The partial cross sections for production of protons in high-energy proton-nucleus collisions are estimated using the conservation of baryon number constraint on semiempirical cross-section formulas.

NUCLEAR REACTIONS Deduce $\sigma$ for protons in high-energy proton-nucleus ($6<~A<~60$) collisions.

The Dirac equation employing an impulse approximation optical potential based on $\mathrm{NN}$ phase shifts has been shown to provide a description of the intermediate energy proton-nucleus spin-dependent elastic scattering data not yet found in the context of a Schrödinger approach. Using analytic methods generalized to the Dirac equation, we trace this success to the nonlinear density contributions which arise as a natural consequence of the Dirac approach. This new understanding resurrects the hope of using intermediate energy protons as a probe of nuclear structure details.

NUCLEAR REACTIONS Intermediate energy. Dirac impulse approximation, Dirac-eikonal amplitude, analytic methods, the Dirac approach and nuclear structure.

The energy spectrum and deexcitation pattern of ${}_{}{}^{218}{}_{}{}^{}\mathrm{Ra}$ cannot be explained within the interacting boson approximation unless $g$ bosons are included. This is done by restricting the basis to fully aligned states. The framework developed is applicable to any situation in which a vibrational pattern prevails.

NUCLEAR STRUCTURE Interacting boson approximation with high-spin bosons. ${}_{}{}^{218}{}_{}{}^{}\mathrm{Ra}$ calculated energy levels and $\frac{B\left(E1\mathrm{}\right)\mathrm{}}{B\left(E2\mathrm{}\right)\mathrm{}}$ branching ratios.

Proton emission from $\Lambda$-stable coherent (${\mathrm{K}}^{-}$, ${\pi }^{-}$) hypernuclear excitations populates low-lying levels in the daughter hypernucleus, which subsequently decay by $\gamma$ radiation. The calculation of relative yields for such proton emission is outlined and illustrated for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and the significance of the corresponding $\gamma$ lines in ${}_{\Lambda }{}^{15}{}_{}{}^{}\mathrm{N}$ and ${}_{\Lambda }{}^{13}{}_{}{}^{}\mathrm{C}$ is discussed.

NUCLEAR STRUCTURE Hypernuclei; gamma transitions in light hypernuclei; spin dependence of $\Lambda N$ interaction.

We generalize Kramers's rate expression for diffusion over a potential barrier to the case of a diffusion problem for $n$ degrees of freedom. These can be thought of as the shape degrees of freedom of a fissioning nucleus. We present our formula for the fission width and discuss its dependence on the parameters—the mass tensor, the friction tensor, and the shape of the potential landscape.

NUCLEAR REACTIONS, FISSION Diffusion, transition state method.

The reaction ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\mathrm{p}, \gamma ){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ has been investigated in the energy range $E_{\mathrm{p}}=0.07-2.20\mathrm{}$ MeV. The broad resonant structure previously observed in the ground state transition near $E_{\mathrm{p}}=1.2\mathrm{}$ MeV has been seen also in $\gamma$-ray transitions to excited states. The observed excitation functions as well as the $\gamma$-ray angular distributions can be explained by assuming several broad overlapping resonances. The low-energy data ($E_{\mathrm{p}}<0.6\mathrm{}$ MeV) reveal the existence of two $s$-wave resonances at $E_{\mathrm{p}}=0.010\mathrm{} \mathrm{and} 0.56$ MeV. Spectroscopic factors for several final states have been obtained from observation of direct capture processes to them; they are in fair agreement with results from stripping reaction studies. The present data also provide information on partial and total widths of the states at $E_x=8-9\mathrm{}$ MeV. The energy range investigated corresponds to the temperature range of $T=(0.01-5)\mathrm{}\times {10}^9$ K. The thermonuclear reaction rates deduced from the present results are compared with previously reported values.

NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\mathrm{p}, \gamma )$, $E_{\mathrm{p}}=0.07-2.20\mathrm{}$ MeV; measured $\gamma$ yield for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ states up to $E_x=10.7\mathrm{}$ MeV. Deduced resonance parameters, branching ratios, and direct capture contributions for proton-unbound states; deduced spectroscopic factors, $\frac{{\Gamma }_{\gamma }}{{\Gamma }_{\mathrm{tot}}}$, and ${\Gamma }_{\mathrm{tot}}$ for several $\alpha$-unbound states. Calculated thermonuclear reaction rate for $T=(0.01-5)\mathrm{}\times {10}^9$ K.

