In ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(t,p)\mathrm{}$ at $E_t=15\mathrm{}$ MeV, sixteen angular distributions were measured for states to $E_x=7.1\mathrm{}$ MeV. Comparison with distorted-wave Born approximation calculations using empirical wave functions has been made, enabling extraction of absolute normalizations. Twenty-one higher-lying levels have had their excitation energies determined.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(t,p)\mathrm{}{}_{}{}^{18}{}_{}{}^{}\mathrm{O}$; $E=15\mathrm{}$ MeV; measured $\sigma (E_p,\theta )$, $\theta =7.5\mathrm{}°-105°$. ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ levels. DWBA microscopic analysis.

We study the limit of many equivalent channels in the entropy approach to nuclear reactions. A third order phase transition appears at the crticial point $\overline{S}=0.5\mathrm{}$, where $\overline{S}$ is the optical $S$ matrix. Analytic expressions are given for the fluctuation cross sections in this limit and we find excellent agreement with the exact results for $N$, the number of open channels, as small as 10. We also find good agreement with other theories except in the limit of no absorption $\overline{S}=1.0\mathrm{}$.

NUCLEAR REACTIONS Fluctuating cross sections and enhancement factors from maximum entropy. Equivalent channels.

Recently developed Padé approximant techniques are applied to two sets of ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\mathrm{NN}$ scattering data. In the first, the unconstrained ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\mathrm{np}$ phase shifts of MacGregor et al. are used to generate a scattering function, $F\left(k^2\right)=kcot\left({\delta }_0\right)$, which is fitted with high precision. A six-parameter [3/2] Padé fit gives four terms of the effective range expansion; the resulting Marchenko-type potential is expressible as the sum of a Yukawa one-pion-exchange potential and a shorter range part, the repulsion peaking at the origin at near 4 GeV. In a second application, Padé fits are made to the scattering function of the Reid soft-core potential. The [3/2] approximant which fits $F\left(k^2\right)$ through the wave numbers consistent with the Lambert, Corbella, and Thomé criterion, to $k=2.5\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$, leads to a potential with a core height of 4.6 × ${10}^4$ GeV. In both [3/2] potentials the volume integrals are large and negative, and cannot be made positive by adjoining more repulsive high energy phase shifts. By application to the Reid soft-core potential the Padé formalism is shown to generate useful [$\frac{L}{L-1\mathrm{}}$] Padé approximants with increasing $L$. The analytic structure of $F\left(k^2\right)$ beyond $k=224\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$ is used in the construction of higher Padé approximants that (a) satisfy the Lambert, Corbella, and Thomé criterion and (b) might lead to saturation.

NUCLEAR REACTIONS Padé approximants used to solve inverse scattering problem for $\mathrm{NN}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phase shifts; effective range expansion and short range repulsion computed.

New data (cross section, polarization, Wolfenstein parameters, and spin-correlations) on proton-proton and neutron-proton scattering have been recently published by differenc groups. These include high precision and/or original measurements covering the energy range $6 \mathrm{MeV}<T_{\mathrm{lab}}<800\mathrm{} \mathrm{MeV}$. A direct comparison of these data with the values produced by the Paris $\mathrm{NN}$ potential for energies $T_{\mathrm{lab}}<350\mathrm{}$ MeV is reported here. The agreement between theory and experiment is very satisfactory both for low and medium energies. The total ${\chi }^2$ for the world $\mathrm{NN}$ data set for $T_{\mathrm{lab}}<350\mathrm{}$ MeV is also reported and compared with those given by the phase shift analysis of Arndt et al. and by the phenomenological Reid soft-core potential.

NUCLEAR REACTIONS Nucleon-nucleon interaction, comparison of the Paris $\mathrm{NN}$ potential predictions with new experimental data.

Elastic and inelastic scattering of $\alpha$ particles on the deformed nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are investigated in the range of incident $\alpha$-particle energies of 9 to 11 MeV by using the coupled-channel method with an orthogonality condition. A doubly folded potential generated by the shell model wave functions of the $\alpha$ particle and the deformed nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is employed for the relative motion between the $\alpha$ particle and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Good agreement between theory and experiment is obtained for the elastic and inelastic angular distributions and the resonance structures. It is found, from the Born series expansion of the $T$ matrix, that the orthogonality constraint stresses the effects of the channel coupling between the elastic and inelastic processes, and it indicates that the distorted-wave Born approximation does not work well in this system.

