Levels in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ up to an excitation energy of 2.8 MeV were studied through the ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$($p,p^{\prime }\gamma$) reaction at an incident proton energy $E_p=5.0\mathrm{}$ MeV. Singles $\gamma$-ray spectra were obtained with a high resolution Ge(Li) detector at angles of observation ${\Theta }_{\gamma }=0\mathrm{}°,30\mathrm{}°,55\mathrm{}°,70\mathrm{}°,90\mathrm{}°,\mathrm{and} 125°$ and a second (monitor) Ge(Li) fixed at ${\Theta }_{\gamma }\left(\mathrm{monitor}\right)=90\mathrm{}°$. The lifetimes of 18 levels were determined through the Doppler shift attenuation method by studying the systematic energy shift of $\gamma$-ray peaks in the angular distribution data. The analysis of angular distributions yielded multipole mixing ratios and $J^{\pi }$ values for several states. The experimental information, wherever complete, was employed to calculate reduced transition probabilities. The results obtained here are compared with theoretical predictions in the framework of the weak-coupling model.

NUCLEAR REACTIONS ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ ($p,p^{\prime }\gamma$), $E_p=5.0\mathrm{}$ MeV enriched target. Measured $E_{\gamma }$, $I_{\gamma }\left(\Theta \right)$, $\Delta E_{\gamma }\left(\Theta \right)$, deduced $\tau$, $\delta$, $B\left(\Lambda \right)$ values; Ge(Li) detector.

The ($p,d$) and ($d,t$) reactions on ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{96}{}_{}{}^{}\mathrm{Mo}$ have been used at bombarding energies of ∼40 MeV to populate neutron hole states of ${}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$. Excitation energies and angular distributions were measured for levels up to ∼5 MeV in excitation. A distorted-wave Born approximation analysis was used to make $l$ assignments and to obtain spectroscopic factors. Three distinct groups of weakly excited levels, one corresponding to $l=4\mathrm{}$ and two corresponding to $l=1\mathrm{}$, were observed above 2.3 MeV excitation in both nuclei. A quasiparticle-core coupling model is used to predict the properties of ${}_{}{}^{93,95}{}_{}{}^{}\mathrm{Mo}$ nuclei and fair agreement with the experiments is obtained.

[NUCLEAR REACTIONS, NUCLEAR STRUCTURE ${}_{}{}^{94,96}{}_{}{}^{}\mathrm{Mo}$($p,d$), ${}_{}{}^{94,96}{}_{}{}^{}\mathrm{Mo}$($d,t$), $E\simeq 40$ MeV, measured $\sigma \left(\theta \right)$, ${}_{}{}^{93,95}{}_{}{}^{}\mathrm{Mo}$ levels, deduced $l$, $C^2{S}_n$; calculated $J$, $\pi$, $S_n$, quasiparticle-core coupling model.]

The ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$($t,\alpha$)${}_{}{}^{233}{}_{}{}^{}\mathrm{Pa}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$($t,\alpha$)${}_{}{}^{235}{}_{}{}^{}\mathrm{Pa}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$($t,\alpha$)${}_{}{}^{237}{}_{}{}^{}\mathrm{Pa}$, ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$($t,\alpha$)${}_{}{}^{229}{}_{}{}^{}\mathrm{Ac}$, and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$($t,\alpha$)${}_{}{}^{231}{}_{}{}^{}\mathrm{Ac}$ reactions were studied with a 15-MeV triton beam. The reaction results are interpreted in terms of a distorted-wave-Born-approximation analysis. Theoretical cross sections, calculated in the framework of the Nilsson model with pairing and Coriolis interactions included, are compared with experimental values. The following Nilsson proton configurations are identified in all of the residual nuclei: ${1/2}^{+}$[400], ${3/2}^{+}$[402], ${3/2}^{+}$[651], ${1/2}^{-}$[530]. The ${1/2}^{-}$[541] and ${9/2}^{-}$[514] configurations are tentatively assigned. Due to the increase in deformation with neutron number, the ground state configuration of the Pa isotopes changes from ${3/2}^{-}$[530] to ${1/2}^{+}$[400] as $A$ increases.

