The variational bounds on scattering parameters are reformulated without the explicit use of multichannel projection operators, thus avoiding completely the difficulty of nonorthogonality in rearrangement and exchange collisions. Resonance-energy calculations can be carried out using the operator which is effectively projected on the closed channels.

The differential cross section for the ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}(p, {\gamma }_0){}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ reaction has been measured at 90° for $0.6\le E_p\le 6.3$ MeV. Compound resonances in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ have been located at (12.17±0.04)-, 12.55±0.03-, 12.91±0.02-, 14.33±0.02-, and 15.3±0.1-MeV excitation energy. The last four are probably analogs to the lowest four levels in ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$. Total widths and ground-state $\gamma$-ray widths of these levels are presented. The spins of the 12.55- and 14.33-MeV levels are shown to be ${\frac{1}{2}}^{+}\left({\frac{3}{2}}^{+}\right)$ and ${\frac{5}{2}}^{\mathrm{}(+)\mathrm{}}\left({\frac{3}{2}}^{-}\right)$, respectively.

The left-unitary operators that introduce the correlations of the hard core in an uncorrelated bound-state wave function of a finite number $A$ of particles are explicitly determined up to a unitary transformation. Left unitarity is required in order to keep orthonormality. Using a shell-model basis, transformed according to the correlation operator, it is possible to diagonalize the Hamiltonian in a subspace of the full Hilbert space with the technique of Bloch and Horowitz. Ground as well as excited states are treated on the same footing. In practice, the diagonalization is accomplished using the original single-particle basis and transforming back the Hamiltonian. This results in an $A$-body operator for which a cluster expansion is possible. In this cluster expansion, there are three- and four-body terms easy to evaluate, because they factorize. A particularly interesting application can be made to few-body systems, evaluating the integrals numerically. The unique approximation is then connected with the cut of the basis. The method developed seems comparatively simple and is free of the mathematical problems of the hard core.

Using a complex square-well distorting potential, the quasifree inelastic scattering of protons has been calculated in the impulse approximation. Calculations were performed for the nucleus ${\mathrm{C}}^{12}$ at both 160 and 1014 MeV to compare with experiment. The calculation was done with parameters determined from other data and was therefore essentially parameter-free. The agreement with experiment is quite satisfactory and relatively independent of the parameters. While the magnitude of the cross section is well determined, the location of the quasifree peak is in disagreement with experiment and only slightly shifted from the no-distortion case.

Using a theory previously developed for the ${\mathrm{O}}^{16}$ nucleus, the energy levels of ${\mathrm{He}}^4$ were calculated using the nuclear shell model and the random-phase approximation (RPA). Though no attempt was made to optimize the parameters of the calculation, the predicted energies of the excited states compare favorably with those determined from experimental analyses. Qualitative agreement with experiment is obtained for the calculated electron inelastic-scattering form factor to the first $0^{+}$ excited state and for the integrated photoabsorption cross section. However, the prediction of the majority of the $E1\mathrm{}$ strength in the higher of the 1—, $T=1\mathrm{}$ levels does not conform to most experiments which indicate the lower level to have the stronger ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ component. The RPA produces some improvement over an ordinary shell-model calculation by decreasing the energies of the lower excited states by several hundred keV and by increasing the relative $E1\mathrm{}$ strength of the lower 1—, $T=1\mathrm{}$ level.

Elastic and inelastic excitation functions and differential cross sections of $\alpha$ particles scattered from ${\mathrm{C}}^{12}$ have been measured. Excitation functions were taken from 18.90 to 30.06 MeV in 20-keV steps. Differential cross sections were measured at the energies of anomalies in the excitation functions. Optical-model and phase-shift fits to the elastic angular distributions were attempted without success. A statistical analysis of the excitation function indicates that the reaction is proceeding mainly through the compound nucleus with a coherence width $\Gamma$ of 360 keV (c.m.).

We show that the ${\mathrm{He}}^3$ and ${\mathrm{H}}^3$ photodisintegration reactions are to a large extent independent of the detailed properties of the three-nucleon ground state, but depend crucially on the nuclear interaction in the final continuum states. The bound-state properties considered are the analytic form of the principal $S$ state, the asymptotic behavior, the $S^{\prime }$ state, and the two-nucleon short-range repulsion. Since the rms radius of the bound state determines the over-all magnitude of the cross section, predictions of different wave functions with the same radius are compared. The final states are described by the Faddeev equations in the separable approximation. If the final-state interactions are correctly included, then the low-energy cross sections for the ${\mathrm{He}}^3(\gamma , p)d$ reaction are enhanced by 20-25%, and the cross sections for ${\mathrm{He}}^3(\gamma , n)2p$ are reduced by approximately 100%. A simultaneous but rough agreement is possible for the total two- and three-body breakup cross sections and the charge form factors of the three-particle nuclei; but, within the theoretical framework adopted, the two-body differential cross sections at 90° and the charge-form-factor data cannot be reconciled.

