A model-insensitive data-to-data formula based on an analytic expression for the scattering of a Dirac particle from a nucleus is derived for the energy dependence of the scattering. Using this formula, the Dirac impulse approximation is found to account for the energy dependence of proton scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ in the 500-800 MeV regime. The energy dependence cannot, however, be accounted for to energies below 200 MeV. The method introduced in the analysis is applicable to a wide variety of scattering problems.

The importance of imposing the orthogonality condition between the initial and final state wave functions for a correct description of the direct contribution to the monopole cross section is demonstrated in the context of a study of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\pi ,{\pi }^{\prime })$. Two step effects, previously found important for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ monopole excitation, are less important in this reaction. Very general estimates of two-step contributions are derived. These indicate that multistep effects will be small in medium energy monopole excitations away from forward angles.

Eikonal expansions are developed for the equivalent cases of the Dirac equation with scalar and vector potentials and the Schrödinger equation with central and spin-orbit potentials. Second-order corrections to the Glauber approximation are developed. Numerical calculations relevant to proton-nucleus elastic scattering illustrate that the sequence of eikonal amplitudes converge to the Dirac amplitudes in the 300-800 MeV range considered and for forward scattering angles $0°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\lesssim 40°$.

The experimentally measured $\frac{({\mu }^{-},\mathrm{charged}\mathrm{particle})}{({\mu }^{-},\mathrm{n})}$ and ($\frac{\mathrm{p},\mathrm{n}}{\mathrm{p},{\mathrm{p}}^{\prime }}$) ratios for the emission of energetic nucleons are used to estimate the time evolution of a system of secondary nucleons produced in a direct interaction of a projectile or captured muon. The values of these ratios indicate that chemical equilibrium is not achieved among the secondary nucleons in noncomposite induced reactions, and this restricts the time scale for the emission of energetic nucleons to be about 0.7 × ${10}^{-23\mathrm{}}$ sec. It is shown that the reason why thermal equilibrium can be reached so rapidly for a particular nucleon species is that the sum of the particle spectra produced in multiple direct reactions looks surprisingly thermal. The rate equations used to estimate the reaction times for muon and nucleon induced reactions are then applied to heavy ion collisions, and it is shown that chemical equilibrium can be reached more rapidly, as one would expect.

The thermal model, which has been applied successfully to inclusive cross sections in heavy ion reactions, is applied here to the (p,p′) and ($\mathrm{p},\pi$) reactions. The thermal source temperatures and velocities determined in proton induced reactions are similar to those found in heavy ion reactions, although the temperatures are cooler in proton induced reactions. Several methods can be used to estimate the number of nucleons in the thermal source, and these are found to give roughly consistent answers. Using a classical dense gas model, an estimate is made of the lifetime of the hot source. As one might expect, the lifetime is calculated to be in the ${10}^{-23\mathrm{}}$ sec range, indicating that the hot region probably does not cleanly separate from the nucleus before it cools off. A discussion of the limiting temperature behavior observed in this analysis is also given.

The decays of ${}_{}{}^{236}{}_{}{}^{}\mathrm{Th}$ and its ${}_{}{}^{236}{}_{}{}^{}\mathrm{Pa}$ daughter were studied by $\gamma$-ray spectroscopy. By means of radiochemical methods and a continuous separation technique pure sources of parent and daughter were prepared so that each was free (or almost free) of the other. For ${}_{}{}^{236}{}_{}{}^{}\mathrm{Th}$, 14 of the 17 observed $\gamma$ rays are new; for ${}_{}{}^{236}{}_{}{}^{}\mathrm{Pa}$ 16 new $\gamma$ rays were found. Absolute intensities of all the $\gamma$ rays were determined with the aid of $4\pi$ beta measurements on ${}_{}{}^{236}{}_{}{}^{}\mathrm{Pa}$. A new decay scheme is proposed for ${}_{}{}^{236}{}_{}{}^{}\mathrm{Th}$ and a considerably expanded one is given for ${}_{}{}^{236}{}_{}{}^{}\mathrm{Pa}$. The half-lives determined are 37.5±0.2 min for ${}_{}{}^{236}{}_{}{}^{}\mathrm{Th}$ and 9.1±0.1 min for ${}_{}{}^{236}{}_{}{}^{}\mathrm{Pa}$.

