The heavy-ion energy-dependent optical potentials for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{Pb}$ system are deduced from a dispersion relation. These potentials are used to analyze the elastic scattering, fusion, and spin distributions of compound nuclei for the system in a unified way based on the direct reaction theory. It turns out that the energy dependence of the optical potential is essential in explaining the data at near- and sub-barrier energies. The real part of the energy-dependent optical potential deduced was also used in calculating the elastic and fusion cross sections by the conventional barrier penetration model using an incoming wave boundary condition. The predictions of the elastic scattering, fusion cross sections, and the spin distributions of compound nuclei are not satisfactory compared with those from the direct reaction approach. It seems to originate from the fact that this model neglects absorption around the Coulomb barrier region.

Calculations are performed for the continuum spectra of protons, deuterons, and tritons emitted from α- and h-induced reactions of the breakup type. It is shown that the sum of the elastic breakup and breakup-fusion contributions fit the major parts of the observed spectra, except for the (α, p) case, where the theory underestimates experiment. It is then shown that the contributions from the quasi-elastic channel, in which T=1 dinucleons are created, account for most of the remaining (α,p) cross section. The quasi-elastic breakup and breakup-fusion are further shown to nicely fit two-proton coincidence data. The question of radial regions where the various modes of reactions dominantly occur is clarified, making it possible to understand why the various modes of reactions explain certain portions of the observed spectra.

Three-body models of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ are used to investigate the structure of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) vertex amplitude. Within the three-body framework, the formalism of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) overlap amplitude is delineated. From this overlap, the formula for the central physical quantity, namely, the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution, is derived. It is shown that the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution satisfies a sum rule consistent with its probability interpretation. The sum rule is used as a check on the numerical calculation of the joint momentum distribution and to isolate terms that contribute insignificantly. By integration of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution over a given range of the nα excitation energy, the momentum distribution of the valence proton in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is obtained. From both the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution and the p-(nα) momentum distribution, the dynamical structure of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) vertex according to three-body models is uncovered.

Three-body models of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nucleus are used to derive the coincidence cross sections for the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(p,2p)nα. It is shown that in the plane-wave impulse approximation, the fourfold differential cross section factorizes in such a way that the ${}_{}{}^6{}_{}{}^{}$Li→p+(nα) joint momentum distribution may be extracted from experimental measurements. The calculated results are compared to data from various ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(p,2p)nα experiments with incident energies ranging from 100 to 460 MeV. Differences between predictions of various three-body models and of various representations of the underlying two-body interactions are examined. It is concluded that meaningful comparisons are possible only if the beam energy is high enough to ensure proton pole dominance and the detector energy resolution good enough to distinguish crucial spectral features.

Three-body models of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ are used to describe the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(e,e’p)nα. Under the impulse approximation, the differential cross section for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(e,e’p)nα reaction with unpolarized particles factorizes into a product of a kinematical factor, the (off-shell) electron-proton cross section, and a distorted spectral function of the ejected proton in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nucleus. A prescription by De Forest is used to carry the ep cross section off the proton mass shell. The spectral function, containing all of the nuclear physics in the reaction, is found from the ${}_{}{}^6{}_{}{}^{}$Li→p+(nα) vertex amplitude. A unified theoretical description of both the bound state and the (nα) scattering state is employed to predict the ${}_{}{}^6{}_{}{}^{}$Li→p+(nα) vertex amplitude. For (nα) relative energies below 16 MeV and proton momenta below 200 MeV/c, the $P_{3/2}$ αN resonance dominates the shape of the spectral function. However, the contribution of the outgoing scattering wave due to the $S_{1/2}$ αN interaction has a significant role for momenta of the (nα) pair below 40 MeV/c, making the 2s orbitals in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ control the behavior of the momentum distribution near zero momentum transfer to the (nα) pair. Recent coincidence experiments give good agreement with theory. Experimental resolutions are currently not quite capable of discriminating between various $S_{1/2}$ αN interactions used in the three-body calculation.

We test the strong approximation of the Mo?ller wave operator scheme in coordinate space for N-N scattering using the local Malfliet-Tjon IV potential. Using spline expansion functions we obtain a finite-dimensional Hamiltonian matrix with a band structure which brings about a considerable numerical advantage when diagonalizing it. We compute the S matrix and find satisfactory agreement with a standard solution. We also compute the violation of energy conservation.

