$\gamma -\gamma$ directional-correlation measurements were carried out with a NaI-Ge(Li) detector system on the transitions in ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ whose levels are populated from the decay of ${}_{}{}^{156}{}_{}{}^{}\mathrm{Eu}$. Directional correlations of the 88.95-keV $\gamma$ ray with 11 transitions which directly feed and 4 which involve a skipped transition to the 88.95-keV state were simultaneously measured. A $\delta$ value of ${-5.9\mathrm{}}_{-2.8\mathrm{}}^{+1.4\mathrm{}}$ was measured for the 1040.44-keV, $2_{\beta }^{+}\to 2_g^{+}$ transition which is thus (${97.2}_{-2.1\mathrm{}}^{+1.5\mathrm{}}$)% $E2\mathrm{}$. The 1065.14-keV, $2_{\gamma }^{+}\to 2_g^{+}$ transition has a $\delta =-18\mathrm{}\pm 3$ and a (99.7 ± 0.1)% $E2\mathrm{}$ component. Three $1^{+}\to 2_g^{+}$ transitions of 1877.03, 1937.71, and 2097.70 keV have $E2\mathrm{}$ admixtures of (${13.8}_{-2.9\mathrm{}}^{+3.0\mathrm{}}$), (${24.5}_{-1.9\mathrm{}}^{+2.0\mathrm{}}$), and (${59.0}_{-9.0\mathrm{}}^{+25.2\mathrm{}}$)%, respectively, while the 811.77-keV, $1^{+}\to 2_{\gamma }^{+}$ transition is (${0.1}_{-0.1\mathrm{}}^{+0.4\mathrm{}}$)% $E2\mathrm{}$.

A realistic nucleon-nucleon potential is used to formulate a simple Thomas-Fermi method for nuclear-structure calculations. The potential-energy density has only one free parameter, which is found by fitting with Bhargava and Sprung's calculation. The short-range repulsion is absorbed in the term containing the free parameter. The compressibility comes out to be good. We illustrate our method in nuclear matter only with ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ states, although the method is applicable in the general case.

Differential cross sections from 12.5 to 47.5° were measured for the ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}\mathrm{}(d,p)\mathrm{}$ reaction with 33.3-MeV deuterons. Proton spectra up to 5-MeV excitation in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}$ were observed with a resolution of approximately 25 keV. The excitation energies agreed within experimental error with ($d,p$) experiments at 12 and 15 MeV. The ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}(\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He})$ cross sections were measured at 15 and 20° with 65.7-MeV $\alpha$ particles. Comparisons were made with distorted-wave Born-approximation calculations, and $l$ transfers were assigned to many levels. The $l$ transfers and spectroscopic factors are in satisfactory agreement with previous papers for strong transitions populated by low $l$ transfers. The 33.3-MeV deuteron bombarding energy produced angular distributions permitting analysis of several states not previously interpreted or previously misinterpreted. A comparison of ($d,p$) and ($\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) results provides new information on $l=5\mathrm{}$ transitions. The transitions to states at 1.962 and 2.245 MeV, previously assigned as either $l=4\mathrm{}$ or $l=4\mathrm{} \mathrm{and} 5$, are given $l=5\mathrm{}$ assignments. New $l=5\mathrm{}$ transitions were observed to levels at 2.088, 2.517, 3.516, and 4.069 MeV, and probable $l=5\mathrm{}$ transitions were observed to levels near 2.753, 3.004, 3.160, and 3.634 MeV.

The low-lying excited states of ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ populated by primary and secondary $\gamma$-ray transitions from the reaction ${}_{}{}^{115}{}_{}{}^{}\mathrm{Sn}(n,\gamma ){}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ were studied. Both singles and $\gamma -\gamma$ coincidence techniques were employed with the exclusive use of Ge(Li) detectors. Results obtained from high-energy $\gamma$-ray spectra (∼5.9-10 MeV) were combined with those from low-energy singles spectra (∼100 keV-3.8 MeV) and low-low coincidence spectra in order to infer the excitation energies and branching characteristics of 21 states up to an energy of ∼3.7 keV. A level and decay scheme is proposed including a total of 45 $\gamma$ rays representing ∼90% of the decay intensity. This scheme includes most of the levels having $E_x\le 3$ MeV which were observed previously4 in charged-particle reactions and $\beta$-decay studies. The existence of the $0^{+}$ level having an excitation energy of 2027 keV has been confirmed and a new level at 2545-keV excitation is proposed.