We have studied the decay of 55.4-min ${}_{}{}^{133}{}_{}{}^{}\mathrm{Te}_{}^m{}_{}{}^{}$ to the levels of ${}_{}{}^{133}{}_{}{}^{}\mathrm{I}$. The population of 47 excited states in ${}_{}{}^{133}{}_{}{}^{}\mathrm{I}$ following the decay of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Te}_{}^m{}_{}{}^{}$ is proposed and evidence for ten additional states is discussed. The observed decay patterns are found to be strongly influenced by the levels populated in the $\beta$ decay of the ${\frac{11}{2}}^{-}$ parent cascade through an intermediate energy three-particle ${\frac{19}{2}}^{-}$ isomer rather than simply decaying by $E1\mathrm{} \gamma$ rays to the lower-lying positive parity levels. We discuss the role of these structurally controlled $\gamma$ ray cascades on processes occurring in nuclides near closed shells.

Cross-section and analyzing-power measurements are presented for inelastic proton excitation of the $5^{-}$, $T=0\mathrm{}$ state at 9.70 MeV, the $6^{-}$, $T=0\mathrm{}$ state at 11.58 MeV, and the $6^{-}$, $T=1\mathrm{}$ state at 14.35 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ for incident proton energies of 80, 100, 134, and 180 MeV. These results are analyzed using the distorted-wave impulse approximation, an energy-dependent optical potential derived from the elastic scattering, and several different free and density-dependent forms for the effective nucleon-nucleon interaction. The energy and momentum-transfer dependence of the cross section and analyzing power is examined in detail. The extraction of nuclear structure information from analyses of inelastic proton scattering is discussed.

[NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\overrightarrow{\mathrm{p}},{\mathrm{p}}^{\prime }){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, $E_{\mathrm{p}}=80,100,134,180\mathrm{}$ MeV; measured $\sigma (E_{\mathrm{p}},\theta ),A(E_{\mathrm{p}},\theta );E_{\mathrm{ex}}=9.70\mathrm{}$ MeV ($5^{-}$, $T=0\mathrm{}$), 11.58 MeV ($6^{-}$, $T=0\mathrm{}$), 14.35 MeV ($6^{-}$, $T=1\mathrm{}$). Examination of momentum-transfer and energy dependence of distorted-wave impulse approximation calculations.]

In a recently developed many-body Faddeev theory of rearrangement scattering the transition matrix elements are given in terms of a distorted wave series. We discuss the construction of the distorted waves and evaluate the lowest order contribution to ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}(\overrightarrow{\mathrm{p}},\mathrm{d}){}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ at 96 MeV in zero range. Various approximations are examined and possible extensions of the present calculations are discussed.

[NUCLEAR REACTIONS Intermediate energy (p-d) reactions. Application of microscopic theory of rearrangement scattering. Calculation of distorted waves.]

The proton-oxygen bremsstrahlung cross section is calculated near the 2.66-MeV elastic scattering resonance by using two model-independent approximations, the Feshbach-Yennie approximation and the soft-photon approximation. The soft-photon approximation predicts a typical smooth spectrum, while the Feshbach-Yennie approximation predicts structure in the resonance region. Both the principal term and the correction term are included in our Feshbach-Yennie calculation, but the contribution from the correction term is found to be insignificant. The structure predicted in the Feshbach-Yennie approximation has various forms, from a peak to a dip, depending upon the proton scattering angle. This interesting structure, if verified experimentally, can be used to study the resonance effects, to test the Feshbach-Yennie approximation, and to extract the nuclear time delay. Measurement of the proton-oxygen bremsstrahlung cross section near 2.66 MeV for various proton scattering angles is strongly suggested.

[NUCLEAR REACTIONS p ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ bremsstrahlung near 2.66 MeV, calculate bremsstrahlung cross section.]

Gamma-ray production cross sections have been measured for the gamma-ray lines most strongly excited in the alpha-particle bombardments of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ for alpha-particle energies from threshold to approximately 27 MeV. Tabulations of cross sections averaged over alpha-particle energy bins of 1 MeV are provided for calculations relevant to gamma-ray line astronomy. Examples are given of astrophysical information which might be extracted from spectra acquired with gamma-ray spectrometers in space using these cross sections.

[NUCLEAR REACTIONS $\alpha +{}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},{}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},{}_{}{}^{27}{}_{}{}^{}\mathrm{Al},{}_{}{}^{28}{}_{}{}^{}\mathrm{Si},{}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$. $E=\mathrm{threshold}\mathrm{to} 27$ MeV. Measured gamma-ray production cross sections. Applications to gamma-ray astronomy. Ge(Li) detectors. Enriched targets.]

