular distribution maximum ${\theta }_{max}$ is governed by the value of the ratio $\frac{E}{B}$ of the incident energy to the interaction barrier. The variation of ${\theta }_{max}$ versus $\frac{E}{B}$ is very similar to that of the rainbow angle corresponding to elastic scattering. This might indicate that quasi-elastic transfer and rainbow scattering occur for similar distances of closest approach between colliding nuclei.

NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$(HI,$x$)${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{211}{}_{}{}^{}\mathrm{At}$, ${}_{}{}^{211}{}_{}{}^{}\mathrm{Rn}$, with HI=${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$. Measured $\sigma \left(\theta \right)$, recoil ranges. Deduced most probable reaction path.

A recent experiment by Guet et al. indicates that the width of the $\alpha$-particle angular distribution in long-range-alpha-particle accompanied fission decreases as the fission-fragment kinetic energy $E_F$ increases. Earlier trajectory calculations yielded wide distributions for initial $\alpha$-particle energy $E_{\alpha }^0$ and fragment energy $E_F^0$. It is found that the decreased angular width can be reproduced by trajectory calculations only if the interfragment separation at the scission point is restricted to be around 20.5 fm. This gives rise to a scission-point configuration characterized by $E_{\alpha }^0=0.5\mathrm{}$ MeV and $E_F^0=1.2\mathrm{}$ MeV and explains all the correlations observed in the asymptotic values of $E_F$, $E_{\alpha }$, and the angle of the $\alpha$ particle.

NUCLEAR REACTIONS, FISSION LRA-fission ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$, trajectory calculations, scission configuration.

We measured neutron angular and energy distributions from 710-MeV alphas stopping in targets of water, carbon, steel, and lead for neutron energies from 3 MeV to above 300 MeV. We also measured neutron spectra from 640-MeV alphas stopping in lead. These spectra are similar to the 710-MeV spectra but are reduced in magnitude by about 20 percent. The angular distributions are forward peaked and have a broad bump at about 120 MeV in the 0- and 6-degree spectra. The 710-MeV integrated yields above 10 MeV are about 0.5 neutron per incident alpha, independent of the target. The measured spectra from the water target are consistent with the calculations of an intranuclear cascade model at the forward angles, but are larger than the calculations at the backward angles.

NUCLEAR REACTIONS ${\mathrm{H}}_2$O, C, steel, Pb($\alpha$,$\mathrm{xn}$), $E=710\mathrm{}$ MeV; Pb($\alpha$,$\mathrm{xn}$), $E=640\mathrm{}$ MeV. Measured unidirectional spectra and yields from thick targets. Deduced total integrated neutron yields above 10 MeV. Compared spectra with intranuclear-cascade model.

Differential cross sections have been measured over a wide range of angles for the well resolved and/or strongly excited peaks in the inelastic proton spectra from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ targets. Inelastic analyzing powers were also measured for the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ transitions. Microscopic distorted-wave impulse approximation analyses of the $2_1$${}_{}{}^{+}{}_{}{}^{}\mathrm{transitions}$ in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ yield values for the ratio $\frac{B\left(N2\mathrm{}\right)\mathrm{}}{B\left(E2\mathrm{}\right)\mathrm{}}$. Collective-model distorted-wave Born-approximation calculations for the high-spin levels at 8.85 and 9.24 MeV in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ suggest spin and parity assignments of $6^{+}$ and $5^{-}$, respectively.

NUCLEAR REACTIONS ${}_{}{}^{40,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$($\overrightarrow{p}$,$p^{\prime }$); measured $\sigma \left(\theta \right)$, $A\left(\theta \right)$; deduced optical-model parameters, $B\left(N2\mathrm{}\right)\mathrm{}$, DWBA analysis.