The angular distribution of the internal bremsstrahlung accompanying allowed electron-capture transitions is calculated using the theory of Glauber and Martin. It is shown that when Coulomb effects as well as relativistic and screening corrections are taken into account, the asymmetry coefficients associated with the radiative capture of $K$- and $L$-shell electrons acquire a dependence on photon energy which is quite pronounced at energies below about $Z\alpha m{c}^2$. This is quite contrary to the results of previous calculations, which have predicted these coefficients to be energy independent. The present results are found to give much better agreement with recent experimental observations than that obtained with the previous theory.

Accurate differential-cross-section data for proton-proton elastic scattering are presented at 9.690, 9.918, and 13.600 MeV. These data agree with current energy-dependent phase-shift analyses and resolve discrepancies between previous sets of data and between those data and the phenomenological analysis.

The energy moments of spectral distributions are used to investigate the structure of spectroscopic calculations. Eigenvalue distributions are used to predict energy spectra, which are compared with the results of matrix diagonalization. The nature of the corresponding eigenvectors is similarly analyzed. The propagation of moments for scalar and configuration distributions is illustrated throughout the $\mathrm{sd}$ shell. These scalar moments are then used to estimate the trend in theoretical binding energies for these nuclei and in turn are compared with empirical data. Finally, we investigate the dependence of the energy and wave function of the ground state of ${\mathrm{O}}^{16}$ upon the vector space underlying a theoretical calculation. The unrenormalized Kuo-Brown matrix elements are employed in this analysis, and the role of multiple particle-hole excitations is discussed.

The differential cross section for neutron-proton scattering has been measured at 152 ± 1 MeV. Protons were detected in the angular range of 5 to 50° relative to the incident beam direction, corresponding to neutron scattering angles of 169 to 78° in the c.m. system. The angular distribution is consistent with earlier data at the smaller proton angles, but significant discrepancies are apparent at angles greater than 25°.

The existence of phase-equivalent ambiguities in the generalized optical model is investigated using a coupled-channel analysis of $\alpha +{}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at 17 MeV. When compound-nucleus contributions are included in the analysis it is found that the phase-equivalent ambiguities typical of the spherical optical potential still occur when the potential is nonspherical. The values obtained for the deformation parameter which are appropriate for the rotational states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ are found to be relatively insensitive to the choice of a phase-equivalent potential. A simple explanation of this insensitivity has not yet been found.

The method-I angular correlation technique of Litherland and Ferguson has been applied to the reaction ${\mathrm{Ni}}^{64}(p,n\gamma ){\mathrm{Cu}}^{64}$. Spin assignments were obtained for the following levels in ${\mathrm{Cu}}^{64}$: 1 (0 keV), 2(159 keV), (1, 2) (278 keV), 1 (344 keV), 3 (362 keV), and 1 (663 keV). $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios for the 159- and 203-keV transitions were determined. A weak transition from the 362-keV level to the ground state was observed.

Energy levels in ${\mathrm{Sc}}^{44}$ have been studied using the ${\mathrm{Sc}}^{45}\mathrm{}(d,t)\mathrm{}{\mathrm{Sc}}^{44}$ reaction at 19.5-MeV incident energy. Thirty-six levels in ${\mathrm{Sc}}^{44}$ below an excitation energy of 3.2 MeV were observed. Angular distributions were measured, and compared with the distorted-wave Born-approximation theory to obtain transferred $l$ values and spectroscopic factors. A considerable amount of $l=1\mathrm{}$ strength was found, indicating the presence of $2p$ neutrons in the ground state of ${\mathrm{Sc}}^{45}$. A recent shell-model calculation using an ${\left(f_{\frac{7}{2}}\right)}^4$ configuration shows qualitative agreement with experiment.

A method for the evaluation of the average angular distribution, over a range of energy, of particles evaporated in succession from a compound nucleus is presented. The method is applied to the analysis of the angular distribution in the reaction ${\mathrm{Fe}}^{56}(\alpha ,p){\mathrm{Co}}^{59}$ and the reaction ${\mathrm{Cu}}^{63}({\mathrm{C}}^{12},p){\mathrm{Se}}^{74}$. The analysis indicated that nuclei at high excitation have rigid moments of inertia.