Elastic and inelastic proton differential cross sections for excitation of the following levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$: $2_1^{+}$(4.43 MeV), $4_1^{+}$(14.08 MeV), $0_2^{+}$(7.65 MeV), and $3_1^{-}$(9.64 MeV) have been measured at three incident energies between 30 and 40 MeV. The data have been described by coupled channel calculations and form factors obtained by coupling surface vibrations to static deformations. The reproduction of the $0_2^{+}$ state data, if this state is assumed to be a $\beta$-vibrational state, requires a quadrupole $\beta$-vibrational amplitude which is 57% of the static quadrupole deformation and a mixing of the breathing mode of the nucleus with an amplitude that would correspond to about 1% of the $E0\mathrm{}$ energy weighted sum rule. For the $3_1^{-}$ state it is found that the performed calculations are sensitive to the $K$ projection, with the angular distribution of the $3_1^{-}$ state being better fitted assuming $K^{\pi }=3^{-}$ band. Coupled channel calculations using microscopic form factors obtained from wave functions generated using the resonating group method have also been performed and are compared to the experimental data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(p,p′), $E_{\mathrm{p}}=29.95, 35.2, \mathrm{and} 39.9$ MeV; measured $\sigma (E_x, \theta )$; compared with coupled channel analyses using rotor-vibrator model and microscopic $3-\alpha$ cluster wave functions; deduced coupling parameters.

It is argued that the pion mediated interaction between two nucleon chiral bags should lead to changes in bag radii, relative to the value for an isolated nucleon if bag shapes are maintained. These changes are calculated as a function of the separation distance for several nucleon spin-isospin states, with the isolated nucleon size and compressibility regarded as parameters. Sizeable radius changes are found for typical values of these parameters, and for separations probed in medium energy (≳70 MeV) nucleon-nucleon collisions.

NUCLEAR REACTIONS Chiral bag pair; static approximation; spherical deformation calculated as function of separation.

A study of nonrelativistic resonating group method quark exchange kernels shows that even large changes in the relative [6] and [42] space symmetry of the six-quark system do not make significant changes in the extreme short range parts of the NN interaction. The repulsive core heights of equivalent local potentials derived by the Wentzel-Kramers-Brillouin approximation from the Wigner transform of the quark exchange kernels are changed by only ∼20% under a large change in the relative [6] and [42] space symmetry of the antisymmetrized internal six-quark resonating group method wave function.

NUCLEAR REACTIONS Six-quark model, NN interaction, equivalent local potentials via WKB and Wigner transforms.

The excitation of a many-body system by a time-dependent perturbation is considered within the framework of functional integration. The stationary phase approximation to a functional-integral representation of the final expectation values of many-body observables in the interaction picture leads to a new time-dependent mean-field theory. The resulting equations of motion depend upon the observable itself and consequently are nonlocal in time. The method is illustrated by an analytically soluble application to the forced harmonic oscillator.

NUCLEAR REACTIONS Functional integral representation of expectation values of many-body observables. Stationary phase approximation. Time-dependent mean fields.

A single parameter set was adopted for the hybrid and geometry dependent hybrid models. The nuclear density profile was modified for consistency with results of the Myers nuclear droplet model. Optical model parameters were modified to give better global results for inverse reaction cross sections in the precompound energy range up to 90 MeV. Two types of multiple precompound decay processes are defined, and the more important of the two is incorporated into the precompound decay formalism. This results in two to five orders of magnitude improvement in predicting ${}_{}{}^{202}{}_{}{}^{}\mathrm{Hg}$(p,2p) and ${}_{}{}^{202}{}_{}{}^{}\mathrm{Hg}$(p,2pn) product yields for proton energies up to 86 MeV. The global parameter set and formulation of this work is compared with (n, $x\mathrm{n}$) and (n,p) spectra for 14 MeV incident neutrons, for (p,n) spectra with 18-90 MeV protons, and with (p,p′) spectra for 39-90 MeV protons. The geometry dependent hybrid model gives the better overall agreement, in most cases within the 20-30% limit of significance attached to the model. Some discussion is given of methods by which the calculations might be further improved.