The influence of the interaction between the magnetic moment of a neutron and the Coulomb field of a target proton is investigated. For this interaction, channel spin is not conserved. A formalism is developed which includes the resulting singlet-triplet mixing. The scattering amplitude, or $M$ matrix, is presented, and its elements are related to the coefficients of the most general form of the $M$ matrix. Expressions for the nine most common nucleon-nucleon-scattering observables are obtained, including the effects of the singlet-triplet mixing. Coupled radial wave equations are derived and solved to reveal the phase-shift modifications. Calculations are performed over an energy range from 25 to 210 MeV using nuclear phase shifts previously determined from best ${\chi }^2$ fits to the scattering data. Our calculations indicate that all nine of the scattering observables considered are significantly influenced by the Mott-Schwinger interaction, but only for very small (<5°) scattering angles.

The $\beta$ decay of ${\mathrm{F}}^{21}$ has been investigated, utilizing the ${\mathrm{F}}^{19}(t, p){\mathrm{F}}^{21}$ reaction to form the ${\mathrm{F}}^{21}$ activity and a 1.3-MeV mechanically-chopped beam. The existence of previously reported $\beta$ branches to the ground and first two excited states of ${\mathrm{Ne}}^{21}$ has been confirmed, and an upper limit for decay to the third excited state of ${\mathrm{Ne}}^{21}$ has been established by detecting $\beta -\gamma$ coincidences and $\beta$-ray singles with NaI(Tl) and plastic scintillation detectors. The ${\mathrm{Ne}}^{21}$ levels in keV, ${\mathrm{F}}^{21}$ $\beta$ branches populating these levels in percent, and corresponding $log\mathrm{ft}$ values are 0.0, 29±6, 5.23±0.10; 350, 63±6, 4.76±0.05; 1746, 7.6±1.0, 5.07±0.07. The $log\mathrm{ft}$ values measured in the present work differ markedly from those previously reported. Measurements of the excitation energies of the first two excited states of ${\mathrm{Ne}}^{21}$ yielded (in keV) 350.5±0.3 and 1745.6±0.4, respectively. The upper limit on the percent branch to the third excited state is 0.15%, corresponding to a limit on the $log\mathrm{ft}$ of 6.0.

The lowest $T=2\mathrm{}$ states of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been formed using the ($p, t$) reaction. The isospin-forbidden proton ($\Delta T=1\mathrm{} or 2$) and $\alpha$-particle ($\Delta T=2\mathrm{}$) decay modes of these states have been determined by counting triton-proton and triton-$\alpha$ coincidence events. The major decay modes of the states are ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}({\alpha }_1+{\alpha }_2, {\alpha }_3+{\alpha }_4)$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}\left(p_0\right)$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\left({\alpha }_0\right)$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\left(p_0\right)$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\left({\alpha }_0\right)$. Simple Coulomb calculations were performed for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$; these assumed pure shell-model configurations and considered isospin mixing in only the ($1d, 1f$) shells. They did not predict the relatively large $\Delta T=2\mathrm{}$ isospin impurities necessary to explain the observed $\alpha$-particle decay.

Cross sections for the production of ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$ have been determined from the separated isotopes of magnesium, silicon, and sulfur, using 300- and 400-MeV protons. These values, together with previous measurements, provide data for targets of each mass number of 23 to 34 inclusive for ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ and from 25 to 34 inclusive for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$. The main feature of the results is that the cross section is highest for those targets having the $\frac{N}{Z}$ closest to that of the products. Thus, events involving the loss of about the same number of neutrons as protons have the highest probability. Cascade-evaporation calculations were performed for 400-MeV protons on each of these nuclides. The calculations reproduce the experimental trends.

The elastic and inelastic scattering of iron capture $\gamma$ rays from the 7.64-MeV $M1\mathrm{}$ levels in ${\mathrm{Cd}}^{112}$ and ${\mathrm{Ni}}^{62}$ were studied with a Ge(Li) spectrometer. Eleven energy levels in ${\mathrm{Cd}}^{112}$ and three in ${\mathrm{Ni}}^{62}$ observed in this experiment are compared with the levels excited in ($d, p$) experiments. Angular distribution measurements were made for four strong transitions in ${\mathrm{Cd}}^{112}$ and two in ${\mathrm{Ni}}^{62}$, giving the following spin assignments: ${\mathrm{Cd}}^{112}$: 0.62-MeV level (2), 1.23-MeV (0), 1.88-MeV (0), 7.64-MeV (1); ${\mathrm{Ni}}^{62}$: 2.06-MeV (0), 7.64-MeV (1). In both nuclei, only the $0^{+}$ member of the two-quadrupole phonon triplet ($0^{+}$, $2^{+}$, $4^{+}$) is strongly excited in this experiment, indicating very different components in the wave functions of the $0^{+}$ and $2^{+}$ members.

