The decays of 8.5-min ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}_{}^g{}_{}{}^{}$ and 2.5-min ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}_{}^m{}_{}{}^{}$ have been studied with a variety of $\gamma$ and ${\beta }^{+}$ detectors in many different singles and coincidence configurations. States in ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$ populated by ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}_{}^g{}_{}{}^{}$ decay were found to lie at 0 ($J^{\pi }={\frac{7}{2}}^{-}$), 377.9 (${\frac{5}{2}}^{-}$), 1288.0 (${\frac{3}{2}}^{-}$), 1619.9 (${\frac{9}{2}}^{-}$), 2273.5 (${\frac{5}{2}}^{-}$), 2685.6 (${\frac{7}{2}}^{-}$), 2946.6 (${\frac{9}{2}}^{-}$), 3126.7 (${\frac{9}{2}}^{-}, {\frac{7}{2}}^{-}, {\frac{5}{2}}^{-}$), and 3248.0 keV (${\left[\frac{9}{2}\right]}^{-}$). States in ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}$ populated by 3040.6-keV (${\frac{19}{2}}^{-}$) ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}_{}^m{}_{}{}^{}$ decay were confirmed at 0 (${\frac{7}{2}}^{-}$), 1328.1 (${\frac{9}{2}}^{-}$), and 2339.6 keV (${\frac{11}{2}}^{-}$). In addition, a 3040.6-keV $E6\mathrm{}$ and a 1712.6-keV $M5\mathrm{}$ transition were found to compete with the 701.1-keV $E4\mathrm{}$ isomeric transition in deexciting ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}$, this being the first observation of such high multipolarities. The $E6\mathrm{}$ has an intensity of 6.0×${10}^{-4\mathrm{}}$ and the $M5\mathrm{}$ an intensity of 1.3×${10}^{-2\mathrm{}}$ relative to the $E4\mathrm{}$ transition. The $E4\mathrm{}$, $M5\mathrm{}$, and $E6\mathrm{}$ transitions are retarded by respective factors of 7.6, 4.2, and 4.3 with respect to single-particle estimates and by somewhat larger factors with respect to simple shell-model estimates.

RADIOACTIVITY ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}_{}^{g,m}{}_{}{}^{}$ [from ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}(p, 3n)$]; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $E_{{\beta }^{+}}$, $I_{{\beta }^{+}}$, $\gamma -{\beta }^{+}$ coin; calculated $log\mathrm{ft}$; ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$ deduced levels $J^{\pi }$; calculated shell-model wave functions, $\gamma$ transition probabilities.

The decay of 20.90-min ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pm}$ has been studied with Ge(Li) and NaI(Tl) $\gamma$-ray detectors in a variety of singles and coincidence configurations, including Ge(Li)-Ge(Li) two-parameter "megachannel" coincidence experiments, anticoincidence experiments, and pair (${\gamma }^{\pm }-\gamma$) experiments to determine the relative ${\beta }^{+}$ feedings. Fifty-two $\gamma$ rays were identified from this decay, and 43 of these (> 99% of the $\gamma$ intensity) were placed in a decay scheme containing 23 levels in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Nd}$. $J^{\pi }$ assignments or limits were made for all of the states. The structures of the lower-lying states in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Nd}$ are discussed in terms of the shell model, and possible structures are also suggested for many of the higher-lying states. We compare our results with those of previous studies and also with particle-transfer data.

RADIOACTIVITY ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pm}$; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin, ${\gamma }^{\pm }\gamma$ coin, deduced ${\alpha }_K$; ${}_{}{}^{141}{}_{}{}^{}\mathrm{Nd}$ deduced levels, $J$, $\pi$.

Single $\gamma$ ray, $\gamma -\gamma$ coincidence, and level spectrometer studies have been performed on the decay of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Fe}$ ($T_{\frac{1}{2}}=5.98\mathrm{}\pm 0.06$ min). 48 $\gamma$ transitions with energies up to 3365 keV are assigned to this decay and 22 levels are proposed in the ${}_{}{}^{61}{}_{}{}^{}\mathrm{Fe}$ decay scheme. Spins and parities of levels in ${}_{}{}^{61}{}_{}{}^{}\mathrm{Co}$ are given. The level structure of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Co}$ is compared with neighboring odd Co nuclei.