We have further studied the parity admixtures in nuclear $\gamma$ transitions by measuring the circular polarization of $\gamma$ rays from five nuclei with a technique different from that of our work I and II in this series. The experiments were performed with a forward-scattering rapidly reversing Compton polarimeter and a phase-sensitive detection system. The analyzing efficiency of the Compton polarimeter, including effects of multiple scattering, was determined by Monte Carlo calculations. It was necessary in most experiments to apply corrections for polarized bremsstrahlung associated with $\beta$ decays. Calculations of bremsstrahlung effects were verified by experiments on ${}_{}{}^{198}{}_{}{}^{}\mathrm{Au}$ and ${}_{}{}^{177}{}_{}{}^{}\mathrm{Lu}$. The residual asymmetry of the polarimeter itself was determined by control experiments on ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$. The values of $P_{\gamma }$ obtained were ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ 501 keV, $P_{\gamma }=(-23\mathrm{}\pm 6)\times {10}^{-4\mathrm{}}$; ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$ 363 keV, $P_{\gamma }=(-1\mathrm{}\pm 5)\times {10}^{-4\mathrm{}}$; ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$ 279 keV, $P_{\gamma }=(-0.04\mathrm{}\pm 0.10)\times {10}^{-4\mathrm{}}$; ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ 482 keV, $P_{\gamma }=(-0.031\mathrm{}\pm 0.025)\times {10}^{-4\mathrm{}}$; ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ 1189 keV, $P_{\gamma }=(-0.25\mathrm{}\pm 0.40)\times {10}^{-4\mathrm{}}$. A survey and a discussion of these results is presented.

An isomeric state of ${}_{}{}^{222}{}_{}{}^{}\mathrm{Ac}$ with a half-life of 66 ± 3 sec has been discovered in bombardments of lead with ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ ions. The isomer decays by $\alpha$-particle emission and has a complex spectrum with major $\alpha$-particle groups at 6.46 (2%), 6.71 (8%), 6.75 (15%), 6.81 (27%), 6.84 (10%), 6.89 (15%), 6.97 (8%), and 7.00 MeV (15%). Evidence for the decay of the isomeric state both by isomeric transition (<10%) and by electron capture (∼1%) is presented. The half-life of ${}_{}{}^{218}{}_{}{}^{}\mathrm{Fr}$ was measured to be 0.7 ± 0.6 msec.

The $\beta$ decay of 43-sec and 4.41-min ${}_{}{}^{104}{}_{}{}^{}\mathrm{Rh}$ has been investigated with a high-resolution Ge (Li) detector. In addition to the 16 $\gamma$ rays reported earlier, we have observed three new $\gamma$ rays of energies, 839.90, 1264.84, and 1689.1 keV. We have identified the $\gamma$ rays belonging to the 43-sec and 4.41-min decays. With the help of Ge(Li)-Ge(Li) two-parameter coincidence measurements, all 19 of the $\gamma$ rays assigned to the ${}_{}{}^{104}{}_{}{}^{}\mathrm{Rh}$ decay have been fitted into 11 excited states of ${}_{}{}^{104}{}_{}{}^{}\mathrm{Pd}$ at 555.81, 1323.59, 1333.58, 1341.68, 1792.86, 1793.83, 1820.65, 2082.38, 2181.58, 2244.9, and 2265.31 keV and one excited state in ${}_{}{}^{104}{}_{}{}^{}\mathrm{Ru}$ at 358.12 keV. The energy levels at 1323.59, 1333.58, 1341.68, and 1792.86 keV have been assigned unique spin values of 4, 0, 2, 0, respectively, from the results of NaI-Ge(Li) directional-correlation measurements.

