The $\frac{K}{{\beta }^{+}}$ ratio in the decays of ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ have been measured as (9.6 ± 0.3) × ${10}^{-4\mathrm{}}$ and (10.7 ± 0.6) × ${10}^{-4\mathrm{}}$, respectively. A gas-flow proportional counter, operating in anticoincidence with the surrounding plastic scintillator, was used. Theoretical $\frac{K}{{\beta }^{+}}$ ratios for ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ were computed, using exchange-overlap corrections calculated by Vatai and, separately, exchange corrections extrapolated from the results of Bahcall for $14\le Z\le 37$. The experimental results were found to be in better agreement with Vatai's calculations.

We give an explicit analytic formula for the leading terms in the square of the matrix element for nucleon-nucleon bremsstrahlung in the relativistic, model-independent, soft-photon theory of Nyman. Such a formula should simplify direct and detailed comparisons of this soft-photon theory with experiment and with the predictions of other models. These comparisons have been difficult because Nyman in his original calculation of $\mathrm{NN}\to \mathrm{NN}\gamma$ was forced by the extremely complicated matrix element to use entirely numerical procedures. To obtain an analytic result we have used the Burnett-Kroll theorem, which makes it possible to bypass many of the complications of a straightforward algebraic calculation. We also emphasize the general utility of the Burnett-Kroll theorem as a calculational tool for obtaining in an almost trivial fashion the leading terms in the squares of very complicated radiative matrix elements.

A potential form alternate to the customary Yukawa form is deduced. This nonlocal potential incorporates retardation of the meson and nucleon normalization factors. A phenomenological potential patterned after the Reid soft-core potential is constructed. This new phenomenological potential is compared with the Reid potential off the energy shell. The off-shell changes lead to a decrease in the binding energy of nuclear matter of 1.5 MeV/particle in the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ state and an increase of 0.1 MeV/particle in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state.

Measurements of the $n-d$ total cross section to a precision of 1% are reported for the energy range 25-60 MeV. Nearly monoenergetic neutron beams were used whose energy was determined to about ±100 keV. The experimental values of ${\sigma }_{\mathrm{nd}}$ for energies ≥36 MeV are several percent larger than previous measurements in this range. Assuming charge symmetry, ${\sigma }_{\mathrm{nn}}$ can be calculated from the $T=1\mathrm{}$ phase shifts. The differences between experimental values of (${\sigma }_{\mathrm{nd}}-{\sigma }_{\mathrm{np}}$) and ${\sigma }_{\mathrm{nn}}$ calculations are small and fairly well accounted for by correction terms based on the method of Glauber.

The absolute cross section for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(p,pn)\mathrm{}{}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reaction has been measured in an external beam of the Argonne zero gradient synchrotron at 8.5-GeV/c momentum (7.6-GeV protons). Proton fluxes were measured with a scintillation counter telescope, and the 20.4 min ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ activity induced in $\frac{1}{8}$-in.-thick plastic scintillators was determined both by internal scintillation counting and by ${\beta }^{+}$-annihilation radiation counting with a NaI(T1) well crystal. A correction for the formation of ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ by secondary particles was determined and a correction was made for the small ${\pi }^{+}$ contamination of the proton beam. The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(p,pn)\mathrm{}{}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ cross section at 7.6 GeV is 28.2 ± 0.6 mb.

A previous perturbative calculation of elastic nucleon-deuteron scattering using nucleon-nucleon $S$-, $P$-, and $D$-wave forces is extended to include the rank-1 ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ tensor force of Yamaguchi and Yamaguchi. We find that both the tensor and the $P$-wave forces are important to the rank-2 polarizations of the deuteron. Using these forces we achieve excellent agreement with the data for these polarizations at 5.75 and 10.85 MeV. A comparison of calculations with just the tensor force to the exact calculations of Aarons and Sloan demonstrates the reliability of the perturbation technique.

Using the exact solution of a particle decaying from a square well, it is shown that the strength function, ($\frac{\Gamma }{D}$), is unbounded and has the form $\left(\frac{2\pi \Gamma }{D}\right)=-\ln \mathrm{}(1-T)\mathrm{}$ suggested by Moldauer (for average parameters), where $T$ is the transmission.