Employing ${\mathrm{Ca}}^{48}$ and ${\mathrm{Ni}}^{56}$ as cores for ${\mathrm{Cr}}^{52}$ and ${\mathrm{Ni}}^{60}$, respectively, the shell-model properties of these nuclei are described using the renormalized reaction matrix elements of the Hamada-Johnston nucleon-nucleon potential. For ${\mathrm{Cr}}^{52}$, the seniorities 2 and 4 of the ${f_{\frac{7}{2}}}^4$ configuration are mixed through intermediate states of other configurations in an attempt to explain the branching ratios from $J=6\mathrm{}$ and $J=5\mathrm{}$ levels to the low-lying $J=4\mathrm{}$ levels; and also the effect of increasing the configuration space is explicitly studied. A qualitative agreement between the calculated and experimental spectra is found, and the wave functions thus obtained are not found to be suitable for the description of transition rates. For ${\mathrm{Ni}}^{60}$, the effect of including the additional $g_{\frac{9}{2}}$ orbital is also investigated. The calculated energy levels agree fairly well with the experimental levels, but the wave functions do not provide a satisfactory explanation for the observed transition rates. The even Ni isotopes are then described in the framework of the modified Tamm-Dancoff approximation (MTDA). The agreement for the energy levels for ${\mathrm{Ni}}^{60}$ between the shell-model and the MTDA results is of the same quality, but the MTDA result indeed shows an improvement over the shell-model results in describing the vibrational characteristic of the second excited $2^{+}$ state. The MTDA results for Ni isotopes appear to be fairly satisfactory.

The multipole mixing ratios for the 53.17-, 79.63-, 80.99-, 160.63-, and 302.83-keV transitions in ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ were measured via $\gamma -\gamma$ directional correlation measurements employing two Ge(Li) detectors. Correlations for the cascades 276-161, 356-81, 303-81, 80-81, (276-80)+(276-81), 53-384, and 53-303 keV were investigated. Results for the last three correlations have not been reported previously. The present results are consistent with a $J^{\pi }$ sequence of ${\frac{7}{2}}^{+}$, ${\frac{5}{2}}^{+}$, ${\frac{5}{2}}^{+}$, ${\frac{3}{2}}^{+}$, and ${\mathrm{½}}^{+}$ for the ground state and the 81-, 161-, 384-, and 437-keV levels in ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$. With the 276-, 356-, and 384-keV transitions assumed to be pure $E2\mathrm{}$, the mixing ratios $\delta$ for $\frac{E2\mathrm{}}{M1\mathrm{}}$ obtained are 161 keV: ${-1.03\mathrm{}}_{-0.13\mathrm{}}^{+0.08\mathrm{}}$; 81 keV: ${+0.148\mathrm{}}_{-0.008\mathrm{}}^{+0.009\mathrm{}}$; 303 keV: ${-0.164\mathrm{}}_{-0.072\mathrm{}}^{+0.105\mathrm{}}$; 80 keV; +0.022±0.040 (average from two independent correlations); and 53 keV: ${-0.114\mathrm{}}_{-0.047\mathrm{}}^{+0.046\mathrm{}}$ (average from two independent correlations). These results are compared with previously reported mixing ratios from $\gamma -\gamma$ and $e_K-\gamma$ correlations and from ${\alpha }_K$, $\frac{K}{L}$, and $L$-subshell ratio measurements. From these results and previously reported lifetimes, $\gamma$-ray-transition retardation and enhancement factors are calculated and compared with predictions of current models for the nucleus.

The proton pickup reaction ($t, \alpha$) has been used to investigate states in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{206}{}_{}{}^{}\mathrm{Tl}$. The angular distributions resulting from populating five states in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ which are predominantly single-hole in character have been analyzed to obtain spectroscopic factors. In the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}(t, \alpha ){}_{}{}^{206}{}_{}{}^{}\mathrm{Tl}$ spectrum, doublets corresponding to the interaction of proton holes in the four lowest-lying orbits with a $3p_{\frac{1}{2}}$ neutron hole are the strongest states observed. The $2d_j$ proton-hole strength is found in several levels of ${}_{}{}^{206}{}_{}{}^{}\mathrm{Tl}$. The positions and intensities of the observed levels are in quantitative agreement with the nuclear-structure calculations of Kuo.