Surprisingly large discrepancies have been found between some measured and calculated cross sections for sub-Coulomb transfer reactions on several actinide nuclei. The calculated cross sections of strongly excited states with $J\ge \frac{7}{2}$ are generally too small by a factor of 2-3, such as Siemssen and Erskine had observed in the reaction ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}\mathrm{}(d,p)\mathrm{}{}_{}{}^{183}{}_{}{}^{}\mathrm{W}$. A few exceptions to the above rule are found for weakly excited states. In the present study, the use of very low bombarding energies results in an important simplification of the analysis in that the calculated cross sections then are insensitive to uncertainties in the optical-model parameters. The present results suggest that the discrepancy in cross sections probably results from inadequate treatment of the asymptotic tail of the bound-state wave function rather than from neglect of inelastic scattering processes in the incoming and outgoing waves.

Results are given for high-resolution neutron-resonance-spectroscopy studies of the separated erbium isotopes (164, 166, 167, 168, 170) using the Nevis Synchrocyclotron. These results, particularly ${\mathrm{Er}}^{166}$ to 4200 eV ($n=109\mathrm{}$ levels), give the first excellent agreement with the Dyson-Mehta (DM) $\Delta$ statistic which applies for the statistical orthogonal ensemble (O.E.) of Wigner and Dyson. The observed ${\mathrm{Er}}^{166}$ levels seem to be a nearly pure and complete $s$ population, fitting Wigner's nearest-neighbor spacing law and the Porter-Thomas (PT) single-channel ${\Gamma }_n^0$ distribution. The weakest ${\mathrm{Er}}^{168}$ and ${\mathrm{Er}}^{170}$ levels include some $p$ levels (excess of weak ${\Gamma }_n^0$ values) which are separated by a Bayes-theorem method yielding resulting $s$ populations which also give good fits to all statistical O.E. tests. Unexpectedly, the ${\mathrm{Er}}^{166}$ levels give a nonzero correlation coefficient between adjacent ${\Gamma }_n^0$ values of $\rho ({\Gamma }_{\mathrm{nj}}^0,{\Gamma }_{nj+1\mathrm{}}^0)=-0.21\mathrm{}\pm 0.08$, and with less fluctuation in $\Sigma {\Gamma }_n^0$ over adjacent intervals than expected for an uncorrelated PT series of ${\Gamma }_n^0$ values. Assuming a true $p$ level density 3 times that for $s$ levels, $S_1$ values are calculated on the basis of the observed excess of weak levels and our known level detection threshold. We obtain ${10}^4{S}_0=1.70\mathrm{}\pm 0.23, 1.89\pm 0.20, 1.50\pm 0.21, \mathrm{and} 1.54\pm 0.22$ for 166, 167, 168, 170; and ${10}^4{S}_1=\le 0.75, 0.70\pm 0.20, \mathrm{and} 0.80\pm 0.25$ for 166, 168, 170. We find $\Delta =0.455\mathrm{}$ ($n=109\mathrm{}$) for ${\mathrm{Er}}^{166}$, 0.287 ($n=50\mathrm{}$) for ${\mathrm{Er}}^{168}$, and 0.359 ($n=31\mathrm{}$) for ${\mathrm{Er}}^{170}$ vs DM's predicted $\Delta =0.47\mathrm{}\pm 0.11, 0.39\pm 0.11, \mathrm{and} 0.34\pm 0.11$. For a large $n$, $\Delta$ is much larger for an uncorrelated Wigner (U.W.) spacing sequence or for an incomplete or impure $s$ level O.E. set. The correlation coefficient for adjacent spacings, $\rho (S_j,S_{j+1\mathrm{}})\equiv \rho =-0.22, -0.29, -0.09\mathrm{}$ for 166, 168, 170 vs $\rho \approx -0.27\mathrm{}$ (±0.09, 0.13, 0.17 for 166, 168, 170) (O.E.). The probability is 0.0004 for $[\Delta +\rho ]\le \mathrm{the} {\mathrm{Er}}^{166}(4.2\mathrm{}-\mathrm{keV})$ value for a U.W. set. The $〈D〉$ values for $s$ levels, if our $s$ level count is correct, are 38.4, 4.06, 95.3, and 155 eV [$\pm \frac{0.9}{n}$ fractional uncertainty (O.E.)] for $n=109, 30, 50, \mathrm{and} 31$ for 166, 167, 168, 170.