NUCLEAR REACTIONS Elastic and inelastic scattering of $\alpha$ particles on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; coupled-channel orthogonality condition model, folded potential; calculated angular distributions and phase shifts, resonances of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; Born series of $T$ matrices.

Sixty-seven levels of ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ have been observed with ≅12 keV resolution via the ($p,d$) reaction at 25 MeV and spectroscopic factors have been extracted for most of them. Among these levels, 34 were previously unobserved and it was possible to propose parity and spin limits for 13. The ($p,d$) study was complemented by a cursory investigation of the ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}(p,\alpha ){}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ reactions at, respectively, 36 and 25 MeV and use was made in some cases of the results of a previous ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}\mathrm{}(p,t)\mathrm{}{}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ study at 26 MeV. The most striking results are the appreciable population of the $4_2^{+}$ level in the ($p,d$) reaction, $\frac{C^2{S}_{4_2^{+}}}{C^2{S}_{4_1^{+}}}=50\mathrm{}$, $\frac{C^2{S}_{4_2^{+}}}{C^2{S}_{0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+}}}=0.5\mathrm{}$, and of the $0_2^{+}$ level in the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reaction, $\frac{C^2{S}_{0_2^{+}}}{C^2{S}_{0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+}}}=0.45\mathrm{}$, showing the existence of appreciable particle components in these levels generally described as collective.

NUCLEAR REACTIONS ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}\mathrm{}(p,d)\mathrm{}$, $E=25\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ deduced levels, $l$, $J$, $\pi$, $S$; DWBA analysis. ${}_{}{}^{193}{}_{}{}^{}\mathrm{Ir}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$, $E=36\mathrm{}$ MeV; ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}(p,\alpha )$, $E=25\mathrm{}$ MeV; deduced levels. Enriched targets, magnetic spectrometer.

Nineteen levels up to 5.1 MeV in ${}_{}{}^{52}{}_{}{}^{}\mathrm{Ti}$ and 52 levels up to 4.7 MeV in ${}_{}{}^{53}{}_{}{}^{}\mathrm{V}$ have been identified using the ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}\mathrm{}(t,p)\mathrm{}$ and ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(t,p)\mathrm{}$ reactions. Measured angular distributions were compared with results of distorted-wave Born-approximation calculations. In ${}_{}{}^{52}{}_{}{}^{}\mathrm{Ti}$, the experimental angular distributions agree with distorted-wave Born-approximation shapes for four states whose $J^{\pi }$ values were previously known. For six levels we make clear $L$ (and hence $J^{\pi }$) assignments, and we present tentative assignments for six additional levels. In ${}_{}{}^{53}{}_{}{}^{}\mathrm{V}$, no discrepancies were found between spin assignments suggested in earlier studies and the spin limitations imposed by the $L$ values extracted from the ($t,p$) angular distributions. The present results along with the experimental results from an earlier ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}\mathrm{}(t,p)\mathrm{}{}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ study were used to test mixed-configuration shell-model calculations for the three residual nuclei. The agreement between the experimental and predicted level schemes is good up to 1.5 MeV, but above this energy a number of levels are present which are not predicted by the calculation. The shell-model wave functions were also used to calculate spectroscopic amplitudes for two-nucleon transfer reactions. In all three residual nuclei, fair agreement is found between the experimental strengths and the strengths predicted by the calculations.

NUCLEAR REACTIONS ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}\mathrm{}(t,p)\mathrm{}{}_{}{}^{52}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(t,p)\mathrm{}{}_{}{}^{53}{}_{}{}^{}\mathrm{V}$, $E_t=15\mathrm{}$ MeV, $\sigma (\theta ,E_p)$, DWBA analysis; ${}_{}{}^{52}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{53}{}_{}{}^{}\mathrm{V}$ deduced $L$, $J$, $\pi$, enhancement factors; shell-model calculations; ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$, DWBA analysis, deduced enhancement factors.

The ($p,t$) reaction has been used to study the behavior of two-neutron holes in the even Sm isotopes at high excitation energy. The tritons were analyzed with a counter telescope, quadrupole-dipole-dipole-dipole spectrograph, and an Enge split-pole spectrograph. Both broad and narrow structures are observed at excitation energies above 5 MeV. Some of these can be interpreted in terms of the low-energy structure of ${}_{}{}^{142}{}_{}{}^{}\mathrm{Sm}$.

