The $\gamma$ rays from neutron capture in the 14.1-eV resonance in ${\mathrm{Xe}}^{131}$ have been studied. A target of ${\mathrm{Na}}_4$Xe${\mathrm{O}}_6$ was irradiated in a thermal-neutron beam and in monoenergetic neutron beams of 5.16-, 9.47-, and 14.1-eV energy from a neutron diffraction monochromator. The resulting $\gamma$-ray singles spectra were studied with Ge(Li) detectors of $\approx 12-$, 15-, 20-, and 30-${\mathrm{cm}}^3$ active volume. $\gamma$ rays were assigned to the ${\mathrm{Xe}}^{131}(n,\gamma ){\mathrm{Xe}}^{132}$ reaction by a comparison of these spectra. Ge(Li)-Ge(Li) coincidence measurements were carried out on resonance with the 20- and 30-${\mathrm{cm}}^3$ Ge(Li) detectors in combination. 14 ${\mathrm{Xe}}^{132}$ $\gamma$ rays were assigned as primary capture $\gamma$ rays from the 14.1-eV resonance. The energies (in keV) and relative intensities [$I\left(667.5\right)=100\mathrm{}$] of these primary $\gamma$ rays are as follows: 8934.2 ± 1.0 (0.02), 8268.5 ± 0.9 (1.0), 6950.1 ± 2.3 (0.14), 6750.1 ± 0.8 (0.13), 6466.8 ± 0.5 (13.2), 6380.5 ± 0.5 (2.8), 6346.8 ± 2.5 (0.09), 6223.0 ± 1.0 (0.23), 5755.0 ± 1.0 (1.9), 5692.3 ± 1.2 (0.4), 4981.1 ± 1.7 (0.3), 4910.3 ± 2.0 (0.7), 4842.3 ± 1.0 (0.7), and 4745.6 ± 2.5 (0.09). These data together with the information obtained from the coincidence measurements and earlier radioactive-decay studies indicate levels in ${\mathrm{Xe}}^{132}$ with energies 667.5 ± 0.3, 1297.7 ± 0.5, 1440.0 ± 0.3, 1803.9 ± 0.8, 1962.7 ± 0.7, 1985.4 ± 1.0, 2040.2 ± 0.6, 2110.2 ± 0.1, 2168.7 ± 1.3, 2187.2 ± 0.8, 2350.7 ± 0.2, 2394.3 ± 0.5, 2424.9 ± 0.7, 2468.8 ± 0.5, 2555.0 ± 0.6, 2588.66 ± 0.11, 2714.3 ± 1.3, 2754.43 ± 0.13, 3181.3 ± 1.5, 3243.4 ± 1.5, 3954.1 ± 1.0, 4026.5 ± 1.5, 4094.0 ± 1.0, and 4189.5 ± 1.5 keV. The neutron separation energy of ${\mathrm{Xe}}^{132}$ is 8936.3 ± 1.0 keV. The most prominant feature of the ${\mathrm{Xe}}^{132}$ level scheme obtained is the strong feeding of the 2468.8-keV level by the intense 6466.8-keV $\gamma$ ray from the capture state. The observed mode of decay of this level indicates spin and parity $3^{-}$ for this state although spin 2 cannot be ruled out. If the $3^{-}$ assignment is correct, then the 14.1-eV neutron resonance in ${\mathrm{Xe}}^{131}$ has spin 2. The properties of the energy levels of ${\mathrm{Xe}}^{132}$ are discussed.

We have investigated the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\mathrm{}(d,p)\mathrm{}{}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ reaction at deuteron energies of 8.0, 12.0, and 14.0 MeV. Good agreement is obtained with recent results at $E_d=16.4\mathrm{}$ MeV for spectroscopic factors for the low-lying levels of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$. These indicate appreciable mixing among the rotational bands of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$.

We have determined the half-life of ${}_{}{}^{131}{}_{}{}^{}\mathrm{I}$ samples to be 7.969±0.014 day under conditions in which the radiations of 12.0-day ${}_{}{}^{131m}{}_{}{}^{}\mathrm{Xe}$ are not detected, and to be 8.117±0.012 day under conditions in which the radiations of ${}_{}{}^{131m}{}_{}{}^{}\mathrm{Xe}$ are detected. Furthermore, we have seen no variations of half-life due to the physical state of the source to within 0.3%. We believe that these data indicate the half-life variations for ${}_{}{}^{131}{}_{}{}^{}\mathrm{I}$ reported by Bergamini et al. and Kemeny may be accounted for by the escape of daughter ${}_{}{}^{131m}{}_{}{}^{}\mathrm{Xe}$ and/or absorbtion of the radiations of ${}_{}{}^{131m}{}_{}{}^{}\mathrm{Xe}$.