An angular-correlation setup was applied to measure the $e-\gamma$ angular correlations involving the 570- and 1064-keV transitions in ${\mathrm{Pb}}^{207}$. The use of a Si(Li) semiconductor counter as an electron detector allowed the separation of the three $K$, $L$, and $M$ conversion lines for both transitions. $\gamma -\gamma$ angular correlations were also performed. Particle parameters $b_2$ were thus esperimentally determined. The values obtained for the $K$, $L$, and $M$ shells were 1.19(7), 1.13(7), and 1.41(11) for the 570-keV transition and 1.05(5), 1.06(12), and 1.16(15) for the 1064-keV transition. Particle parameters $b_4$ were calculated from the $b_2$ values through a recursion relation. The coefficients $A_4\mathrm{}\left(e\right)\mathrm{}$ could not be determined directly from experiment owing to the lack of statistics, but they were obtained through the $b_4$ particle parameters and the $A_4\left(\gamma \right)$ coefficients. The values for the $K$, $L$, and $M$ shells one -0.020(8), -0.025(9), and ∼-0 are for the $e\left(570\right)-\gamma \mathrm{}\left(1064\right)\mathrm{}$ angular correlations; and -0.049(16), -0.051(30), and -0.072(40) for the $e\left(1064\right)-\gamma \mathrm{}\left(570\right)\mathrm{}$ angular correlations.

Differential cross sections for ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}(\alpha , {}_{}{}^3{}_{}{}^{}\mathrm{He})$ with 65.7-MeV $\alpha$ particles were measured from 15° to 80°. Data were obtained for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ groups corresponding to excitation energies of 0.0, 0.16, 0.32, 0.72, 1.03, 1.25, 1.58, and 3.20 MeV in ${}_{}{}^{117}{}_{}{}^{}\mathrm{Sn}$. The angular distributions were well fitted by zero-range distorted-wave predictions. The spectroscopic factors are generally in good agreement with those obtained in a ($d, p$) experiment.

The changes in binding energy of ${}_{114}{}^{}{}_{}{}^{}X_{}^{298}{}_{}{}^{}$ under deformation into prolate spheroidal shapes have been calculated using the statistical theory of nuclei. The density is restricted only by the requirement that each equidense surface is a spheroid. It is found that the energy is minimized when the density has an approximately uniform surface thickness around the nucleus. To first order the change in binding energy is given well by the liquid-drop model, but at large deformation the statistical theory predicts less drop in energy and, consequently, a slightly more stable nucleus.

High-resolution Ge(Li) and Si(Li) x-ray detectors [404- and 290-eV full width at half-maximum (FWHM) at 6.4 keV, respectively] were employed to study the singles and coincidence spectra of x rays and $\gamma$ rays from the decays of ${\mathrm{Tm}}^{170}$ and ${\mathrm{Tm}}^{171}$. Measurements of the rates of $L_{\alpha }$, $L_{\beta }$, and $L_{\gamma }$ x-ray emission in coincidence with $K_{\alpha 1}$ and $K_{\alpha 2}$ x rays yielded the following values for $L_2$ and $L_3$ subshell-fluorescence yields (${\omega }_2, {\omega }_3$), $L_2-L_{3}X$ Coster-Kronig transition probability ($f_{23}$), and relative $L$ x-ray intensity ratios ($s_2, s_3$): ${\omega }_2=0.182\mathrm{}\pm 0.011$, ${\omega }_3=0.183\mathrm{}\pm 0.011$, $f_{23}=0.170\mathrm{}\pm 0.009$, $s_2=0.192\mathrm{}\pm 0.010$, and $s_3=0.165\mathrm{}\pm 0.009$. The $K$-conversion coefficient of the 84.3-keV $E2\mathrm{}$ transition in ${\mathrm{Yb}}^{170}$ is found to be 1.39±0.04 by the measurement of the intensity ratio for the $K$-x-ray and $\gamma$ transitions (XPG method). The $K$-conversion coefficient of the 66.7-keV transition in ${\mathrm{Yb}}^{171}$ is found to be 7.45±0.36, which leads to a value of 0.34 for the mixing ratio of $\frac{E2\mathrm{}}{M1\mathrm{}}$. The orbital-electron-capture branchings of ${\mathrm{Tm}}^{170}$ to the first excited state (78.6 keV) and to the ground state in ${\mathrm{Er}}^{170}$ are determined to be 0.04 and 0.10%, respectively.

A method is described which allows the calculation of the spin dependence of the probability for fission of compound nuclei from experimental data. The method is applied to the study of the behavior of ${\mathrm{Re}}^{181}$ compound nuclei formed in three different ways with an excitation energy of 70 MeV: ${\mathrm{C}}^{12}$+${\mathrm{Tm}}^{169}$, ${\mathrm{O}}^{16}$+${\mathrm{Ho}}^{165}$, and ${\mathrm{Ne}}^{22}$+${\mathrm{Tb}}^{159}$. The experimental fission cross sections were taken from Sikkeland. The fission probability is found to increase with increasing angular momentum in accord with liquid-drop-model calculations.