NUCLEAR REACTIONS ${}_{}{}^{144,148,150,152,154}{}_{}{}^{}\mathrm{Sm}\mathrm{}(p,t)\mathrm{}$, $E_p=42\mathrm{}$ MeV; enriched targets, QDDD, Enge split-pole spectrograph. Measured $\sigma (E_t,{\theta }_t)$. Deduced ${}_{}{}^{142}{}_{}{}^{}\mathrm{Sm}$ levels $E$, $J$; relate ${}_{}{}^{142}{}_{}{}^{}\mathrm{Sm}$ levels to high-energy structure in heavier Sm isotopes.

Triton spectra from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-induced reactions on ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ targets at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=130\mathrm{}$ MeV have been measured in the $7.5°\le {\theta }_L\le 24°$ angular range in 1.5° steps. The spectra exhibit a broad structure; the centroid energy $E_c$ and the full width at half maximum $\Gamma$ of this "bump" are found to be independent of the target mass number $A$. Their average values are ${\overline{E}}_c=87\mathrm{}$ MeV and $\overline{\Gamma }=48\mathrm{}$ MeV with estimated errors of about ±2 MeV in both cases. Within the error bars the bump cross section is found to be consistent with $A^{\frac{1}{2}}$ proportionality and tends to decrease exponentially with angle; however, $A^{\frac{1}{3}}$ dependence cannot be excluded. In addition, the angular distributions possibly show indications for a weak oscillation pattern.

NUCLEAR REACTIONS $X({}_{}{}^3{}_{}{}^{}\mathrm{He},t)$, $X={}_{}{}^{27}{}_{}{}^{}\mathrm{Al}, {}_{}{}^{59}{}_{}{}^{}\mathrm{Co}, {}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}, {}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$; $E=130\mathrm{}$ MeV; measured $\frac{d^2\sigma (\epsilon ,\theta )}{d\epsilon d\Omega }$; deduced $\frac{d\sigma \left(\theta \right)}{d{\Omega }_L}$, $\Gamma$ (FWHM) and centroid energy $E_c$ of the broad structure.

The cross section and average $\gamma$-ray multiplicity $〈M〉$ were measured for reactions of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ leading to specific $\mathrm{xn}$ and $\alpha \mathrm{xn}$ final channels at five ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ energies from 111 to 168 MeV. For the $6n$, $7n$, and $8n$ channels the cross sections show nonstatistical tails and $〈M〉$ saturates at high energies, indicating that emission of one or more fast neutrons is occurring. The $〈M〉$ data suggest that the partial waves involved in this nonstatistical behavior are predominantly peripheral. Consideration of all available $〈M〉$ data from this and other systems indicates that a strong correlation exists between the structure of the projectile and the first appearance of nonstatistical emission of neutrons and alpha particles. The generalized critical angular momentum model of incomplete fusion is extended, providing successful predictions for all data of the energy at which nonstatistical neutron emission sets in and of the energy variation of $〈M〉$ in the various $\mathrm{xn}$ exit channels.

NUCLEAR REACTIONS ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},xn\gamma ){}_{}{}^{170-x}{}_{}{}^{}\mathrm{Yb}$, $x=5\mathrm{}-11$, ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha \mathrm{xn}\gamma ){}_{}{}^{166-x}{}_{}{}^{}\mathrm{Er}$, $x=4\mathrm{}-10$, $E=111.1, 126.4, 141.1, 155.4, 168.4$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, average and standard deviation of $\gamma$-ray multiplicity distributions, average $\gamma$-ray energies; deduced onset of nonstatistical neutron emission, systematics of $\gamma$-ray multiplicity, incomplete fusion.

Neutron time-of-flight spectra and angular correlations were obtained in coincidence with $\gamma$ rays characteristic of the $\mathrm{xn}(x=8,9,10\mathrm{})\mathrm{}$ and $\alpha \mathrm{xn}(x=7,8\mathrm{})\mathrm{}$ fusion-like products in reactions of 151.9 MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ with ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$. The spectra at all angles (20°, 70°, 100°, 151°) clearly indicate the presence of nonequilibrium neutron emission. The energy spectra can be represented in terms of isotropic emission in the rest frames of two moving sources. The slower of these moves with the speed of the center of mass; its emission corresponds to a temperature of ∼1.7 MeV. The faster source, characterized by a temperature of 5 to 6 MeV, has a velocity of ∼0.4 of that corresponding to the projectile energy above the Coulomb barrier. The yield of fast neutrons as a function of the exit channel is found to be in good agreement with the predictions of an extended incomplete fusion model. Comparisons are made with other models that lead to emission of fast neutrons.