In the framework of the three-nucleon zero-range theory, we have calculated the correlation between the energy of the virtual state of the triton and the doublet neutron-deuteron scattering length. Our results show that the Girard-Fuda plot for the energy of the virtual state as a function of the doublet n-d scattering length is reproduced by this model. We also observe that the plot remains essentially unchanged when the nucleon-nucleon singlet input is varied.

Proton capture reactions on targets of ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ were measured from $E_{\mathrm{p}=20\mathrm{}}$ to 100 MeV. The energy dependence of the ${\theta }_{\gamma }$=60° differential cross sections are presented for captures populating the ground states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Differential-cross-section and analyzing-power angular distributions are presented at bombarding energies of $E_{\mathrm{p}=20.8\mathrm{}}$, 28.35, 49.2, and 49.69 MeV. Calculations from two capture-reaction models are compared to the data.

The electric dipole polarizability of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ is studied theoretically. A consistent interpretation is obtained among the electric dipole polarizability, the quadrupole moment, the tensor analyzing powers for aligned ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ scattering at sub-Coulomb energies, and the radiative capture (or photodis- integration) cross section for the ${}_{}{}^3{}_{}{}^{}$H+α→${\mathrm{}}^7$Li+γ reaction.

A linear expansion analysis of the folding model transition amplitude is used to study the intrinsic sensitivity of the inelastic scattering of intermediate energy nucleons to the radial form of the neutron transition density, given known proton transition densities from electron scattering. Realistic density-dependent effective interactions are used to construct pseudodata. These pseudodata are then reanalyzed and the error matrix is used to calculate an error band for the radial transition density. This approach reveals the sensitivity of the extracted transition density to absorption, medium modifications of the interaction, and the extent and quality of the data in a manner that is largely free of the residual inaccuracies in reaction theory that complicate the analysis of real data. We find that the intrinsic radial sensitivity of nucleon inelastic scattering is best for projectile energies between 200 and 500 MeV, but is adequate to resolve the radial dependence of neutron transition densities even in the interior of heavy nuclei throughout the energy regime 100–800 MeV. We have also compared our method with scale-factor analyses which assume proportionality between neutron and proton densities. For states whose transition densities are similar in the surface, we find scaling to be accurate at the 20% level. However, for light nuclei substantial deviations beyond the first peak of the differential cross section reveal sensitivity to shape differences. This sensitivity is reduced for heavy nuclei. The model dependence of radial densities is also studied. A high-q constraint is used to analyze the contribution of incompleteness error to the deduced error bands and to reduce the model dependence.

We give a perturbative calculation of the effects of final state electronic interactions on the transition rates in allowed beta decay. The results include a simple relativistic expression for the electron screening correction to the total decay rate for low-Z nuclei which corrects a recent calculation by Drukarev and Strikman, and expressions for the corrections to the decay spectra for transitions to particular final atomic states. We discuss briefly applications to superallowed Fermi transitions and the beta decay of tritium.

Elastic scattering of 250 MeV polarized protons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been measured and angular distributions of the cross section and the analyzing power are presented. A relativistic optical-model analysis of these data and other experimental information on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(p,p${)}^{12}$C scattering between 200 and 300 MeV in the framework of Dirac phenomenology has been carried out and leads to a smoothly energy-dependent optical potential.

Effects of the spin-orbit part of the proton distorting potential on the ratio of the transverse and longitudinal response functions are investigated in the exclusive ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(e,e’p${)}^{11}$B reaction as well as in the inclusive reaction. The effect is found to explain the observed data for the parallel exclusive kinematics while it fails to explain the inclusive data. Exclusive experiments at nonparallel kinematics are recommended for further study.

Starting from beam and target spin systems which are polarized in the usual way by applying external magnetic fields, measurements of appropriate final state tensor parameters, viz., {$t_0$,$1^{\mathrm{k}}$, k=1,...,2j} of particle d with spin j in a reaction a+b→d+$c_1$+$c_2$+. . . , are suggested to determine the reaction amplitudes in spin space free from any associated discrete ambiguity.