NUCLEAR REACTIONS ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$($t,\alpha$), ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$($t,\alpha$), ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$($t,\alpha$), ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$($t,\alpha$), and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$-($t,\alpha$), $E=15\mathrm{}$ MeV, measured $\sigma (E_{\alpha },\theta )$, deduced levels, $J$, $\pi$, $K$, enriched targets.

The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$,${}_{}{}^8{}_{}{}^{}\mathrm{He}$)${}_{}{}^{36}{}_{}{}^{}\mathrm{Ca}$ reaction has been used to provide the first observation of the nuclide ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ca}$. The $Q$ value and mass excess were found to be -57.58 ± 0.04 and -6.44 ± 0.04 MeV, respectively. The new mass completes four members of the $A=36\mathrm{}$ isobaric quintet and hence serves as a test of the isobaric multiple mass equation.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{He}$). Measured ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ca}$ mass. Deduced coefficients of the isobaric multiplet mass equation.

The nuclear giant dipole resonance is discussed using a macroscopic model with two new features. The motion is treated as a combination of the usual Goldhaber-Teller displacement mode and the Steinwedel-Jensen acoustic mode, and the restoring forces are all calculated using the droplet model. The $A$ dependence of the resonance energies is well reproduced without any adjustable parameters, and the actual magnitude of the energies serves to fix the value of the effective mass $m^{*}$ used in the theory. The giant dipole resonance is found to contain a large component of the Goldhaber-Teller type of motion, with the Steinwedel-Jensen mode becoming comparable for heavy nuclei. The width $\Gamma$ of the giant dipole resonance is estimated on the basis of an expression for one-body damping.

NUCLEAR REACTIONS Semiclassical theory, nuclear giant dipole resonance, calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, $\Gamma$. Droplet model restoring forces. Coupled modes.

High-spin states have been investigated with the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,$3n$)${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$ reaction by $\gamma -\gamma$ coincidence, $\gamma$-ray angular distribution, and pulsed beam-$\gamma$ timing measurements with Ge(Li) detectors. Decay schemes, level energies, and spin-parity information were obtained for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$ from the data. The positive-parity yrast level sequence was established up to a ${13}^{+}$ state at 3326 keV. An ${11}^{-}$ isomeric level at 2203 keV was found and observed to have a mean lifetime of $\tau =241\mathrm{}\pm 5$ nsec. The $g$ factor of this isomer was measured to be $g=0.88\mathrm{}\pm 0.03$. The observed properties of levels in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$ are compared with shell-model calculations.

NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$(${}_{}{}^7{}_{}{}^{}\mathrm{Li}$,$3n$), $E_{\mathrm{Li}}=34\mathrm{}$ MeV; measured $\gamma -\gamma$ coin, $\gamma (E,\theta ,t)$, spin rotation in $B=11.2\mathrm{}$ kG; deduced level scheme in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Nb}$, $\gamma$ multipolarities, $T_{\frac{1}{2}}$,$J^{\pi }$, $g$ factor. Natural target, Ge(Li) detectors.

The angular distributions of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ inelastically scattered from enriched targets of even mass nickel isotopes measured over the angular range ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\sim 50°\mathrm{to}170°$ are presented. The measured cross sections are compared with the results of distorted-wave Born approximation calculations for inelastic scattering which employ the conventional four parameter optical potential or a folded excitation potential. The folded method improves the description of the data in some cases but does not provide a consistent improvement for all energies and isotopes.

NUCLEAR REACTIONS ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\prime$) ${\mathrm{Ni}}^{*}$($2^{+}$), measured $\sigma \left(\theta \right)$ at $E_{\mathrm{lab}}=42\mathrm{}\mathrm{and}48$ MeV. Calculated $\sigma \left(\theta \right)$ by DWBA using conventional and folded potentials. Deduced deformation lengths.