The $\frac{M}{L}$ orbital-electron-capture ratio in ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$ decay has been measured in a wall-less multiwire proportional counter containing the gaseous radioactive compound ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$${\mathrm{H}}_4$. The counter was filled to 6 atm with argon containing 15 cm Hg propane. Recent advances in proportional-counter spectrometry below 500 eV have extended the sensitivity for precision measurement to the detection of single- and few-electron events down to essentially zero energy, even in the presence of high intensities of more energetic radiation. These improvements are the result not only of the sophistication of the low-noise electronic system, but also of the present investigation of the degradation spectrum (low-energy tails and afterpulses) from spectral peaks, and of the resolution from each other of single- and few-electron spectra by using computer analysis. A fully transistorized electronic system was developed which includes a special dc-coupled logic unit with zero-time recovery (updating) to perform the following operations: (i) to ensure proper anticoincidence functioning of the ring counter; (ii) to provide paralysis pulses necessary to block possible afterpulses following an ionizing event in either the ring or central counter; and (iii) to eliminate the phenomenon of front- and backedge clipping of large pulses into small ones by the action of the anticoincidence gate. Measurements were made of the $K$, $L$, and $M$ peaks, having mean energies of 10.37 keV, 1298, and 158 eV, respectively, and the resulting orbital-electron-capture ratios were determined to be $\frac{P_L}{P_K}=0.117\mathrm{}\pm 0.001$ and $\frac{P_M}{P_L}=0.162\mathrm{}\pm 0.003$. These ratios are compared with theoretical results. Whereas the present $\frac{L}{K}$ capture ratio is in closer agreement with theory corrected for exchange according to Bahcall, the theoretical prediction of the $\frac{M}{L}$ ratio by Bahcall with correction for exchange lies approximately 7% above the present value, which agrees well with a recent theoretical calculation by Vatai. The half-life of ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$ was found by least-squares fitting to be 11.15 ± 0.15 days, by following the decay of $K$ x rays from a solid source with a Ge(Li) x-ray detector.

The ${\beta }^{-}$ decay of ${\mathrm{S}}^{38}$ to states of ${\mathrm{Cl}}^{38}$ has been studied with Si, Ge(Li), and NaI(Tl) detectors. ${\mathrm{S}}^{38}$ was produced in the reaction ${\mathrm{S}}^{36}\mathrm{}(t,p)\mathrm{}{\mathrm{S}}^{38}$ at $E_t=3.26\mathrm{}$ MeV by bombarding ${\mathrm{Ag}}_2$S targets, enriched to 1.93% in ${\mathrm{S}}^{36}$. The half-life was measured to be 169.6 ± 0.7 min. The main $\beta$ branch (83 ± 2)% with end-point energy 1005 ± 20 keV proceeds to a previously unidentified level of ${\mathrm{Cl}}^{38}$ at 1942 keV. A 1941.7 ± 0.2-keV $\gamma$ ray has been observed in coincidence with this branch. The $\Delta T=1\mathrm{} \beta$ transition is allowed ($logft=4.98\mathrm{}\pm 0.03$) giving $J^{\pi }=1^{+}$ for ${\mathrm{Cl}}^{38}$ (1942 keV). The $\gamma$ decay of the 1942-keV level proceeds 100% to the ${\mathrm{Cl}}^{38}$ ground state, and an upper limit of 0.4% can be set for any other possible decay mode. No $\gamma$ rays in coincidence with the 1942-keV $\gamma$ ray were observed. The $\beta$- and $\gamma$-ray measurements determine the $Q$ value for the ${\mathrm{S}}^{38}\left({\beta }^{-}\right){\mathrm{Cl}}^{38}$ reaction as 2947 ± 20 keV. In addition to the main branch a (2.8 ± 0.3)% branch proceeds to the 1746.2 ± 0.4-keV level, which decays predominantly to the ${\mathrm{Cl}}^{38}$ ground state. The $log\mathrm{ft} \mathrm{of} 6.76\pm 0.05$ restricts the 1746-keV level to have $J^{\pi }=0^{-},1^{-}, or 1^{+}$; the ${\mathrm{Cl}}^{37}\mathrm{}(d,p)\mathrm{}$ reaction establishes the parity as odd. No other $\gamma$ rays from ${\mathrm{Cl}}^{38}$ were observed, which leads to a value of (14.2 ± 2)% for the ground-state $\beta$ branch and to a unique first-forbidden matrix element, ${〈G_1〉}^2$, of 1.53 ± 0.22 ${\mathrm{F}}^2$, in excellent agreement with theoretical calculations. The Coulomb energy difference between ${\mathrm{Cl}}^{38}$ and ${\mathrm{S}}^{38}$ is determined as 6051 ± 32 keV. The isobaric-multiplet mass equation is used to predict the masses of the lowest $J^{\pi }=0^{+}$, $T=3\mathrm{}$ states in ${\mathrm{K}}^{38}$, ${\mathrm{Ca}}^{38}$, ${\mathrm{Sc}}^{38}$, and ${\mathrm{Ti}}^{38}$. The predicted mass excess for ${\mathrm{Ti}}^{38}$ is + 10.55 ± 0.78 MeV.