NUCLEAR REACTIONS ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},xn){}_{}{}^{170-x}{}_{}{}^{}\mathrm{Yb}$ $x=8\mathrm{}-10$; ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha xn){}_{}{}^{166-x}{}_{}{}^{}\mathrm{Er}$, $x=7,8\mathrm{}$; $E=151.9\mathrm{}$ MeV; measured $\sigma (E_n,{\theta }_n)$; deduced temperatures, source velocities and yields of equilibrium and pre-equilibrium neutrons, interaction times; compared with incomplete fusion, PEP, and hot-spot models.

The single and mutual inelastic scattering of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to its first excited state has been studied using the technique of particle-$\gamma$ angular correlations. Several angles of observation of the $\gamma$ ray have been employed as well as a wide range of closely-spaced scattering angles for the particles. $\gamma$ rays were detected both in and out of the reaction plane. Measurements made at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=14.5, 18.75, 24.25, 28, \mathrm{and} 30$ MeV have been compared with theoretical predictions calculated assuming an isolated resonance with total angular momentum equal to the grazing partial wave in the entrance channel. In addition, detailed comparisons have been made with the predictions of distorted-wave Born approximation (DWBA) and coupled channels calculations. The results at the various $\gamma$-ray angles are internally consistent, suggesting that the participating reaction amplitudes are fairly well determined from the data. Nevertheless, a completely model-independent description of the reaction mechanism has not been achieved. The comparisons with model calculations indicate that previous speculations concerning the dominant partial waves in these peripheral reactions are probably correct, but none of the specific models considered is able to give a quantitative account of the observed angular correlations. In particular, comparison with the band-crossing model reveals that this model predicts the dominance of a single partial wave to an extent not substantiated by the experimental data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$,${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$,$E_{\mathrm{lab}}=29\mathrm{}-64$ MeV, measured particle-$\gamma$ angular correlations, compared results to predictions of nuclear reaction models.

Elastic scattering of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$,${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at $E_{\mathrm{lab}}=50,60,80,90,\mathrm{and} 100$ MeV was measured in an angular range of $10°<{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}<75\mathrm{}°$. Results were compared with optical model calculations for a variety of optical model potentials. Predictions of the liquid drop, proximity, and folding models were also examined. Reduced absorption and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ cluster exchange phenomena are discussed. Total reaction and fusion cross sections are extracted. The volume integrals of potentials were applied in the optical potential ambiguity treatment and for classifying purposes.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$,${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$); $E=50,60,80,90,\mathrm{and} 100$ MeV; measured $\sigma \left(\theta \right)$, deduced optical model parameters; applied volume integrals of optical potentials; extracted reaction and fusion cross sections.

Inclusive $\gamma$ spectra from the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ interaction have been measured using 55- and 85-MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ions. The identification of $\gamma$ lines allows the determination of mass spectra in the region $12\le A\le 43$. Experimental results are compared with statistical model calculations. The total reaction and fusion cross sections are extracted. Cross sections for inelastic scattering, few nucleon transfers, and deep inelastic scattering are estimated.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_{\mathrm{lab}}=55, 85$ MeV; measured mass spectra for $12<~A<~44$, ${\sigma }_{\mathrm{reaction}}$, ${\sigma }_{\mathrm{fusion}}$; estimated cross sections for inelastic scattering, few nucleon transfer and deep inelastic processes; deduced $l_{\mathrm{cr}}$ values.

The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(E_{\mathrm{lab}}=106\mathrm{} \mathrm{and} 167 \mathrm{MeV})+{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ heavy-ion reaction is analyzed in terms of a modified version of the semiclassical scattering model of Broglia followed by an evaporation calculation. The deflection and energy loss functions are taken from recent time dependent Hartree-Fock calculations. The complete fusion amplitude vs the angular momentum $l$ is obtained phenomenologically. A comparison between the model predictions and experiment is made for the following quantities: the total integrated cross sections for production of a fragment with given $Z$, $\sigma \mathrm{}\left(Z\right)\mathrm{}$; energy distributions ${\left(\frac{d^2\sigma }{d\Omega \mathrm{dE}}\right)}_Z$ at fixed laboratory angle and fragment charge; angular distribution ${\left(\frac{d\sigma }{d\Omega }\right)}_Z$ at fixed fragment charge $Z$ and integrated over energy. The agreement is satisfactory. It is noted that the $Z$ spread observed in this reaction can be described by using only evaporation effects in the highly excited reaction fragments produced in the original inelastic collision.