Revised values of $L$-subshell fluorescence and Coster-Kronig yields at $Z=83\mathrm{}$ are reported here, based on a recalculation of data previously obtained. The revised values are as follows: ${\omega }_2=0.38\mathrm{}\pm 0.02$, $a_2=0.45\mathrm{}\pm 0.02$, ${\omega }_3=0.340\mathrm{}\pm 0.018$, $a_3=0.660\mathrm{}\pm 0.018$, and $n_{L_{2}M}=1.34\mathrm{}\pm 0.14$. The major change is in the value ${\omega }_2$, which now agrees much better with the trend of values for neighboring elements. The revised value of the ionization multiplicity $n_{L_{2}M}$ is in good agreement with a recent theoretical value of 1.29 given by E. G. McGuire. No change results in the previous values for the $L_1$-subshell quantities given by H. U. Freund and R. W. Fink.

The ${\mathrm{He}}^3$ charge form factor has been calculated using phenomenological mixed symmetric $S$- and $D$-state wave-function components along with the symmetric $S$-state component developed previously from the Bressel-Kerman-Rouben potential using an altered Feshbach-Rubinow equivalent two-body method. A zero of the form factor near the experimental value is found for reasonable $S^{\prime }$ and $D$ admixtures. This appears to weaken a suggestion by Tjon, Gibson, and O'Connell concerning the nucleon-nucleon interaction.

Angular distributions and excitation energies have been measured for two levels in ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ previously reported at 5.87 and 5.95 MeV. Present results give energies of 5.932±0.005 and 6.013±0.005 MeV in excellent agreement with $\gamma$-ray measurements.

The half-lives of the excited states at 86.5 and 105.3 keV in ${\mathrm{Gd}}^{155}$ have been determined as $T_{\frac{1}{2}}\left(86.5\mathrm{} \mathrm{keV}\right)=6.3\mathrm{}\pm 0.1$ nsec and $T_{\frac{1}{2}}\left(105.3\mathrm{} \mathrm{keV}\right)=1.18\mathrm{}\pm 0.02$ nsec. The results are compared with the theoretical calculations of $E1\mathrm{}$ transition rates taking into account the retarding effect of pairing correlations. The importance of taking into account wave-function components admixed by the Coriolis coupling is discussed.

A microscopic cranking model is introduced for vibrational nuclei, thus extending the foundation for the phenomenological variable-moment-of-inertia model. The negative value of ${\mathcal{I}}_0$ then emerges naturally. The cranking model approximates energies, static moments, and transition probabilities within the quasirotational subspace. An illustrative application is made to the exactly soluble Moszkowski model.

The solvable two-level pairing model is used to test two new number-conserving approximations. These approximations are compared with the exact results, with perturbation theory, with the BCS method, and with the projected BCS method of Kerman, Lawson, and Macfarlane. It is found that second-order perturbation theory and one of the tested approximations work rather well for not too high values of the pairing-force strength, while for higher values the other approximation turns out to be quite good.

A precise measurement of the $\beta -\gamma$ directional correlation of ${}_{}{}^{203}{}_{}{}^{}\mathrm{Hg}$ as a function of the average $\beta$ energy $\overline{W}$ (in units $m{c}^2$) is reported. The values of the anisotropy coefficient $A_{22}\left(\overline{W}\right)$ in the $\beta -\gamma$ directional correlation function $W\left(\theta \right)=1+A_{22}\left(\overline{W}\right)P_2\left(cos\theta \right)$ are: $A_{22}(\overline{W}=1.15)=-0.007\mathrm{}\pm 0.0009$, $A_{22}(\overline{W}=1.23)=-0.0016\mathrm{}\pm 0.0006$, $A_{22}(\overline{W}=1.31)=-0.0020\mathrm{}\pm 0.0010$, $A_{22}(\overline{W}=1.345)=-0.0018\mathrm{}\pm 0.0005$, and $A_{22}(\overline{W}=1.38)=0.0018\mathrm{}\pm 0.0011$.

The spectra of neutrons emitted following muon capture in carbon and oxygen are presented with a resolution of 6.5% at 5 MeV and a precision of 5%. The carbon spectrum is dominated by a broad peak at 4.2 MeV, while the oxygen spectrum is dominated by a narrower peak at 5.1 MeV. Partial transition rates for these two peaks are given. This structure supports theoretical predictions of the excitation of the giant resonance in the capture process.