RADIOACTIVITY ${}_{}{}^{61}{}_{}{}^{}\mathrm{Fe}$; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $\gamma -\gamma$ anticoin; deduced $log\mathrm{ft}$, $J^{\pi }$. ${}_{}{}^{61}{}_{}{}^{}\mathrm{Co}$; deduced $E_{\mathrm{levels}}$, $J_{\mathrm{levels}}^{\pi }$; compared with odd Co nuclei.

The $\gamma$-ray spectrum of the decay of ${}_{}{}^{158}{}_{}{}^{}\mathrm{Ho}$ in transient equilibrium with 2.3-h ${}_{}{}^{158}{}_{}{}^{}\mathrm{Er}$ has been studied with Ge(Li) detectors. Results of $\gamma$-ray singles and coincidence experiments are reported and a decay scheme for ${}_{}{}^{158}{}_{}{}^{}\mathrm{Ho}$ → ${}_{}{}^{158}{}_{}{}^{}\mathrm{Dy}$ is proposed. New levels have been assigned to the $\beta$-vibrational band and a rotational band built on the two-quasineutron state ($\nu \frac{5}{2^{-}}\mathrm{}\left[523\right]+\nu \frac{3}{2^{-}}\mathrm{}\left[521\right]\mathrm{}$). A new $K=2\mathrm{}$ rotational band with spins up to $6^{+}$ built on a level at 1851.9 keV is proposed. An attempt is made to characterize a group of negative parity states at about 1400 keV, and tentative assignments of the $K=0, 1, \mathrm{and} 2$ octupole vibrational band heads are suggested.

RADIOACTIVITY ${}_{}{}^{158}{}_{}{}^{}\mathrm{Ho}$ [from ${}_{}{}^{148}{}_{}{}^{}\mathrm{Nd}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, 4n)$; ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, 4n)$, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}({}_{}{}^{11}{}_{}{}^{}\mathrm{B}, 4n)$ $(2.3-\mathrm{h}, \mathrm{EC}, {\beta }^{+}){}_{}{}^{158}{}_{}{}^{}\mathrm{Ho}$]; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \gamma$ coin, $T_{\frac{1}{2}}$, deduced $log\mathrm{ft}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Dy}$ deduced levels, $J$, $\pi$, ${\alpha }_K$, $\gamma$ multipolarities. Ge(Li) detectors.

The $\gamma$ radiation following the decay of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Te}_{}^m{}_{}{}^{}$ to levels in ${}_{}{}^{131}{}_{}{}^{}\mathrm{I}$ has been studied. $\gamma -\gamma$ directional correlation measurements have been made using two Ge(Li) detectors. The amplitude mixing ratios for 11 transitions have been determined. A discussion of possible spin assignments for several of the levels is presented.

RADIOACTIVITY ${}_{}{}^{131}{}_{}{}^{}\mathrm{Te}_{}^m{}_{}{}^{}$ from ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}(n, \gamma )$; measured $\gamma \gamma \left(\theta \right)$. ${}_{}{}^{131}{}_{}{}^{}\mathrm{I}$ deduced levels, $J$, $\gamma$ mixing ratios. Enriched target, Ge(Li) detectors.

We calculate the induced Coulomb correction as well as the usual Coulomb correction, to order $\alpha \mathrm{ZR}{W}_0$, to the first forbidden $0^{-}$ ↔ $0^{+}$ $\beta$ decay and demonstrate that the induced correction, through the pseudoscalar form factor term, is dominant among all the Coulomb corrections.

The ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p, {\gamma }_{0,1}){}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ reaction was studied in the region of previously reported low-lying $T=\frac{3}{2}$ states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$. Resonances were observed at $E_p=11.275\mathrm{}\pm 0.006, 12.711\pm 0.006, 13.255\pm 0.006, 14.435\pm 0.010, \mathrm{and} 14.583\pm 0.006$ MeV with $\frac{(2\mathrm{}{J}_R+1){\Gamma }_{P_0}{\Gamma }_{\gamma }}{\Gamma }=1.2\mathrm{}\pm 0.4, 13.6\pm 3.5, 2.5\pm 1.5, 13.0\pm 5.9, \mathrm{and} 11.8\pm 5.3$ eV, respectively. Using reported values for $\frac{(2\mathrm{}{J}_R+1){\Gamma }_{P_0}}{\Gamma }$, radiative widths ${\Gamma }_{\gamma }=6.0\mathrm{}\pm 2.5, 11.3\pm 3.4, 2.8\pm 1.8, 81\pm 54, \mathrm{and} 13.4\pm 7.0$ eV were deduced for the respective resonances. Shell model 2p-1h calculations using realistic Kuo-Brown interaction matrix elements were performed. The computed excitation energies and $B\left(E1\mathrm{}\right)\mathrm{}$ values were found to agree with the experimental results.

NUCLEAR STRUCTURE ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$; measured ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p, \gamma )$; deduced $E_x$, $\Gamma$, $\frac{(2\mathrm{}{J}_R+1){\Gamma }_p{\Gamma }_{\gamma }}{\Gamma }$ of ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}(T=\frac{3}{2})$ levels. 2p-1h calculations performed for negative parity ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}(T=\frac{3}{2})$ levels; compared theoretical $B\left(E1\mathrm{}\right)\mathrm{}$ matrix elements to experimentally deduced values.

$R$-matrix theory and other theories involving a division of the configuration space into an internal and an external region are derived in the frame of a projection operator formalism. The continuity condition particularly is investigated. In connection with this problem, we show that the introduction of the hard sphere phase shift is quite arbitrary and that it can be replaced by any other phase shift.

NUCLEAR REACTIONS $R$-matrix theory: derivation by means of projection operator formalism. Mathematical origin of the hard sphere phase shift.

An $L=0\mathrm{}$ component observed in the angular distribution of the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, d){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reaction leading to a state at 9.13 MeV in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ assigns $J^{\pi }=3^{+}$ to this level. This presumably is the "missing" $3^{+}$ state predicted by Lie but previously unidentified.

NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, d)$, $E\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}\right)=16.5\mathrm{} \mathrm{and} 21.0$ MeV. Measured $\sigma \left(\theta \right)$ for state at $E_x=9.13\mathrm{}$ MeV, assigned $J^{\pi }=3^{+}$.

For the 3.520-MeV state of ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$, a comparison of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(d, p){}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(n, n){}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ results strongly suggests a spin-parity of $1^{-}$ or $2^{+}$.

NUCLEAR REACTIONS ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(d, p)$ $E_d=12.0\mathrm{}$ MeV, enriched target. Measured $\sigma \left(\theta \right)$ for $E_x=3.52\mathrm{}$ MeV. DWBA analysis and comparison with ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(n, n)$.

Angular distributions from the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(t, p){}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ reaction have been analyzed using distorted-wave techniques and employing two-particle-transfer amplitudes from a recent $1p_{\frac{1}{2}}-1\mathrm{}{d}_{\frac{5}{2}}-2\mathrm{}{s}_{\frac{1}{2}}$ shell-model calculation. Ten experimental levels in ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ can be identified with shell-model counterparts. Restrictions are placed on the spin and parity assignments of several of the remaining states.

NUCLEAR REACTIONS DWBA analysis of old ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(t, p)$ data, $E\left(t\right)=12.0\mathrm{}$ MeV. Comparison of data with $p_{\frac{1}{2}}-d_{\frac{5}{2}}-s_{\frac{1}{2}}$ shell-model calculations. Discussion of $J^{\pi }$ assignments.

Approximate positive energy continuum eigenstates of a one-body Hamiltonian, already projected onto a finite dimensional harmonic oscillator basis, are constructed from the set of discrete-energy states obtained by diagonalizing the Hamiltonian. The method should be especially useful for calculating the virtual, continuum, intermediate states in many-particle calculations. The results for the test cases considered, the square well and the nonlocal Hartree-Fock potentials, are quite accurate both in the wave functions and the phase shifts.