NUCLEAR REACTIONS Theoretical analysis of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reactions at $E=106\mathrm{} \mathrm{and} 167$ MeV. Semiclassical scattering model. Deflection and energy loss functions calculated from time dependent Hartree-Fock. Evaporation effects included.

It is suggested that preequilibrium $\alpha$ particles detected in recent experiments arise from a process of delayed fragmentation. This mechanism is discussed, and it is shown to compete successfully with alternative mechanisms in explaining $\alpha$-particle detection in coincidence with heavy fragments for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ collisions at 310 MeV lab.

NUCLEAR REACTIONS Preequilibrium $\alpha$ emission; delayed fragmentation; ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha )X$, $E=310\mathrm{}$ MeV.

In fragmentation reactions of the type ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}+ \mathrm{target}\to {}_{}{}^{15}{}_{}{}^{}\mathrm{O}+X$, the momentum distribution of the outgoing fragment ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ reflects the momentum distribution of the nucleon which is removed from the surface of the projectile nucleus. We derive a relation using Glauber's multiple scattering theory and the Wigner transform of the one-body density matrix. The experimental cross section at 2 GeV/nucl is analyzed with the following result: The uniform and local Fermi-gas models fail to reproduce the momentum distribution on the surface. The shell model with harmonic oscillator wave functions is correct for momenta below the Fermi momentum. Hartree-Fock wave functions describe the data up to 350 MeV/c.

NUCLEAR REACTIONS Heavy ions, relativistic energies; fragmentation reactions; relation to nuclear momentum distribution on the surface.

On the basis of conventional nuclear fluid dynamics, we study the sensitivity of high-energy heavy-ion collisions to a density isomer in the nuclear equation of state, as well as to a variation in the nuclear compressibility coefficient. Our equation of state is a new functional form which has the property that the speed of sound approaches the speed of light in the limit of infinite compression. The equations of relativistic nuclear fluid dynamics are solved numerically in three spatial dimensions by use of a particle-in-cell finite-difference computing method for the reaction ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ at a laboratory bombarding energy per nucleon of 393 MeV. By integrating over the appropriate ranges of impact parameter, we compute the double-differential cross section $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$ corresponding both to all impact parameters and to central collisions constituting 15% of the total cross section. To within numerical uncertainties, the results for the various equations of state are very similar to one another except for central collisions at laboratory angle $\theta =30\mathrm{}°$ and for both central collisions and all impact parameters at $\theta =150\mathrm{}°$. In these cases, over certain ranges of energy, $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$ is larger for the density isomer than for conventional equations of state. The results calculated for all impact parameters are compared with the experimental data of Sandoval et al. for outgoing charged particles.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, $\frac{E_{\mathrm{bom}}}{20}=393\mathrm{}$ MeV; calculated $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$ for outgoing charged particles for all impact parameters and for central collisions. High-energy heavy-ion collisions, relativistic nuclear fluid dynamics, nuclear equation of state, density isomer, particle-in-cell finite-difference computing method.

For ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ beam energies of 2 MeV, $\alpha -\alpha$ coincidence measurements show a large, narrow peak due to the direct reaction $2{}_{}{}^6{}_{}{}^{}\mathrm{Li}\to 3\alpha$, where both ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nuclei contribute one deuteron to make the third $\alpha$ particle. The large volume of three-body phase space allows the various parts of the reaction process to be separated from each other. Excellent fits to the data were obtained using a three-body, extended-range, distorted-wave Born-approximation model. Elastic scattering potentials for the calculation were generated by the double-folding technique in combination with ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ + ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ elastic scattering measurements for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ beam energies from 2 to 5.5 MeV.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$)${}_{}{}^4{}_{}{}^{}\mathrm{He}$${}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E=2\mathrm{}$ MeV; DWBA analysis. ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$), $E=2.0\mathrm{}-5.5$ MeV; fitted $\sigma (\theta ,E)$ with double-folding model potentials.

The energy dependence of the fusion cross section for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ has been studied over the bombarding energy range 80-140 MeV. The gross features of these cross sections are compared with the expectations of entrance channel models and with the results of time-dependent Hartree Fock calculations. A comparison with similar data for the ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ systems gives results which are not inconsistent with a compound nucleus limitation to fusion at high energies. A search for fusion oscillations similar to those found in lighter systems provides some evidence for their occurrence in the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ system.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$; $E_{\mathrm{lab}}=80\mathrm{}-140$ MeV measured evaporation residues, deduced ${\sigma }_{\mathrm{fus}}\mathrm{}\left(E\right)\mathrm{}$. Compared entrance channel, TDHF, and yrast limit models.