NUCLEAR REACTIONS Hybrid, geometry dependent hybrid precompound decay models, improve global parameter set, implement multiple precompound decay. Test new formulation vs spectra from reactions induced by 14 MeV neutrons to 90 MeV protons.

Data for the inclusive (n, $\mathrm{p}x$) reaction for 60 MeV neutrons on ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$ are presented. Angular distributions for $Q$-value bins show a decrease of the forward peaking of the proton emission with increasing neutron excess. A marked dependence of the angle integrated spectra on ($N-Z$) is observed. The data are compared to hybrid and geometry dependent hybrid model calculations. Although these results predict the general shape of the spectra, they do not account for ($N-Z$) dependence. A neutron skin, as given by a hydrodynamic model, is added to the geometry dependent hybrid model, which predicts a higher precompound decay for high impact parameters. These results agree much better with the $N-Z$ dependence of the data.

NUCLEAR REACTIONS ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$(n,p), ${\epsilon }_{\mathrm{n}}=60\mathrm{}$ MeV, measured $\frac{d\sigma }{d\Omega }$, $\frac{d\sigma }{d\epsilon }$; analyze via hybrid and geometry dependent hybrid models; explore importance of neutron skin.

Angular distributions of the analyzing power $A_y(\ominus )$ have been measured for elastic scattering of neutrons from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$ at 10 and 14 MeV and for inelastic scattering to the first $2^{+}$ state of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ at 10 MeV. We have combined the results with previous measurements and analyses of the differential cross sections in the same energy range and have carried out new deformed optical model calculations where the major concern was to study the spin-orbit interaction. The need for an imaginary spin-orbit term $W_{\mathrm{SO}}\mathrm{}\left(r\right)\mathrm{}$ is discussed. The (n, n′) data are important in reducing an ambiguity found between the deformation ${\beta }_{\mathrm{SO}}$ of the real spin-orbit potential and the strength $W_{\mathrm{SO}}$ of the imaginary spin-orbit potential.

NUCLEAR REACTIONS ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$(n,n), $E=10, 14$ MeV; ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$(n,n′), $E=10\mathrm{}$ MeV. Measured $A_y(E, \theta )$. Deduced deformed complex spin-orbit potentials. Coupled channels calculations.

In-beam gamma ray spectroscopy studies have been performed to deduce the level structure of ${}_{}{}^{99}{}_{}{}^{}\mathrm{Ru}$ and ${}_{}{}^{101}{}_{}{}^{}\mathrm{Ru}$ below 3 MeV in excitation energy produced via the $\alpha$, n reaction. Excitation functions between 10.0 and 18.0 MeV bombarding energy, together with $\gamma -\gamma$ coincidence and angular distribution measurements, were carried out to determine the level energies and spins. The results are compared to previous work and to the available theoretical calculations.

NUCLEAR REACTIONS ${}_{}{}^{96,98}{}_{}{}^{}\mathrm{Mo}(\alpha , \mathrm{n}){}_{}{}^{99,101}{}_{}{}^{}\mathrm{Ru}$ $E=10-18\mathrm{}$ MeV; measured $E_{\gamma }$, $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions; ${}_{}{}^{99,101}{}_{}{}^{}\mathrm{Ru}$ deduced levels, $J^{\pi }$; enriched targets, Ge(Li) detectors.

The forward scattering cross section at $\theta =1\mathrm{}° \mathrm{and} 1.7°$ of $E=4-10\mathrm{}$ MeV monoenergetic photons from Pb and Bi targets has been measured. The photon beam was obtained from the $\mathrm{Fe}(\mathrm{n}, \gamma )$ reaction. The elastic cross section at such angles, being dominated by Rayleigh and Delbruck scattering processes, was measured relative to the Compton cross section. The fact that one of the $\gamma$ lines of the $\mathrm{Fe}(\mathrm{n}, \gamma )$ reaction happens to overlap the 7.28 MeV level in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, yielding a strong nuclear resonance fluorescence signal, enabled us to observe, for the first time, an interference effect with the Rayleigh and Delbruck scattering processes. A theoretical expression of the nuclear resonance scattering amplitude for the specific case of the random photoexcitation process is derived. The interference effect of this latter process with Rayleigh and Delbruck scattering is calculated and an excellent agreement with measured values is obtained.