The Feshbach projection formalism is used to calculate the form factors for the (d,n) stripping process to isolated analog resonances. These are used in a standard distorted-wave Born-approximation stripping calculation in which the radial integration over all space is accomplished by including outer space contributions evaluated along the complex contours of Vincent and Fortune. It turns out that the shape and magnitude of the predicted cross section are quite insensitive to the continuum proton wave emanating from the resonant residual state.

[NUCLEAR REACTIONS Stripping to isolated analog resonance states. Calculation of DWBA form factor using Feshbach formalism. Demonstrated that continuum proton wave contributes little to cross section calculations.]

A bremsstrahlung photon beam from electrons with end-point energies of 7.66 and 10.37 MeV was used for photoexciting levels in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$. Values of $g\frac{{\Gamma }_0^2}{\Gamma }$ and $g{\Gamma }_0$ of 22 levels below 10 MeV were obtained using scattering and self-absorption measurements. The values for 7 levels are reported for the first time. The temperature variation of the scattering cross section was measured at $T=300\mathrm{}$ K and $T=78\mathrm{}$ K to study in some detail the effective temperature $T_e$ of metallic ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$. The results of the total $B\left(M{1}_{\uparrow }\right)$ strength of $T=\frac{1}{2}$ levels below 9 MeV were found to be in excellent agreement with the large-scale shell-model calculations.

[NUCLEAR REACTIONS ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(\gamma ,{\gamma }^{\prime }),E=7.66,10,37\mathrm{}$ MeV bremsstrahlung.] Deduced $E_x,g{\Gamma }_0,B\left(M{1}_{\uparrow }\right)$. Natural target.

The n decay of the giant-monopole-resonance region in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been studied in an ($\alpha ,{\alpha }^{\prime }\mathrm{n}$) coincidence experiment at $E_{\alpha }=104\mathrm{}$ MeV. From the fast-neutron emission corresponding to the decay into the low lying single hole states in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ a direct decay component of ≅15% was estimated for the resonant strength. In addition, evidence for a preequilibrium decay was found.

The theory of the strength function for giant resonances is extended to exhibit the explicit energy dependence of the width and shift functions for the giant isovector monopole. An integral sum rule on the width ${\Gamma }_M\mathrm{}\left(E\right)\mathrm{}$ relates its normalization to the second moment $M_2$ of the strength function and leads to a relation ${\Gamma }_M\left(E_M\right)\frac{{\Gamma }_s}{4}=M_2$ between $M_2$ and the width at the maximum, which involves the width ${\Gamma }_s$ of the distribution in energy of the spreading matrix elements. An estimate of ${\Gamma }_M\left(E_M\right)\simeq 8$ MeV based on the absorptive part of the optical potential together with random-phase approximation calculations of $M_2$ leads to the result $\frac{{\Gamma }_s}{2\simeq 2\hslash \omega }$, supporting the intermediate coupling model of Lane, Thomas, and Wigner. Using the sum rule expressions of Lane and Mekjian to evaluate the Coulomb matrix element $M_{\mathrm{AM}}$ between an isobaric analog state and its corresponding isovector monopole, we test this strength function for the isovector monopole by calculating the spreading widths for the ground state analogs of nuclei from ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The good agreement with the systematic dependence upon mass number and isospin resolves the long-standing discrepancy between the estimate ${\Gamma }_M\left(E_M\right)\sim 8-10$ MeV and the value ${\Gamma }_M\left(E_A\right)\le 2$ MeV needed to account for the spreading widths of the isobaric analog state.

Differential cross sections for proton scattering on ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$ have been measured at $E_{\mathrm{p}}=51\mathrm{}$ MeV. The data are analyzed by coupled channels calculations, with coupling amplitudes taken from the interacting boson approximation. Information on transition potentials is obtained. The reliability of the method is discussed.

[NUCLEAR REACTIONS Proton scattering on ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$; $E_{\mathrm{p}}=51\mathrm{}$ MeV; enriched targets. Measured $\sigma \left(\theta \right)$. Optical model and coupled channels analysis. Interacting boson approximation transition densities.]

The ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ nucleus has been studied via the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(\alpha ,2\mathrm{}\mathrm{p}\gamma )$ reaction at $E_{\alpha }=32\mathrm{}$ MeV using in-beam $\gamma$ spectroscopy techniques. High-spin states up to 10 MeV excitation have been established. Among the five branches depopulating the yrast $J^{\pi }=7^{-}$ state has been found an $E3\mathrm{}$ transition down to the $4^{+}$ state. Comparison with direct reaction results suggests the very likely ${[{\nu f}_{\frac{5}{2}},{\nu g}_{\frac{9}{2}}]}_{7^{-}}$ configuration for the $J^{\pi }=7^{-}$ yrast state at 5349 keV, suggesting then the ${[\nu {(p_{\frac{1}{2}},p_{\frac{3}{2}},f_{\frac{5}{2}})}_{2^{+}}^2\times {({\nu f}_{\frac{5}{2}},{\nu g}_{\frac{9}{2}})}_{7^{-}}^2]}_{9^{-}}$ configuration for the $J^{\pi }=9^{-}$ yrast state. Other high-spin states might be accounted for by the breaking of the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ core.

[NUCLEAR REACTIONS ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(\alpha ,2\mathrm{}\mathrm{p}\gamma )$, $E=23-40\mathrm{}$ MeV; measured $E_{\gamma },I_{\gamma \gamma }\left(\theta \right),\gamma -\gamma$ coincidences, lifetimes by DSAM, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ deduced high-spin levels, $J,\pi$.]

Elastic and inelastic scattering of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been investigated at 209.8 MeV with high resolution. The angular distributions can be well described by coupled channel calculations when the ion-ion potential has a diffusivity of 0.65 fm. Deformation lengths extracted are in good agreement with those obtained from analysis of light ion reaction data.

Elastic and inelastic cross section data for exciting the ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ $2_1^{}{}_{}{}^{+}$ (1.27 MeV) state by 132 MeV ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ scattering from a ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ target are presented. The data are analyzed by a rotational model coupled-channels calculation including the $0^{+}$ ground state and the $2_1^{}{}_{}{}^{+}$, and $4_1^{}{}_{}{}^{+}$ states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$. We extract ${\beta }_2$ and ${\beta }_4$ deformation parameters, as well as $M(E2;0^{+}-2_1^{+}),M(E2;2_1^{+}-2_1^{+}),M(E4;0^{+}-4_1^{+})$, and $M(E2;2_1^{+}-4_1^{+})$ matrix elements for ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ and compare these quantities to those obtained for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. The extracted $2_1^{}{}_{}{}^{+}$ reorientation matrix element is considerably larger than shell-model predictions. Addition of a negative spin-orbit potential improves the fit to the $2_1^{}{}_{}{}^{+}$ differential cross section.

[NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$,${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$,${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}\prime$) $E_{\mathrm{lab}}=132\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$; deduced optical potential, quadrupole and hexadecapole deformation parameters and transition matrix elements of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ by a coupled-channels analysis. Enriched target.]

Evaporation residue cross sections have been measured for the systems ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ + ${}_{}{}^{112,116,120,124}{}_{}{}^{}\mathrm{Sn}$ at incident energies between 130 MeV and 247 MeV. Total cross sections were measured by direct detection of recoil nuclei in a particle counter telescope. In addition, total and partial cross sections were determined from $K$-vacancy production cross sections and $K$ x-ray multiplicities of the evaporation residues. The x-ray multiplicities are of the order of ∼ 1 and vary slowly with target mass and incident energy, indicating that x-ray detection can be reliably used to study fusion cross sections induced by heavy projectiles in this mass region. The total evaporation residue cross sections rise with increasing energy, saturate at ∼ 190-MeV incident energy, and decrease slightly at higher energies. The saturation value shows distinct differences between systems and ranges from ∼600 mb for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ + ${}_{}{}^{112}{}_{}{}^{}\mathrm{Sn}$ to ∼800 mb for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ + ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$. The gross behavior of the partial evaporation residue cross sections is in agreement with statistical model calculations, but there remain deviations in the element distribution of the evaporation residues which might be explained by contributions from incomplete fusion reactions. As a byproduct we have measured $K$-vacancy production cross sections for atomic excitation of the target atoms by the projectiles and compared them with theoretical predictions.

[NUCLEAR REACTIONS ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ + ${}_{}{}^{112,116,120,124}{}_{}{}^{}\mathrm{Sn}$, evaporation residue cross sections $\sigma (E,\theta )$ and $\sigma \mathrm{}(E,Z)\mathrm{}$, $K$ x-ray cross sections and multiplicities; statistical model calculations.]