The $\beta$ decays of ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$ to the 4.44-MeV first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been studied by means of $\beta -\gamma$ coincidence measurements using a $4\pi$ plastic scintillator and a NaI(Tl) detector. The ratio of ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$/${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ $\beta$-ray branches to the 4.44-MeV state is found to be 1.52 ± 0.06 leading to $\frac{f{t}^{+}}{f{t}^{-}}=1.06\mathrm{}\pm 0.04$ for this branch. This result removes the only severe exception to the systematic trend of positive $\delta =\left(\frac{f{t}^{+}}{f{t}^{-}}\right)-1\mathrm{}$ for mirror decays and is in agreement with a recent calculation of the binding-energy effect. In separate measurements the absolute $\beta$-ray branch of ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ to the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ 4.44-MeV state is found to be (1.27 ± 0.06)%.

The interaction of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ with ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ was found to yield three ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nuclei via a direct process, as well as through intermediate ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ states. Large peaks attributed to direct interactions were observed in the experimental data at bombarding energies of 2.0, 6.0, and 13.0 MeV. These peaks were fitted using a simple model which assumed an $\alpha +d$ cluster structure for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nuclei and an interaction potential which acted only between the deuterons.

An ($n,n^{\prime }\gamma$) coincidence method was used to determine the neutron spin-flip probability in inelastic scattering. The experimental method consists of neutron time-of-flight and neutron-$\gamma$ coincidence techniques with the deexcitation $\gamma$ ray detected perpendicular to the neutron scattering plane. The angular distribution of the spin-flip probability for the first $J^{\pi }=2^{+}$ excitation in carbon has been determined at an energy of 7.48 MeV. The neutron spin-flip results were found to be similar to the proton spin-flip results in this energy region. The experimental results were compared to the predictions of an antisymmetrized distorted-wave calculation which did not provide good fits to the spin-flip data. The spin-flip predictions were sensitive to the optical-model parameters and were dominated by spin-orbit distortion in the elastic channels. The mechanism of core polarization dominated the inelastic amplitudes, masking the effects of the effective interaction on the extracore nucleons.

The scattering reactions of three equal-mass particles constrained to move in a straight line and interacting with each other via zero-range potentials have been analyzed on the basis of the extended $R$-matrix theory. The simplicity of the model facilitates an exposition of the complexities that result from the existence of rearrangement channels and from the possibility for breakup into three-body channels. The conventional expressions for the $K$ matrix and the $T$ matrix are derived on a rigorous basis. A practical method for approximating the continuum of three-body breakup channels by a discrete set is used to carry out a distorted-wave Born approximation (DWBA) $K$-matrix calculation of the probabilities for transmission, knockout, and breakup when one particle is incident on a bound state of the other two. This method is found to give much better results than a DWBA $T$-matrix calculation.

The spin-orbit part $V_{\overrightarrow{I}·\overrightarrow{\mathrm{L}}}$ of the $\alpha$-nucleus interaction is estimated on the basis of the nucleon-$\alpha$ spin-orbit potential. Here $\overrightarrow{I}$ is the spin of the target nucleus and $\overrightarrow{\mathrm{L}}$ is the orbital angular momentum of $\alpha$-nucleus relative motion. The calculation assumes that the target nucleus undergoes no virtual excitation during the collision and that core polarization effects are absent. Numerical results are obtained for the nuclei of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The result for the two first cases is found to be an order of magnitude smaller than the phenomenological values of $V_{\overrightarrow{I}·\overrightarrow{\mathrm{L}}}$ quoted in the literature. For ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ the value of $V_{\overrightarrow{I}·\overrightarrow{\mathrm{L}}}$ is nearly 10 times larger than for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, a result which depends on the fact that for the valence nucleon $j=l-\frac{1}{2}$ in the former case, and $j=l+\frac{1}{2}$ in the latter case. For ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ no phenomenological values of $V_{\overrightarrow{I}·\overrightarrow{\mathrm{L}}}$ appear to be known.

The branching ratio of the $0^{+}$ state of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ at 2561 keV for decay by $e^{+}-e^{-}$ pair emission to the $0^{+}$ ground state is measured to be (0.17 ± 0.025)%. The lifetime of this third excited state of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ is not known; the main decay mode is by $E2\mathrm{}$ decay to the 1408-keV $2^{+}$ first excited state. In addition $\gamma$-ray spectra were measured with a Ge(Li) detector and excitation energies and branching ratios were determined for levels up to 3.834 MeV.

The elastic $\alpha$ scattering to backward angles has been studied for ${}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$ between 40.7 and 72.3 MeV. The cross sections for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are larger than those for the higher isotopes up to the highest energies. They show backward increases that disappear above 50 MeV. The enhancement factor for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ over ${}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$ varies smoothly with energy. ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ does also show a backward cross-section enhancement over ${}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$. $\alpha$-cluster rotational bands in the ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ compound state, four-nucleon correlations in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and the $l$-dependent optical model are discussed as approaches to understand the anomaly. The rotator model appears to agree qualitatively with the experimental data. It involves rotational bands extending at least up to $J=16\mathrm{}$ in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$.