We have studied states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ between 10.91- and 13.02-MeV excitation as resonances in the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(p,\gamma ){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(p,p^{\prime }\gamma )$ reactions. Several new states are reported, and the elastic, inelastic, and $\gamma$-ray partial widths are given for some of the levels. The levels are compared with corresponding levels in the mirror nucleus ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. Of particular interest are the ${\frac{1}{2}}^{+}$ and ${\frac{5}{2}}^{+}$, $T=\frac{3}{2}$ states which should lie in this region. The results imply more mixing of these states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ with nearby $T=\frac{1}{2}$ levels than is observed in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. However, most of the $T=\frac{3}{2}$ strength in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ remains unaccounted for.

The use of the first-order unitary model to calculate nucleon polarizations in elastic nucleon-deuteron scattering at energies up to 40 MeV is investigated. One shortcoming of extant unitary-model calculations, that of inadequate two-nucleon input, is partially remedied by introducing a variety of more realistic models for the two-nucleon interaction. It is found that even with the latter interactions the unitary model fails to represent the nucleon polarization, and, as is to be expected from the work of Sloan et al., to a lesser degree, the elastic differential cross section. The nucleon polarization is found to be extremely sensitive even at fairly low energies to the presence of the $P$-wave components of the two-nucleon amplitudes when the three-particle scattering is computed via the unitary and other approximations. This indicates that any method (exact or otherwise) for computing polarizations in $N-d$ scattering must include these components.

Two distinct types of perturbation theories for three-particle scattering which are based upon the decomposition of the two-particle transition operators into dominant and weak parts are investigated. The relationship of these two techniques and their usefulness in practical calculations are discussed.

The double-stripping reaction ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ has been studied with a magnetic spectrograph at an incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energy of 18 MeV, with an energy resolution of about 30 keV. Differential cross sections have been measured for transitions to states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ up to an excitation energy of 11 MeV. The data have been analyzed in the distorted-wave Born approximation using the Glendenning formalism and the multishell shell-model wave functions of Zuker, Buck, and McGrory for states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$. The model wave functions are found to fit the data quite well for a number of low lying-states. However, several exceptions are also found.

The total ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ low-energy reaction cross section has been reanalyzed. Three phenomena suggest an $\alpha$-particle model for the reaction: (1) the giant resonances, (2) the intermediate-structure resonances, and (3) anomalous branching ratios. The energy dependence of the total cross section over the energy range 2.4 to 9.0 MeV cannot be explained solely by the energy dependence of the penetration of the Coulomb barrier. There is some nuclear structure. The structure can be explained by an optical potential based on the $\alpha$ model leading to absorption under the barrier. It could also be explained with two giant resonances in a Woods-Saxon potential. The intermediate structure is explained as due to special states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ built of a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core and three $\alpha$ particles, and so are the anomalous branching ratios.

Astrophysical reaction rates were calculated for a number of possible optical potentials. The giant resonances affect the extrapolation to the energies of astrophysical interest and lead to an uncertainty of a factor of 3 to 10 in the astrophysical reaction rate at $T_9\simeq 0.6$, where $T_9\equiv {10}^{-9\mathrm{}}T$°K.