NUCLEAR REACTIONS Pb, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(\gamma , \gamma )$, $E=4.2-9.3\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, Delbruck and Rayleigh scattering, nuclear resonance fluorescence, interference effects.

The exciton model for the pre-equilibrium emission of light composite particles proposed and applied to the (p, $\alpha$) reaction of Iwamoto-Harada is further investigated for the energy spectra of the (p,d), (p,t), and (p,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions with incident energy of several tens of MeV's. Calculated results could reproduce an overall feature of those spectra. The dominance of the pickup-type contribution which occurs in the course of the equilibration process was found to be common for all composite particles. The degree of fitting to the data is excellent for (p,t) reactions to the same extent as for (p, $\alpha$) reactions, and is somewhat less for the high energy part of energy spectra of (p,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) and (p,d) reactions. The relative ratio of yields of high energy composite particles was also reproduced fairly well with our model. These facts suggest that the simple reaction mechanism assumed in our model accounts for characteristics of the pre-equilibrium emission of light composite particles.

NUCLEAR REACTIONS Exciton model, composite particle emission mechanism; (p,d), (p,t), (p,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) on ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$; calculated energy spectra.

Energy and angular distributions of neutrons, protons, and alpha particles were measured in coincidence with the projectilelike fragment in deep inelastic collisions of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ on ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$ at 102 and 142 MeV. Using an event-by-event analysis which takes into account particle emission from both fragments and the recoil correction due to light particle emission, we show that our data are consistent with the assumption that the light particles are evaporated in the rest frame of the fully accelerated projectilelike and targetlike fragments. This conclusion is based on the results for neutrons and alpha particles. But because of kinematic limitations which affect the alpha particle data, the conclusions based on the latter are less definitive.

NUCLEAR REACTIONS ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, X)$, $E=102, 142$ MeV, measured n, p, $\alpha$ in coincidence with projectilelike fragment; deduced c.m. energy spectra and multiplicities of the light particles. Results consistent with evaporation from the heavy fragments.

Differential cross sections for the production of $Z=1, 2$ particles are measured for 52, 100, and 147 MeV/nucleon ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ projectiles. The projectile energy and target-mass dependencies are examined and compared with measurements in other projectile energy regimes. Central and peripheral collisions are found to give comparable contributions to the light ion yields, with the dominant process varying with the emission angle. The spectra are parametrized both in terms of a single heated, moving source and as a sum of fragmentation and central collision sources, and velocity and temperature parameters are presented. For composite particles, coalescence parameters and source radii are also extracted.

NUCLEAR REACTIONS $\mathrm{Ni}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, X)$, $E=0.8, 1.6, 2.4$ GeV;$\mathrm{Au}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, X)$, $E=1.6, 2.4$ GeV; Al, $\mathrm{Sn}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, X)$, $E=1.6\mathrm{}$ GeV; measured $\sigma (E, \theta )$ for $X=\mathrm{p},\mathrm{d},\mathrm{t}, {}_{}{}^3{}_{}{}^{}\mathrm{He}, {}_{}{}^4{}_{}{}^{}\mathrm{He}$; deduced model parameters.

Subject to the assumption that sub-barrier fusion is described by an effective one-dimensional energy-independent local potential barrier, the Jeffreys-Wentzel-Kramers-Brillouin approximation for the fusion cross sections is inverted to determine this effective potential. Potential barriers, with their associated experimental errors, are presented for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and the assumption of a local effective potential is shown to be inadequate for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$+${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$.

NUCLEAR REACTIONS Inversion formula relating fusion cross sections to ion-ion potential.

The quadrupole moments were determined by means of Coulomb excitation experiments. Highly enriched targets were bombarded with 53 MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions. Elastically and inelastically scattered ions were detected in a split pole spectrograph. The results are in good agreement with muonic x-ray data.

NUCLEAR REACTIONS ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$′); ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$′); $E=53\mathrm{}$ MeV, ${\theta }_{\mathrm{lab}}=143\mathrm{}°$; measured $\frac{{\sigma }_{\mathrm{el}}}{{\sigma }_{\mathrm{ine}}}$. Enriched targets. Coupled channel semiclassical and quantum mechanical analysis.