By use of finite-difference methods we solve in three spatial dimensions the classical relativistic equations of motion for the collision of two heavy nuclei. These equations express the conservation of nucleon number, momentum, and energy, for a specified nuclear equation of state. For ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ at laboratory bombarding energies per nucleon of 250 MeV and 2.1 GeV, we calculate the time evolution of the matter distribution for several impact parameters. Nearly central collisions deform and compress the system enormously, whereas in peripheral collisions the projectile is fragmented into a portion that proceeds roughly straight ahead at its original velocity and other portion that deposits its energy in the target. For a given impact parameter we construct from the velocity vectors at some large time the energy and angular distributions for the expanding matter. An integration of these results over impact parameter then gives us the double differential cross section $\frac{d^2\sigma }{d\mathrm{Ed}\Omega }$. For the 250-MeV case we compare calculated and experimental results in the form of proton energy spectra for four laboratory angles ranging from 30° to 120°. The calculations reproduce correctly the experimental slopes at each angle, as well as the overall decrease in the experimental cross section when going from forward to backward angles. However, at 30° the calculated values are only one-half the experimental ones, whereas at 120° they are twice as large. These comparisons, together with comparisons of calculations done by other workers, suggest that heavy nuclei are partially transparent to each other during collisions at high energy, but that the process is not solely a superposition of individual nucleon-nucleon collisions. Instead, coherent collective-field effects play some role.

NUCLEAR REACTIONS High-energy heavy-ion ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, $\frac{E_{\mathrm{bom}}}{20}=250\mathrm{}$ MeV, 2.1 GeV. Calculated $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$ for outgoing matter and compared with experimental data. Relativistic nuclear fluid dynamics, hydrodynamic model, nuclear equation of state, particle-in-cell finite-difference computing method.

Cross sections for forming compound nuclei in symmetric very-heavy-ion reactions are calculated by use of the criterion that the dynamical trajectory for the fusing system must pass inside the fission saddle point in a multidimensional space in order to form a compound nucleus. The dynamical trajectory is obtained by solving numerically the modified classical Lagrange equations of motion for a system whose shape is specified in terms of smoothly joined portions of three quadratic surfaces of revolution. This restriction to nuclear shapes that are axially symmetric (about an axis that is in general rotating in space) is a good approximation for systems with small angular momentum, but it may be seriously deficient for systems with large angular momentum. The nuclear potential energy of deformation is determined by means of a macroscopic model that includes the Coulomb energy and the nuclear macroscopic energy. This latter quantity is calculated in terms of a double volume integral of a Yukawa two-body interaction potential, which includes the surface energy of the liquid-drop model but also takes into account the lowering in energy due to the finite range of the nuclear force. For systems with angular momentum, we include a centrifugal pseudopotential calculated for rigid-body rotation. The kinetic energy of collective motion is calculated for nuclear flow that is a superposition of incompressible, nearly irrotational collective-shape motion and rigid-body rotation. Nuclear dissipation (the transfer of energy of collective motion into internal single-particle excitation energy) is included in the formulation by means of Rayleigh's dissipation function. However, to emphasize that compound-nucleus cross sections become small for very heavy systems even in the absence of dissipation, our current results are presented for the case of zero dissipation. For nuclear systems lighter than about ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$ + ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$ → ${}_{}{}^{220}{}_{}{}^{}\mathrm{U}$ and for relatively low angular momentum, the fission saddle point lies outside the point of hard contact in heavy-ion reactions, which permits the compound-nucleus cross section at relatively low bombarding energy to be calculated in terms of a one-dimensional interaction barrier, as is customarily done. For heavier nuclear systems and/or for high angular momentum, the fission saddle point lies inside the contact point, which reduces the compound-nucleus cross section compared with that calculated for a one-dimensional interaction barrier.

