A nonlocal energy-dependent imaginary optical potential is calculated for neutron scattering from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ in the intermediate structure model with weak particle-vibration coupling. The energy range studied is 0-12 MeV and the partial waves considered are $l=0-4\mathrm{}$. The corresponding contribution to the real potential has also been obtained and is relatively small; this potential is presented for $s$ waves. The imaginary potential is used to calculate the absorption cross section in this energy range for each partial wave. Both compound-nucleus and inelastic contributions to the potential and the absorption cross section are included. Below 5 MeV compound-nucleus contributions are dominant. Above this energy inelastic excitations based on single-particle resonances and compound-nucleus states based on giant resonances contribute, with the former being more significant. A comparison of the calculated absorption to experiment for $s$, $p$, $d$, and $f$ waves is made below the inelastic threshold of 2.6 MeV. The agreement, except for $p$ waves, is quite good in terms of the number of resonances and other significant details of the cross section. The calculated absorption cross sections up to 12 MeV are compared to the results from a phenomenological local surface-peaked imaginary potential. The nonlocal potential is also surface peaked and the details of its radial behavior for an arbitrary energy are given in a contour plot.

[NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(n,n)\mathrm{}$, $E=0-12\mathrm{}$ MeV; calculated nonlocal imaginary optical potential and absorption. Comparison with experiment and with a local imaginary potential. Particle-vibration doorways.]

The contribution to the magnetic moment of the deuteron due to the influence of a spin-orbit term in the nucleon-nucleon interaction is reconsidered, in view of apparent errors in previous estimates.

[NUCLEAR MOMENTS ${}_{}{}^2{}_{}{}^{}\mathrm{H}$; calculated $\mu$. Percentage $D$ state deduced.]

Calculations of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,2p)\mathrm{}{}_{}{}^3{}_{}{}^{}\mathrm{H}$ reaction in the distorted-wave impulse approximation do not reproduce the experimental data. The recent agreement obtained using a less sophisticated reaction model would seem to arise from the use of total cross sections which are too large.

[NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,2p)\mathrm{}$ $E=65.0-600.0\mathrm{}$ MeV. DWIA analysis.]

The large difference between the cross sections for the quasifree scattering in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,pd)\mathrm{}$ and $(p,p{}_{}{}^3{}_{}{}^{}\mathrm{He}) \mathrm{}(p,pt)\mathrm{}$ reactions are accounted for on the basis of separation energies.

[NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,pd)\mathrm{}$, ($p,p{}_{}{}^3{}_{}{}^{}\mathrm{He}$), ($p,pt$), $E=156,590\mathrm{}$ MeV; calculated $\sigma \mathrm{}\left(q\right)\mathrm{}$.]

New measurements by Lee and Boehm of electronic x-ray isotope shifts in lead substantially reduce, but do not eliminate, the discrepancy between electronic x-ray and muonic isotope shifts in this element. For the isotope pairs ${}_{}{}^{208-207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{206-204}{}_{}{}^{}\mathrm{Pb}$, we confirm the conclusion of Lee and Boehm that electronic and muonic data are now consistent. For the isotope pair ${}_{}{}^{208-206}{}_{}{}^{}\mathrm{Pb}$, the reported electronic x-ray shift is less by at least 22% (2 standard deviations) than what would be expected on the basis of the muonic data. Internal inconsistencies in the muonic data for this pair of isotopes can be removed by postulating a nuclear resonance that pushes the $2p_{\frac{3}{2}}$ state up by 0.3 keV or the $2p_{\frac{1}{2}}$ state down by 0.3 keV. For the isotope pair ${}_{}{}^{208-204}{}_{}{}^{}\mathrm{Pb}$, the discrepancy between electronic and muonic data is in the same direction as for ${}_{}{}^{208-206}{}_{}{}^{}\mathrm{Pb}$, but it is somewhat smaller and may not be significant.

[NUCLEAR STRUCTURE ${}_{}{}^{208,207,206,204}{}_{}{}^{}\mathrm{Pb}$; analyzed muonic isotope shifts, compared electronic shifts.]

The unusual properties of ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$ fission are explained by the statistical theory of fission in the same manner as the usual properties of fission of the other fissioning nuclides are explained.