Thin-target cross sections were determined by radiochemical means for the production of the radionuclides ${}_{}{}^{65}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Mn}$, and ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ by 82-, 111-, 187-, 283-, and 416-MeV protons incident on natural copper. The experimental results are compared with values in the literature, expected trends in the excitation functions, and values calculated via empirical formulas and Monte Carlo treatments.

Coherence widths of the compound nucleus ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ were determined from excitation functions of the differential cross section for the reactions ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}(p,\alpha ){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha ){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The proton-induced reaction provided a lower average spin of the compound nucleus. Excitation functions were measured for ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}(p,\alpha ){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ from 13.90- to 14.24- and from 26.62- to 30.56-MeV compound-nucleus energy. The average coherence widths were 11 ± 1.2 and 95 ± 15 keV, respectively. For the oxygen-induced reaction, excitation functions were measured from 28.99 to 34.42 MeV with a resulting 73 ± 7-keV coherence width, which is nearly the same as for the lower-spin proton-induced case.

These coherence widths were used to test the Gilbert and Cameron level-density formulation. Good agreement with the above data was obtained if the compound nucleus ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ is considered to be spherical in this formulation. The increase in the calculated width for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ induced reaction with increasing excitation energy is greater than indicated by combining our data with another measurement at higher excitation.

The energy dependence of elastic $\alpha$ scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ between 39.6 and 115.4 MeV is determined using a microscopic optical model. The agreement between theory and experiment improves as the energy increases. We find that both the real and imaginary parts of the optical potential are well described by a strength depending linearly on energy. For the real part the slope is about half the corresponding value for proton scattering; no theoretical estimates of this quantity are presently available.

The analysis of (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) reactions at 70 MeV to isobaric analog ground states of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ have shown an energy dependence in the extracted isospin-dependent interaction strengths consistent with results at lower energies; the interaction strengths are approximately 50% smaller than at lower bombarding energies. The shapes of the form factors in a macroscopic analysis are nuclei-dependent. A mass-three optical potential with a real strength of about 110 MeV and a volume imaginary term is strongly preferred in the (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) calculations.

Chemically and isotopically separated sources of ${}_{}{}^{205}{}_{}{}^{}\mathrm{Bi}$ were used to study the level structure of ${}_{}{}^{205}{}_{}{}^{}\mathrm{Pb}$. $\gamma$-ray data were taken with Ge(Li) detectors in the singles mode, with a Compton suppression spectrometer, and with a Ge(Li)-Ge(Li) two-parameter analyzer system in a 4096 × 2048 coincidence mode. Conversion-electron data were taken with a Si(Li) detector. From these data 146 transitions were identified in the decay of ${}_{}{}^{205}{}_{}{}^{}\mathrm{Bi}$, and 130 were placed in a level scheme which included 26 definite and 1 tentatively assigned levels. Previously suggested levels at 1575.26, 1705.03, 1965.9, and 2521.40 keV were confirmed from coincidence data, while a 1129.9-keV level was not. New levels at 1756.4 and 1842.01 are established and an 1818-keV level tentatively assigned. Several new spin and parity assignments are made. Experimental results are compared with recent shell-model calculations.

An investigation for the existence of asymmetric shapes having symmetry about the $X-Y$, $Y-Z$, and $Z-X$ planes, is carried out for the even-even $2p-1f$ shell nuclei by using the self-consistent Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) procedures. The results for a central Yukawa interaction and core-polarized Kuo-Brown matrix elements for the Hamada-Johnston interaction are reported. It is found that for those $N=Z$ nuclei which favor triaxial shape, the HF gap is increased considerably as compared to their corresponding HF gap for the axially symmetric shape. For $N\ne Z$ nuclei, though the HF approach may yield triaxial solutions with somewhat lower energies as compared to the axial HF results, these solutions converge to their respective HFB shapes having axis of symmetry in the presence of pairing. For those cases where the HFB approximation yields triaxial solution with minimum energy, the gain in binding energy due to pairing correlations is found to be compensated by the decrease in the HF contribution to the HFB energy, resulting in no over-all gain in binding over the corresponding triaxial HF solution. The pairing energy, intrinsic quadrupole moments, and pickup strengths of those nuclei which favor triaxial solutions are compared with the corresponding axially symmetric results.