NUCLEAR REACTIONS ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ + ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ → ${}_{}{}^{200}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$ + ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$ → ${}_{}{}^{220}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$ + ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$ → ${}_{}{}^{248}{}_{}{}^{}\mathrm{Fm}$. Calculated compound-nucleus cross sections. Liquid-drop model, hydrodynamical model, nuclear potential energy of deformation, nuclear inertia, dynamical trajectory, compound-nucleus formation, heavy-ion fusion, quasifission, highly inelastic heavy-ion collisions.

Neutron induced fission and total cross sections of ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ have been measured over the neutron energy range from a few eV to 8.9 MeV. Neutron and fission widths for 118 cross section resonances below 1500 eV have been determined and give a class I level spacing of 10.6 ± 0.5 eV and an $s$-wave strength function of (0.86 ± 0.11) × ${10}^{-4\mathrm{}}$. These fine structure resonances form two narrow intermediate structure resonances in the subthreshold fission cross section of ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$. Parameters for the Lorentzian energy dependence of the mean fission width are deduced by maximum likelihood analysis on the assumption that, relative to this mean, the observed fission widths have a Porter-Thomas distribution. Two large fission widths measured for resonances at 1092.5 and 1134 eV prompted a likelihood ratio test which indicates the presence of a narrow intermediate structure resonances at 580 and at 1227 eV. The class II level spacing derived from the observation of seven intermediate structure resonances below 14 keV is 2.1 ± 0.3 keV. Broad structures in the fission cross section at 310, 550, and 770 keV are assumed to be due to $\beta$-vibrational levels in the second minimum of the Strutinsky potential. Fluctuations due to the presence of class II resonances are strongly evident for each of these vibrational levels. It is shown that the fluctuations near 310 keV are consistent with parameters deduced from the low energy data and this allows parameters for the double humped fission barrier potential to be obtained.

NUCLEAR REACTIONS ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ ($n,f$), $E=3\mathrm{}$ eV-8.9 MeV; measured ${\sigma }_f\mathrm{}\left(E\right)\mathrm{}$. ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ ($n$, total) $E=20-1500\mathrm{}$ eV; measured ${\sigma }_t\mathrm{}\left(E\right)\mathrm{}$. Determined $D_I$, $D_{\mathrm{II}}$, $S_0$, fission widths and neutron widths (118 levels below 1500 eV). Deduced $E_0$, width (two class II levels), barrier heights $V_A$, $V_B$.

Average delayed-neutron energies for 16 isotopes of Br, Rb, I, and Cs have been measured by means of detector ring counting rate ratios in a polyethylene-moderated neutron counter system. An on-line mass spectrometer facility was used to give chemically and mass separated sources of delayed-neutron precursors. A simple expression predicts general trends of the average delayed-neutron energies. Average delayed-neutron energies of individual precursors were weighted by the corresponding delayed-neutron yields and combined to give average energies for all six delayed-neutron groups commonly used in reactor kinetics calculations.

RADIOACTIVITY ${}_{}{}^{87,88,89}{}_{}{}^{}\mathrm{Br}$, ${}_{}{}^{92,93,94,95,96,97}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{137}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{141,142,143,144,145,146}{}_{}{}^{}\mathrm{Cs}$; measured average delayed-neutron energy; on-line mass separation, polyethylene-moderated neutron counter.

Delayed-neutron emission probabilities ($P_n$) were measured for 16 isotopes of Br, Rb, I, and Cs. Sources of chemically and mass separated nuclides were obtained from an on-line mass spectrometer facility. Neutrons were counted in a multitube polyethylene-moderated detector. The total number of precursor atoms was determined by direct counting of ions deposited on the first dynode of an electron multiplier. The $P_n$ values from this work generally agree with earlier measurements for the longer-lived precursors but are consistently higher for the shorter-lived precursors. A log-log plot of $P_n$ versus the reduced energy window $\frac{(Q_{\beta }-B_n)}{(Q_{\beta }-C)}$ gives a straight line with a slope of 6.0 ± 1.4 in agreement with simplified theoretical predictions. Half-lives of Rb and Cs nuclides measured by neutron decay curves are given.