[NUCLEAR REACTION, FISSION ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}\mathrm{}\left(\mathrm{sf}\right)\mathrm{}$, mass and energy distributions, energy dependence. Statistical theory.]

In the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, two $4^{+}$ states (at $E_x=10.35\mathrm{} \mathrm{and} 11.096$ MeV) are populated with relative strengths of $\frac{\sigma \mathrm{}\left(11.096\right)\mathrm{}}{\sigma \mathrm{}\left(10.35\right)\mathrm{}}\approx 0.5$ even though their reduced $\alpha$-particle widths to the g.s. of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are in the ratio $\frac{S_{\alpha }\mathrm{}\left(11.096\right)\mathrm{}}{S_{\alpha }\mathrm{}\left(10.35\right)\mathrm{}}<{10}^{-2\mathrm{}}$. A two-step process proceeding through the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ offers a likely mechanism of the enhanced feeding of the 11.096-MeV state.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d)$, $E=32\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$.]

An examination of the results of the optical-model analyses of the experimental data obtained by the scattering of protons with energies varying from 9.8 to 61.4 MeV from target nuclei in the mass range from 40 to 208 is carried out to look for the linear dependence of the real potential-well depth on the target mass number $A$ which had been unexpectedly revealed in the analysis of 11-MeV proton scattering from nuclei having a mass between 45 and 70. It is found that such an $A$ dependence cannot be extrapolated as such to heavier nuclei at any energy. An assumed linear variation over the whole mass region yields a coefficient which is an order of magnitude smaller than that deduced for the restricted mass region and which has a much wider scatter from linear dependence. Such a behavior could possibly be stimulated in part by the isospin-dependent potential, the Coulomb correction term in the potential, and the closed-shell effects.

[NUCLEAR REACTIONS Proton elastic scattering, optical-model analyses, well depth search, studied $A$ dependence for $E_p=9.8-61.4\mathrm{}$ MeV; target $A=40-208\mathrm{}$.]

The low-energy theorem and the vector-dominance model is used to derive the vector-meson exchange current in terms of pion photoproduction amplitudes. The corresponding correction to the Gamow-Teller matrix element for the triton $\beta$ decay is found to be of the same order of magnitude as the correction due to the pion exchange current.

[RADIOACTIVITY ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, calculated Gamow-Teller matrix element.]

The ${\frac{3}{2}}^{-}\to {\frac{7}{2}}^{-}$ 1.57-MeV $\beta$ transition in ${}_{}{}^{59}{}_{}{}^{}\mathrm{Fe}$ decay is important for $log\mathrm{ft}$ systematics because it has been considered to have the lowest $log\mathrm{ft}$ value for any second-forbidden nonunique $\mathbf{\beta }$ transition. We have measured the intensity of the 1.57-MeV $\beta$ group with an iron-free $\pi \sqrt{2}$ spectrometer. Our intensity value of 0.18 ± 0.04 per 100 decays leads to $logft=11.15\mathrm{}\pm 0.11$. This $log\mathrm{ft}$ value strengthens the experimental bases for the "strong rule" proposed by Raman and Gove, that second-forbidden $\mathbf{\beta }$ transitions have $log\mathrm{ft}\ge 11.0$.

[RADIOACTIVITY ${}_{}{}^{59}{}_{}{}^{}\mathrm{Fe}$ [from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}(n,\gamma )$]; measured $E_{\beta }$, $I_{\beta }$. ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ deduced levels, $Q$, $log\mathrm{ft}$. $\pi \sqrt{2}$ spectrometer.]

A new set of coupled integral equations for the transition operators of a nonrelativistic quantum-mechanical $n$- body system is presented. These equations are a generalization to the many-body system of a special case of a set suggested for the three-body problem by Kouri, Baer, and Levin. The Kouri-Baer-Levin formalism effectively couples together the Lippmann-Schwinger integral equations for the transition operators for all open channels thus simultaneously imposing all asymptotic boundary conditions. The effect of our specialization of these equations is to make the kernel of the integral equations connected so that the resulting equations appear to be a suitable basis for many-body calculations.

The mass of the negative kaon has been determined to be 493.66±0.19 MeV from measurements of kaonic-atom x-ray energies. The value depends upon considering calculated contributions to the complete atomic cascade.