Electrons with incident energies between 52.3 and 90.0 MeV have been scattered from the nucleus of ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$. Spectra of scattered electrons corresponding to excitation energies up to 32 MeV were observed at angles of 75° and 145°. Form factors of the states at 2.12, 4,44, 5.02, 8.57, and 8.93 MeV, and of the continuum region up to 30 MeV, have been separated into longitudinal and transverse components. The ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ dipole giant resonance is smooth relative to those of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. A mixed $M1-E2\mathrm{}$ transition was observed at 13.0 MeV and a broad transverse resonance, possibly magnetic, was seen at 15.5 MeV.

NUCLEAR REACTIONS ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}(e, e^{\prime })$, $E=52.3-90.0\mathrm{}$ MeV, $\theta =75\mathrm{}°-145\mathrm{}°$; measured $\sigma \left(E^{\prime }\theta \right)$; deduced $B\left(E2\mathrm{}\right)\mathrm{}$, $B\left(M1\mathrm{}\right)\mathrm{}$, giant resonance differential form factors.

The (${\pi }^{+}, 2p$) reaction has been studied on targets of ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ with 70-MeV pions. All kinematical quantities needed to define completely the final state were determined. The data are presented in an unbiased form, integrated over well-defined regions in phase space, and are thus readily comparable with available theoretical calculations. Data were obtained for opening angles both on and off the kinematics of the free process, ${\pi }^{+}+d\to p+p$. Thus a more extensive test of the applicability of a pole model or impulse approximation which assumes absorption on a quasideuteron could be made. For ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ the center of mass angular distribution was determined and compared with that for ${\pi }^{+}$ absorption on a free deuteron. Nuclear structure effects appear to play an important role for capture on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, since little excitation of the low-lying levels of the residual nuclei was observed, in contrast to theoretical predictions. For events leading to low excitation of the residual nucleus, theoretical curves in recoil and relative momentum, Treiman-Yang angle, and opening angle calculated for a pole model or plane wave impulse approximation gave general agreement with the measured distributions even for events off the kinematics of the free $\pi d$ process.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({\pi }^{+}, pp)$, $E=70\mathrm{}$ MeV, measured $\sigma (E_1, E_2, {\theta }_1, {\theta }_2)$.

We report results of calculations of the parity-mixing observables in the capture of thermal neutrons by protons. The calculations are exact and employ the Reid soft-core potential and the conventional Cabibbo model potential to describe the strong and weak nucleon-nucleon interactions, respectively. The calculated photon circular polarization is -2×${10}^{-8\mathrm{}}$ which is two orders of magnitude less than the experimental value, but of the same sign.

NUCLEAR REACTIONS ${}_{}{}^1{}_{}{}^{}\mathrm{H}(n, \gamma )$; thermal neutrons, calculated circular polarization of $\gamma$, Reid soft-core potential, conventional Cabibbo parity violating potential.

A general multichannel scattering formalism based on Schwinger-type variational principles and capable of treating rearrangements was recently presented by Tobocman. The approach involved combining variational functionals for individual transition operators with new coupled integral equations for these operators derived recently by Baer and Kouri and by Kouri and Levin. In this paper, we present general variational principles whose Euler equations are precisely the new coupled channel $T_{\alpha \beta }$ operator equations obtained by Kouri and Levin. The results are expressions which are stationary with respect to variations in all the $T_{\alpha \beta }$ simultaneously rather than just for a single $T_{\alpha \beta }$ operator. It is shown that such matrix generalizations may be obtained for a variety of functionals. With the specific choice of a channel permuting array (as discussed by Tobocman and by Kouri and Levin), the present formalism provides a valid computational basis for general many-body (e.g. nuclear) reactions, since then the iterated kernels of the resulting coupled channel $T_{\alpha \beta }$ operator equations are completely connected.