The unified model in intermediate coupling has been applied to the odd-mass isotopes of indium ${\mathrm{In}}^{109-117}$. Using three free parameters: the dimensionless interaction parameter, $\xi$; the effective $2^{+}$ phonon energy of the core, $\hslash \omega$; and the single-particle energy separations, $E_j$, theoretical energy spectra were fitted to the experimental spectra. The wave functions obtained during the diagonalization of the Hamiltonian were used in calculating magnetic dipole moments for the ground and first excited states, the quadrupole moments of the ground states, and $M1\mathrm{}$ and $E2\mathrm{}$ reduced transition probabilities for transitions between the second and first excited states. In reproducing the observed values of the magnetic dipole and electric quadrupole moments, effective values of the spin $g$ factor and interaction strength parameter were employed. These were found to vary remarkably smoothly with the mass number $A$. The following values for the hitherto unmeasured properties of the indium isotopes are predicted: magnetic moment of the ground state of ${\mathrm{In}}^{117}$, $5.516{\mu }_N$; the quadrupole moment of the ground state of ${\mathrm{In}}^{117}$; 1.057×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$; and the $B\left(M1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ values for ${\mathrm{In}}^{113}$ for the decay of the second excited state to the first excited, $0.708e^2\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ and $0.149e^2\times {\left({10}^{-24\mathrm{}} {\mathrm{cm}}^2\right)}^2$, respectively. The results compare favorably with those obtained by other investigators using other models.

Recently we found that the usual optical model predicts the existence of "inner states" localized within the absorptive region. They cause highly nonlinear effects in the familiar eigenstates. We have now obtained analogous results for a coupled-channels model.

The reaction ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=2.2\mathrm{}$ MeV has been used to investigate the $\gamma$ decay of states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The $\gamma$-ray spectrum from a NaI(Tl) detector in coincidence with protons leading to the 15.11-MeV state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ exhibits transitions of 2.38 ± 0.02, 4.44, 7.48 ± 0.03, 10.71 ± 0.05, and 15.11 MeV. Relative $\gamma$-ray branches from the 15.11-MeV state to the 12.71-, 7.65-, 4.44-MeV and ground states are (1.4 ± 0.4), (2.6 ± 0.7), (2.3 ± 0.9), and (92 ± 2)%, respectively, where an allowance of 1.6% has been made for a possible but unobserved 15.11 → 10.3 transition. Also observed were $\gamma$-ray branches of (15 ± 4) and (85 ± 4)% from the 12.71-MeV state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to the 4.44-MeV and ground states, respectively. $\gamma$-branching intensities from the 15.11-MeV state are compared with the corresponding $\beta$-transition rates of ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ to these same states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and the conclusions about the orbital contribution to the $M1\mathrm{}$ $\gamma$-ray transition strength are compared with shell-model expectations. Previously reported evidence for an isospin-forbidden $\alpha$-decay branch from the 15.11-MeV level is discussed in the light of the present results.

Elastic electron scattering experiments were performed on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ at momentum transfers less than 1 ${\mathrm{F}}^{-1\mathrm{}}$. Charge form factors are reported, and model-independent as well as model-dependent rms radii are calculated. The model-independent radii for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ are 2.51 ± 0.10 and 2.35 ± 0.10 F, respectively.

Partially polarized 3-MeV neutrons have been scattered from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ contained in a high-pressure gas scintillation cell. The resulting asymmetry in the elastic scattering was determined for seven scattering angles from 40 to 120° (lab). Time-of-flight techniques and neutron-$\gamma$-ray discrimination in the side detectors were used for background reduction. The measured asymmetry is small for angles less than 60° (lab) and reaches a maximum value at approximately 110° (c.m.). The maximum asymmetry determined from the present experiment corresponds to a polarization of +0.50. The differential polarization can be fitted within experimental uncertainties by assuming that $D$-wave effects are negligible. The principal features of the data are qualitatively reproduced by Dodder's reaction-matrix calculations which use the Werntz-Meyerhof level parameters for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

Current theoretical models for the pion-nucleus interaction in the (3,3)-resonance region are discussed. We conclude that nonlocal potentials of the Kisslinger type are inadequate. The most promising potential is local and closely related to the Glauber model. Some properties of the Glauber model are also studied. Thus we show that the multiple-scattering series can be summed and charge-exchange effects can easily be accounted for.