RADIOACTIVITY ${}_{}{}^{87,88,89}{}_{}{}^{}\mathrm{Br}$, ${}_{}{}^{92,93,94,95,96,97}{}_{}{}^{}\mathrm{Rb}$ ${}_{}{}^{137,138}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{141,142,143,144,145}{}_{}{}^{}\mathrm{Cs}$; measured $P_n$, $T_{\frac{1}{2}}$; on-line mass separation, polyethylene-moderated neutron counter.

The dependence of the proton odd-even effect on the excitation energy of the fissioning nucleus and the mean kinetic energy of the fission fragments is examined in thermal neutron fission of ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ and in "fast" neutron fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$. The proton odd-even effect observed in thermal neutron fission is found to decrease with increasing excitation energy and/or with increasing atomic number of the fissioning even $Z$ nucleus. Possible factors responsible for the magnitude of the odd-even effect are discussed. An evaluation is made of a neutron odd-even effect, based on the observed mean proton odd-even effect, and consequently the mass distribution of fission fragments prior to neutron emission is calculated. A good fit is found between the calculated and the measured fragment mass yield curves and between calculated and measured neutron emission as a function of mass.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$($n,f$), ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$($n,f$), ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$($n,f$), ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$($n,f$), calculated odd-even effect; deduced systematics of the odd-even effect.

The elastic scattering of intermediate energy pions from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and the single charge exchange scattering from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated with a theoretical momentum space optical potential including spin, nucleon recoil, Fermi motion and binding, and a Lorentz invariant angle transformation. Realistic nuclear form factors and a $\pi N T$ matrix with a finite range are employed. An examination is made of the $\pi$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and $\pi$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ total and differential cross section data of several experimental groups and the possibility of extracting information on the magnetic moment form factor of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is investigated. Comparisons are made with the procedures and results of several theoretical groups to determine the relevant physical differences and the areas in need of improvement.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(${\pi }^{\pm },{\pi }^{\pm }$), ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(${\pi }^{\pm },{\pi }^{\pm }$) elastic, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(${\pi }^{-},{\pi }^0$) ${}_{}{}^3{}_{}{}^{}\mathrm{He}$; $E=100-260\mathrm{}$ MeV; $\sigma \left(\theta \right)$ and ${\sigma }_{\mathrm{TOT}}$; theoretical calculation, momentum space optical potential; binding, recoil, Fermi motion, angle transformation; compare data and other calculations.

Angular distributions have been measured at 66 MeV for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${\pi }^{+},p$)${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ reaction leading to the ${\left(p_{\frac{3}{2}}\right)}^{-1\mathrm{}}$ hole state at 6.18 MeV and the ${\left(p_{\frac{1}{2}}\right)}^{-1\mathrm{}}$ hole ground state of ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$. The ratio of the two differential cross sections lies between 6 and 13 over the whole measured angular range. A comparison is made with preliminary calculations of Miller. At 45° and 105° a measurement has also been performed on the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${\pi }^{-},p$)${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ at the same incident energy.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (${\pi }^{+},p$), $E_{\pi }=66\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$; comparison with DWBA calculations; reaction mechanism discussed.

The $s$-wave pion production process (at ${\overrightarrow{\mathrm{q}}}_{\pi }=0\mathrm{}$) is calculated as a function of the mass of the produced pion. The invariant matrix element is found to be surprisingly constant over a large range of pion mass.

NUCLEAR REACTION Threshold ${\pi }^{-}d\to \mathrm{nn}$, off-mass-shell extrapolation.