We use an impact parameter representation of the scattering amplitude to predict nucleus-nucleus and nucleon-nucleus total, reaction, and elastic cross sections at intermediate and high energies. We investigate the question of factorization for these quantities and find that factorization holds to 20% if the radii of the projectile and target nuclei do not differ by more than 50%. This fact and the gross violation of factorization when the nuclei are very different in size are interpreted in the context of a simple geometric model. The dependence of composite particle cross sections and factorization ratios on the size of the elementary nucleon-nucleon cross section ${\sigma }_{\mathrm{NN}}^T$ is investigated. It is shown that strict functional factorization for total and reaction cross sections in the impact parameter scheme only applies in the limit of a "weak" ${\sigma }_{\mathrm{NN}}^T$, for which a single scattering approximation is valid. This situation is not realized in practice, and nucleus-nucleus cross sections are instead found to be close to a geometric limit for all but the lightest nuclei. The energy dependence of nucleus-nucleus cross sections is found to be negligible above 100 MeV/particle.

The ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d, p){}_{}{}^8{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n){}_{}{}^8{}_{}{}^{}\mathrm{B}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, \alpha ){}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, p){}_{}{}^7{}_{}{}^{}\mathrm{Li}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, n){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ reactions have been studied, chiefly at bombarding energies below 3.8 MeV. All five of these reactions have potential applications in controlled thermonuclear systems. Total cross sections, believed to be accurate to 15%, which is sufficient for reactor design, have been determined in all cases. Residual activity was counted in the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d, p)$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n)$ studies while the yield of the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ 428-keV $\gamma$ ray was measured in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, n)$ investigation. Extensive angular distribution measurements were made for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, \alpha )$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, p)$ reactions and some discussion is given of the reaction mechanisms. Wherever possible, detailed comparisons are given to previously reported results.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d, p)$, $E=\mathrm{thresh}.-3.8\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n)$, $E=\mathrm{thresh}.-7.5\mathrm{}$ MeV measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, \alpha )$, $E=0.5-3.4\mathrm{}$ MeV, measured $\sigma (E, \theta )$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, p)$, $E=0.5-3.4\mathrm{}$ MeV measured $\sigma (E, \theta )$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d, n)$, $E=0.5-3.4\mathrm{}$ MeV, measured 0.428 MeV $\gamma$, deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$.

The muon capture matrix elements ${M_v}^2$, ${M_a}^2$, and ${M_p}^2$ are calculated for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ using the closure approximation and utilizing the linked cluster expansion to introduce correlations in the nuclear target wave functions. An important set of diagrams is summed by replacing uncorrelated wave functions with Bethe-Goldstone wave functions. However, we also find it necessary to include diagrams insuring that the pair number operator is unchanged and (for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) particle-hole diagrams to account for the fact that oscillator orbitals rather than Hartree-Fock orbitals are used for the uncorrelated basis. Typical results for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ are ${M_v}^{2\left(\mathrm{corr}\right)}=0.82\mathrm{}{M_a}^{2\left(\mathrm{corr}\right)}=0.74\mathrm{}{M_p}^{2\left(\mathrm{corr}\right)}=0.58\mathrm{}{M}^{2\left(\mathrm{osc}\right)}$, while for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${M_v}^{2\left(\mathrm{corr}\right)}=0.88\mathrm{}{M_a}^{2\left(\mathrm{corr}\right)}=0.78\mathrm{}{M_p}^{2\left(\mathrm{corr}\right)}=0.76\mathrm{}{M}^{2\left(\mathrm{osc}\right)}$. The bulk of the effects arise from correlations induced by the tensor component of the nucleon-nucleon interaction. We find that including correlations reduces the predicted total capture rate by ∼30% in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ∼20% in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, calculated total muon capture rate, closure and nuclear correlations.

The angular distributions of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(t, p){}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ transitions to 13 states in ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ have been analyzed by distorted wave techniques. Two-particle transfer amplitudes from recent ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^3$ shell-model calculations have been utilized to aid in the interpretation of the structure of ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$. The theoretical calculations reproduce the $L$ admixtures in the angular distributions remarkably well for many of the low-lying states. Ratios of measured-to-predicted cross sections are consistent to within a factor of 3. The correspondence between the experimentally known states of ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ and those predicted by the shell-model calculations is discussed; most of the states with known $J^{\pi }$ are well accounted for.

NUCLEAR REACTIONS ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(t, p)$: $E=12.0\mathrm{}$ MeV, DWBA analysis of old data using shell-model wave functions.