The spectrum of the internal bremsstrahlung accompanying the orbital electron capture in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ was investigated in the energy range from 180 to 465 keV. The disintegration energy of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ to the second excited state of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ was found to be 674 ± 30 keV. The ratio of the probabilities of the total radiative capture to the nonradiative $1s$ electron capture was found to be (0.98 ± 0.2) × ${10}^{-4\mathrm{}}$ as compared to the theoretically predicted value of 1.35 × ${10}^{-4\mathrm{}}$ for the investigated energy range. A comparison with the results of other intensity measurements of the internal bremsstrahlung is given.

The recoil-distance method has been used with the ${\mathrm{Al}}^{27}(\alpha ,n){\mathrm{P}}^{30}$ reaction to measure the life-times of the 1.453- and 1.974-MeV levels in ${\mathrm{P}}^{30}$. A mean lifetime of $\tau =9.2\mathrm{}\pm 0.5$ psec was obtained for the $2^{+}$ 1.453-MeV level and $\tau =6.8\mathrm{}\pm 0.4$ psec was obtained for the $3^{+}$ 1.974-MeV level. A Ge(Li) $\gamma$ spectrum was measured in coincidence with neutrons to identify the ${\mathrm{P}}^{30}$ transitions. Comparisons of the resulting reduced transition probabilities with shell-model calculations have been made.

The ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(p,\gamma ){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(p,\gamma ){}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ reactions have been investigated in the energy range $E_p=2.3\mathrm{} \mathrm{to} 3.0$ MeV. Excitation functions for the transition to the ground state, with a total resolution of 2 keV, were determined for each reaction over this energy region. Using thick targets and both a single Ge(Li) detector and a Ge(Li) detector incorporated into a pair spectrometer, total summed spectra for the 700-keV region were obtained. The average total cross section of ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(p,{\gamma }_0){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(p,{\gamma }_0){}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ was 12 ± 5 μb and 17 ± 7 μb, respectively. These total summed spectra, which represent the total $\gamma$-ray yield in this region, have been examined for a possible dependence of the intensity on the $J^{\pi }$ of the final state. The data suggest such a $J$-dependence hypothesis, but detailed theoretical analysis of the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(p,\gamma ){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ reaction does not completely agree with experiment. A spectrum from a Ge(Li) detector in coincidence with a NaI(Tl) detector was accumulated for the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(p,\gamma ){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ reaction. The decay scheme of the states of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ up to an excitation energy of 3.621 MeV was determined and the implications about spins and parities are consistent with accepted assignments.

Protons emitted from the bombardment of deuterium with a 16.5-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beam have been measured at ${\theta }_p={30}^{\circ }$, in coincidence with the other charged particles from the reaction. Angular correlations at $6.6<~E_p<~7.8$ MeV have been obtained and compared with a modified-Born-approximation calculation of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ stripping. The angle-energy correlation and the $p-{}_{}{}^3{}_{}{}^{}\mathrm{H}$ to $p-{}_{}{}^3{}_{}{}^{}\mathrm{He}$ branching ratio can be reproduced if the ${}_{}{}^3{}_{}{}^{}\mathrm{H}+p$ phase shifts of Meyerhof and McElearney and the ${}_{}{}^3{}_{}{}^{}\mathrm{He}+n$ phase shifts of Bransden, Robertson, and Swan are used to describe the respective interactions in the final states. In agreement with Barit et al., the triplet $s$-wave ${}_{}{}^3{}_{}{}^{}\mathrm{He}+n$ phase shifts are found to be negative.

The low-lying level structure of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ has been studied using the thermal-neutron capture reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}(n,\gamma ){}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ on an isotopically separated target of ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$. The $\gamma$-ray spectrum from this reaction has been studied in the energy range from 0.1 to 10.1 MeV using a Li-drifted Ge spectrometer system. $\gamma -\gamma$ coincidence measurements using Ge(Li) detectors have also been made. Spin and parity assignments for the excited states below 2450 keV are proposed, primarily on the basis of $\gamma$-ray branching to levels with established spin and parity values. The proposed level energy [keV ($I^{\pi }$)] values are $0\left({\frac{3}{2}}^{+}\right)$, $980.4\left({\frac{1}{2}}^{+}\right)$, $1293.4\left({\frac{7}{2}}^{-}\right)$, $1559.9\left({\frac{1}{2}}^{+}\right)$, $1582.0\left({\frac{5}{2}}^{+}\right)$, $1677.5({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$, $1698.1({\frac{5}{2}}^{\pm },{\frac{7}{2}}^{+})$, $2144.1\left({\frac{5}{2}}^{+}\right)$, $2166.0({\frac{1}{2}}^{+},{\frac{3}{2}}^{\pm })$, $2316.5({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$, $2447.9({\frac{1}{2}}^{\pm },{\frac{3}{2}}^{\pm })$. Additional levels have been observed at 2494.7, 2507.9, 2527.9, 2599.8, 2681.5, 2712.2, 2756.5, 2760.7, 3042.1, 3142.1, 3164.5, 3213.4, 3235.6, and 3281.1 keV. These low-lying excited states of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ are discussed in terms of two-particle, one-hole configurations of the form $p{\left(d_{\frac{3}{2}}\right)}^{-1\mathrm{}}n{\left(f_{\frac{7}{2}}\right)}^2$.