Corrections to the Glauber model for intermediate energy proton-$\alpha$ elastic scattering have been calculated at the lab energies $K_L=0.58,1,\mathrm{and}2.1$ GeV using the multiple diffraction expansion formalism. In this expansion, the Glauber amplitude appears as a leading term in a perturbation series. Leading corrections due to (i) wave spreading (noneikonal), (ii) internal excitation (recoil), as well as (iii) zero-point motion (different Galilean frames) effects are obtained in a simple model. Their structures are analyzed and their energy dependences are examined. The wave-spreading and internal-excitation corrections agree with those obtained by Wallace. The use of Wallace's relativistic kinematics changes the differential cross section significantly. A new zero-point motion correction is found to be important. A simple dependence of the results on the sign of $\rho$ ($\equiv \frac{\mathrm{Re}f}{\mathrm{Im}f}$ of the $\mathrm{NN}$ scattering amplitude) is pointed out. The relative importance of these corrections decreases as energy increases, as expected. The significance of our results is briefly discussed.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ($p,p$), $K_L=0.58,1,2.1\mathrm{}$ GeV; calculated $\sigma (K_L,\theta )$; wave spreading, internal excitation, and zero-point motion corrections to Glauber theory.

The cross sections for boron isotope production in carbon spallation by 40, 50, 150, 600 MeV, 25 GeV protons and 100-160 MeV $\alpha$ particles have been measured. Isotope ratio measurements were performed by sputtering mass spectrometry. An isotope dilution-like method in solid phase was developed for absolute cross section measurements. The present work and previous experimental results allow cosmic ray propagation calculations based mainly on experimental cross section values. The abundances of the light cosmic ray elements were calculated using the "leaky-box" model. The variations of the abundances of light secondary elements are accounted for by a rigidity dependence of the mean free path against escape. The density of the propagation medium is discussed using the ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ decay. The calculated values of the boron and lithium isotopic ratios in cosmic rays, practically independent of the propagation assumptions, are found to be independent of the energy from 1 to 100 GeV per nucleon.

NUCLEAR REACTIONS $\mathrm{C}(p,x)$, $\mathrm{C}(\alpha ,y)$, $E=40,50,150,600$ MeV, 25 GeV protons, 100-160 MeV $\alpha$ particles; measured $\sigma \text{'}\mathrm{s}$; natural target; mass spectrometry. Propagation of light cosmic ray nuclei.

The disappearance rate of muons from the $1s$ state of muonic actinide atoms has been measured by detecting muon-decay electrons. The experimental muon lifetimes are (79.2 ± 2.0), (75.4 ± 1.9), (73.5 ± 2.0), and (73.4 ± 2.8) nsec for muonic ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235,238}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, respectively. The muon-capture rates deduced from the data are compared with the predictions of various theories. The experimental values are consistent with the systematics of muon-capture rates in the heavy elements but are generally higher than theoretical predictions, which take deformation of the nuclear charge distribution into account. The results provide no evidence for a muon-induced isomeric fission process.

RADIOACTIVITY Muonic atoms ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{235,238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$; measured muon-disappearance rates, deduced total muon-capture rates, upper limit for population of shape-isomeric states.

The half-lives of the Fermi super-allowed $\beta$-ray transitions from ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}_{}^m{}_{}{}^{}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Co}$ have been measured by multiscaling $\beta$ rays detected in a plastic scintillator. The activities were made via the reactions ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}(t,n){}_{}{}^{26}{}_{}{}^{}\mathrm{Al}_{}^m{}_{}{}^{}$ at $E_t=3.1\mathrm{}$ MeV, ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$($p,n$)${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$ at $E_p=10\mathrm{}$ MeV, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$($p,n$)${}_{}{}^{54}{}_{}{}^{}\mathrm{Co}$ at $E_p=10\mathrm{}$ MeV, respectively. Results for the half-lives were as follows: ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}_{}^m{}_{}{}^{}-6339.5\mathrm{}\pm 4.5$ msec; ${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$ - 422.52 ± 0.45 msec; and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Co}$ - 193.28 ± 0.18 msec. A previously published experiment on the ${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$ half-life has been reanalyzed and found to be in agreement with the present work. Recommended values for the half-lives of the eight accurately measured super-allowed Fermi $\beta$ emitters are presented. We discuss the effect of arbitrary symmetry breaking in gauge theories on the extraction of the mean quark charge and conclude that the associated uncertainty is unlikely to be large.

RADIOACTIVITY ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}_{}^m{}_{}{}^{}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Co}$; measured $T_{\frac{1}{2}}$; compared with systematics.