A generalized two-state coexistence model developed to describe the $0^{+\mathcal{’}}$ to ground state cross-section ratios in the (p,t) and (t,p) reactions on even-even nuclei is applied to the zinc isotopes. We demonstrate that two-state mixing wave functions for the ground state and excited $0^{+}$’ state in ${}_{}{}^{\mathrm{A}}{}_{}{}^{}\mathrm{Zn}$ can quantitatively account for all σ${(0\mathrm{}}^{+\mathcal{’}}$)/σ (g.s.) ratios in Zn(p,t) and Zn(t,p). Finally, we couple these $0^{+}$ wave functions with a set of two-state mixing $2^{+}$ wave functions to describe the E2 transition-rate data in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$.

Nuclear levels in ${}_{}{}^{111}{}_{}{}^{}\mathrm{In}$ have been investigated by means of the ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$${(}^3$He,d${)}^{111}$In reaction at an incident energy of 22.5 MeV. The outgoing deuterons were analyzed by a magnetic spectrograph and a resolution of 16 keV was achieved. A total of 34 levels, up to 3.3 MeV excitation, were observed, 25 of them previously unknown. A distorted-wave Born approximation analysis has been performed to assign angular momentum transfers to the transitions and to determine spectroscopic factors for the residual states. Total spin assignments have tentatively been made with the help of shell-model predictions. The results are compared to previous experimental data and to nuclear structure calculations on the odd indium isotopes.

The energy and angular distributions from the ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$(n,xp), ${}_{}{}^{\mathrm{nat}}{}_{}{}^{}\mathrm{Ag}$(n,xp), and ${}_{}{}^{\mathrm{nat}}{}_{}{}^{}\mathrm{In}$(n,xp) reactions were investigated by means of a multitelescope system. Targets, thick compared to the range of the most energetic protons, were used and the double-differential proton emission cross sections were derived by unfolding. The results for both the angle-integrated proton spectra and the proton energy dependence of the angular distributions are very similar for all three measured cases and confirm that the (n,p) reaction at 14 MeV is dominated by precompound emission in the studied mass range. The angle-integrated results are compared with calculations based on the statistical model of nuclear reactions including both precompound particle emission and subsequent particle evaporation. It is shown that the proton spectra can be adequately described within this model, if the usual pairing correction for level densities is also applied to the exciton state densities used in the calculation of precompound particle emission and the matrix element for internal transitions is chosen in such a way that the rate of 3→5 exciton transitions is adjusted to 5×${10}^{21}$ ${\sec }^{\mathrm{-}1}$. With this choice of parameters it is simultaneously possible to describe the neutron spectra in the ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$(n,n’) reaction except at the highest energies where an additional direct reaction component is required. The angular distributions which show a strongly energy dependent forward-backward asymmetry are in fair agreement with the phenomenological model of Kalbach-Mann and with those of direct reaction theory for continuum cross sections.

Forty states of ${}_{}{}^{84}{}_{}{}^{}\mathrm{Se}$ have been observed in the reaction ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$(t,p), at a triton energy of 17 MeV. For most of them, $J^{\pi }$ values have been determined from the measured angular distributions. Excited states with $J^{\pi }$${=0\mathrm{}}^{+}$, $2^{+}$, and $4^{+}$ exhaust approximately 100% of the strength expected in a 2d(5/2, 3s1/2, 2d(3/2 space.

We have measured the neutron capture cross section of gold using the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$(p,n${)}^7$Be reaction for neutron production. This reaction not only provides the integrated neutron flux via the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ activity of the target, but also allows for the simulation of a Maxwellian neutron energy spectrum at kT=25 keV. As this spectrum is emitted in a forward cone of 120° opening angle, the cross section can be measured in good geometry and independent of any other standard. Systematic uncertainties were studied experimentally in a series of activations. The final stellar cross section at kT=25 keV was found to be 648±10 mb, and extrapolation to the common s-process temperature kT=30 keV yields 582±9 mb. This result is used for renormalization of a number of cross sections which had been measured relative to gold.

The structure of ${}_{}{}^{98}{}_{}{}^{}\mathrm{Ru}$ was studied using the ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$${(}^3$He,2nγ${)\mathrm{}}^{98}$Ru reaction, which populated many non-yrast states that had not been observed previously. The experiments included γ-ray excitation functions, angular distributions, linear polarizations, and γ-γ coincidences. It is shown that low-lying non-yrast states in this transitional nucleus can be described in a rotational framework without using a vibrational degree of freedom. The interpretation used a model with two quasiparticles coupled to a symmetric rotor. A surface-delta residual interaction was included.