The lifetime and $\gamma$-ray branching of the 3.90-MeV ($2^{+}$) state of ${\mathrm{Ca}}^{40}$ have been measured using the reactions ${\mathrm{Ca}}^{40}(p,p^{\prime }){\mathrm{Ca}}^{{40}^{*}}$ at a bombarding energy of 7.32 MeV and ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ at the $E_p=1.344\mathrm{}$-MeV resonance. Consistent values for the lifetime were obtained from the Doppler shifts of the 3.90-MeV $\gamma$ rays in both reactions and from the 0° line shape in the ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ reaction. A value of $\tau =50\mathrm{}\pm 5$ fsec is adopted for the mean lifetime of the 3.90-MeV state. The 3.90→3.35-MeV branching ratio was measured by observing the 0.555-MeV cascade $\gamma$ rays in quadruple coincidence with the two annihilation $\gamma$ rays and the inelastic protons in the ${\mathrm{Ca}}^{40}(p,p^{\prime }){\mathrm{Ca}}^{{40}^{*}}$ reaction, or in triple coincidence with annihilation $\gamma$ rays in the ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ reaction. Results are in agreement and the adopted branch is (7.95 ± 0.8) × ${10}^{-4\mathrm{}}$. By combining the lifetime and branching results, the 0.555-MeV $E2\mathrm{}$ transition rate corresponds to a $B(E2\mathrm{}$; 3.90 ($2^{+}$) → 3.35 ($0^{+}$)) of 250 ± 35 $e^2$ ${\mathrm{fm}}^4$. This result is in excellent agreement with recent theoretical estimates of the transition strength. The mean lifetime of the 5.28-MeV ($4^{+}$) state of ${\mathrm{Ca}}^{40}$ was measured to be 310 ± 60 fsec. The corresponding $B(E2\mathrm{}$; 5.28 ($4^{+}$) → 3.90 ($2^{+}$1)) of 535 ± 110 $e^2$ ${\mathrm{fm}}^4$ is in reasonable agreement with expectations based on a strong-deformation rotational model of the states.

In a recent experiment some high-lying negative-parity states in ${\mathrm{Pr}}^{139}$ have been observed. This paper reports a shell-model calculation of these states with ${\mathrm{Ce}}^{140}$ as the closed core. Some further experiments to explore the levels of ${\mathrm{Pr}}^{139}$ are also suggested.

Energy levels of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ have been studied through the ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}(d,t)$ and ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ reactions induced by 17-MeV deuterons and 30-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particles, respectively. Transferred orbital angular momenta are obtained from (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $\alpha$) angular distributions and from cross-section ratios $R=\frac{d\sigma ({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )}{d\sigma \mathrm{}(d,t)\mathrm{}}$. The ratios $R$ vary by a factor of ${10}^3$ for a change in $l$ from 0 to 7 and provide a very sensitive measure of the angular momentum transfer. Experimentally measured spectroscopic factors are found to be in reasonable agreement with those calculated from Nilsson wave functions. Rotational bands associated with the following Nilsson configurations are identified in ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}: {\frac{5}{2}}^{+}\mathrm{}\left[622\right]\mathrm{}$, ${\frac{7}{2}}^{+}\mathrm{}\left[624\right]\mathrm{}$, ${\frac{1}{2}}^{+}\mathrm{}\left[631\right]\mathrm{}$, ${\frac{7}{2}}^{-}\mathrm{}\left[743\right]\mathrm{}$, ${\frac{3}{2}}^{+}\mathrm{}\left[631\right]\mathrm{}$, ${\frac{1}{2}}^{-}\mathrm{}\left[501\right]\mathrm{}$, and ${\frac{5}{2}}^{-}\mathrm{}\left[752\right]\mathrm{}$.