[NUCLEAR REACTIONS Measured $K^{-}$ x rays, calculated atomic cascade, calculated energies, deduced $K^{-}$ mass.]

The total cross section for the photodisintegration of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, leading to three-body final states is considered in a sequential decay model. Various cluster decompositions of the bound and continuum states are studied. The influence of the (${}_{}{}^3{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) channel on the photoeffect is considered in a schematic coupled-channel model. The models investigated are able to provide a qualitative description of the data. The cluster model for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ appears to provide a more satisfactory over-all description than the shell model. Various open questions remain concerning the importance of nonsequential amplitudes.

[NUCLEAR REACTIONS Photodisintegration of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$; coupled channels; cluster model.]

Polarized neutrons from the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{H}(d,\overrightarrow{n}){}_{}{}^4{}_{}{}^{}\mathrm{He}$ were used to measure $n-d$ elastic scattering polarizations at 16.8 and 21.1 MeV. The results agree well with polarizations from the charge symmetric $p-d$ reaction. The data also follow the trend of recent theoretical calculations.

[NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\overrightarrow{n},n){}_{}{}^2{}_{}{}^{}\mathrm{H}$, $E=16.8\mathrm{} \mathrm{and} 21.1$ MeV, measured $P\left(\theta \right)$.]

We derive the amplitude for $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic collisions, including all multiple scattering, spin-flip, and charge-exchange effects, in the Glauber approximation. A totally antisymmetric ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ground-state wave function, and $\pi N$ elastic scattering amplitudes obtained from phase-shift analyses (through $G$ waves when necessary) are used as input. The results are applied to $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ total cross sections below 1.2 GeV and compared with measurements. The real part of the $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ forward elastic scattering amplitude is calculated and compared with dispersion-relation results. The differential cross section for $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering is calculated for pion energies between 50 and 1120 MeV and compared with data.

[NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}({\pi }^{\pm },{\pi }^{\pm })$, (${\pi }^{\pm },x$), $E=50-1200\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$ and ${\sigma }_{\mathrm{tot}}$.]

The ($\overrightarrow{p},t$) and ($\overrightarrow{p},{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions have been induced on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ targets by polarized protons of 43.8 or 49.6 MeV. Relative differential cross sections and analyzing powers were measured for 32 transitions and compared with zero-range distorted-wave Born-approximation calculations employing Cohen and Kurath wave functions. Although good results for differential cross sections were obtained, attempts to fit analyzing powers were less successful. In general ($\overrightarrow{p} ,t$) results gave better agreement than ($\overrightarrow{p},{}_{}{}^3{}_{}{}^{}\mathrm{He}$), ground state transitions better than those to excited states, and transitions to analog states better than more complex transitions.

[NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\overrightarrow{p},t)$, ($\overrightarrow{p},{}_{}{}^3{}_{}{}^{}\mathrm{He}$), ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(\overrightarrow{p},t)$, ($\overrightarrow{p},{}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=43.8\mathrm{}$ MeV; ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\overrightarrow{p},t)$, ($\overrightarrow{p},{}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=49.6\mathrm{}$ MeV; measured $\sigma (E;\theta )$ and analyzing powers for 32 transitions. DWBA analysis.]

Electron scattering form factors have been measured for the first six excited states in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and for the 2.429-MeV (${\frac{5}{2}}^{-}$) level in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$. The form factors for the lowest $T=1\mathrm{}$ level in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ along with the previously measured ground-state magnetic moment are used to specify the $T=0\mathrm{}$ and $T=1\mathrm{}$ wave functions for the mass-14 system assuming two $p$-shell valence particles in an $\mathrm{LS}$-coupling basis. The amplitudes of the various configurations so derived are generally in poor agreement with previous determinations, although the present wave functions yield values of the lifetime of the first $T=0\mathrm{}$ state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ ground-state quadrupole moment that are in excellent agreement with previous measurements. The present data are not sufficiently precise to allow a direct separation of the $T=0\mathrm{}$ and $T=1\mathrm{}$ components for the first four negative-parity excited states. However, for two of these states which are excited primarily by $C1\mathrm{}$ transitions, a comparison of the radiative strengths determined in this experiment with previous lifetime measurements sets a lower limit of 2% for the $T=1\mathrm{}$ admixture.

[NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{N} (e,e^{\prime })$; measured form factors for first six excited levels; deduced wave functions for first $T=0\mathrm{}$ and $T=1\mathrm{}$ levels in mass 14; ${}_{}{}^9{}_{}{}^{}\mathrm{Be} (e,e^{\prime })$; measured form factors for 2.429-MeV level.]

We investigated the effects on cosmic rays from spallation reactions between cosmic rays and interstellar helium. The spallation cross sections were measured by exposing thin-sandwich targets to the 920-MeV (230-MeV/$N$) external $\alpha$-particle beam of the 184-in. cyclotron at Lawrence Berkeley Laboratory. Cross sections were measured for the production: from ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ of ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ (12.5±0.5 mb); from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ of ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ (46.4±2.7 mb), ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ (6.75±0.5 mb), ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ (18.5±0.9 mb), and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ (18.5±1.3 mb); from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ (20.0±1.2 mb); and from ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ (12.6±0.8 mb). We constructed spallation cross-section ratios for the ratio of $\alpha$-particle-induced to proton-induced reactions ($\equiv {\Sigma }_p^{\alpha }$). We parametrized this ratio by the nucleon difference ($\Delta A$) between the target initial and final states and we fitted this ratio [${\Sigma }_p^{\alpha }\left(\Delta A\right)$] to a linear function in $\Delta A$. We used this function [${\Sigma }_p^{\alpha }\left(\Delta A\right)$] to obtain all of the $\alpha$-particle-spallation cross sections from the corresponding proton-spallation cross sections for targets and products in the elemental range $3\le Z\le 8$, and we applied these cross sections to a cosmic-ray transport calculation wherein we investigated the sensitivity of the cosmic-ray $\frac{L}{M}$ ratio [=(Li + Be + B) / (C + N + O)] and of the abundances of the $L$ and $M$ elements to the helium fraction of the interstellar gas.

[NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\alpha ,x){}_{}{}^{18}{}_{}{}^{}\mathrm{F}; {}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha ,x){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,x){}_{}{}^7{}_{}{}^{}\mathrm{Be}; {}_{}{}^9{}_{}{}^{}\mathrm{Be}(\alpha ,x){}_{}{}^7{}_{}{}^{}\mathrm{Be}$, $E=920\mathrm{}$ MeV; measured $\sigma$; NaI detector. Examined effect interstellar He on cosmic rays.]

Separable-potential three-body ($\alpha \mathrm{nn}$) models of the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ ground state are investigated. Different separable-potential fits to the $\alpha -n$ phase shifts and the low-energy singlet two-nucleon parameters are discussed, after which integral equations are derived for the spectator functions of the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ ground-state wave function assuming $S_{\frac{1}{2}}$, $P_{\frac{1}{2}}$, and $P_{\frac{3}{2}}$ components in the $\alpha -n$ interaction. These equations are solved to determine the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ binding energy and examine its sensitivity to the two-nucleon singlet effective range, its variation upon neglecting different components of the $\alpha -n$ interaction, and its dependence on different analytic forms for the $P$-wave $\alpha -n$ interactions. The spectator functions for the "best" two sets of parameters are generated and tabulated, and for one set the contributions to the ground-state normalization of the various components in the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ ground-state wave function are computed. With the "best" $S_{\frac{1}{2}}$,$P_{\frac{1}{2}}$, and $P_{\frac{3}{2}} \alpha -n$ interactions, the calculated ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ binding energy is 0.542 MeV for a two-nucleon $s$-wave separable potential fitted to the $n-p {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ effective-range parameters, $r_0=2.73\mathrm{}$ fm, and $a=-23.715\mathrm{}$ fm, and 0.359 MeV for the $n-n {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ effective-range parameters, $r_0=2.84\mathrm{}$ fm, and $a=-17\mathrm{}$ fm, compared to the experimental value of 0.969 MeV.

[NUCLEAR STRUCTURE ${}_{}{}^6{}_{}{}^{}\mathrm{He}$; calculated binding energy, wave function, contribution of wave function components to normalization. Three-body, separable-potential model.]

Dominant Coulomb corrections to the spectral functions for allowed nuclear $\beta$ transitions are calculated using the elementary particle approach.

[RADIOACTIVITY Calculated electromagnetic corrections. Allowed $\beta$ decay.]