A number of reaction theories are tested and compared by their application to a simple model of $s$-wave scattering from a two-state nucleus. These theories include the extended $R$-matrix theory of Garside and Tobocman, the $L$-operator formalism of Lane and Robson, and variations of the Brown-de Dominicis theory. We find that the Hüfner-Lemmer version of the Brown-de Dominicis theory gives the best results in the few-level approximation.

Perturbed angular-correlation techniques are proposed for measuring the spin precessions of a polarized nucleus interacting with an axially symmetric electric field gradient. A specific method is suggested which makes use of Coulomb excitation to polarize and excite a nuclear state even as it recoils the nucleus into a suitable crystalline environment. Calculations indicate that this spectroscopic technique should make practical the measurements of the sign and magnitude of quadrupole moments of subnanosecond nuclear states.

In the framework of the $\alpha$-deuteron cluster model, the $J=1\mathrm{}$ deformation is considered in the phenomenological wave function of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ so as to produce the charge form factor and the quadrupole moment at the same time. In our model the deviation from the $S$ state of the relative motion between the $\alpha$ particle and the deuteron compensates the quadrupole moment of the free deuteron, $Q_d^{\exp }=+0.278\mathrm{}\pm 0.008$ ${\mathrm{fm}}^2$, to give that of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, $Q_{\mathrm{Li}}^{\exp }=-0.08\mathrm{}\pm 0.008$ ${\mathrm{fm}}^2$. It is shown that the quadrupole contribution plays an important role in filling up the diffraction minimum around $q^2=8\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$ in the elastic charge form factor.

An experimental study has been made of neutron polarization from the $\mathrm{T}\mathrm{}(d,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction at 30° lab as a function of incident deuteron energy. A liquid-helium polarimeter was employed for this purpose with a 90° spin-precession solenoid. Measurements have been made in two ways, with greatest emphasis placed on the use of the backward reaction, $\mathrm{D}\mathrm{}(t,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$, for a range of triton energies between 4.5 and 19.5 MeV. Equivalent c.m. conditions are obtained for $E_t=\frac{3}{2}{E}_d$, with neutrons emerging in the vicinity of 135° lab. Under these conditions, the neutron energy is near 11 MeV over a wide range of triton energies, where the $n-\mathrm{H}\mathrm{e}$ analyzing power is constant and well known. Measurements were also made from the $\mathrm{T}\mathrm{}(d,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction directly at 30° for a range of deuteron energies between 5 and 15 MeV. The measured polarizations varied from 0.03 at 3-MeV to 0.69 at 13-MeV equivalent deuteron energy. Comparisons are made with prior data. The method also allows extraction of values of the $n-\mathrm{H}\mathrm{e}$ analyzing power for neutron energies between 21 and 29 MeV at 75 and 113° lab.

To consider deuteron-induced reactions within the shell model, it is necessary to include single-particle states with two particles in continuum single-particle states. Expressions are derived for operators whose matrix elements give the transition amplitudes for the processes encountered in deuteron-induced reactions. Each of these operators can be written in terms of a single operator which satisfies an integral equation whose kernel involves the Green's function for two noninteracting particles in the presence of a common potential. This operator is discussed at length. Using single-particle Gamow states, a method is formulated to approximate the connected part of this operator by an operator of finite rank. This approximation is then tested numerically and is found to be effective. Finally, there is a discussion of the implications of the approximation in the scattering amplitudes of interest.

A partial-wave decomposition of the Iwamoto-Yamada cluster energy ${\mathcal{E}}_2$ is used to show that the cluster energy ${\mathcal{E}}_1+{\mathcal{E}}_2$ is consistently more attractive than the reaction-matrix energy $W_1+W_2$ by several MeV per nucleon at all densities. The differenee between these two types of calculations is shown to come from the absence in ${\mathcal{E}}_2$ of the dispersion effect in $W_2$ due to self-consistent hole energies. The necessity for imposing subsidiary conditions on the correlation function for ${\mathcal{E}}_2$— conditions not explicitly required in reaction-matrix calculations—is traced to the absence of the same dispersion effect. This result suggests a possible starting point for a formal comparison of the two expansions.

An experiment to study time-reversal invariance by both absolute and relative tests of detailed balance in the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d,\alpha ){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and its inverse has been performed. Measurements were made at three different excitation energies in a region where compound-nuclear resonances are resolved but overlapping levels are involved. In all cases the results are consistent with the principle of detailed balance, and our lowest uncertainty was ±0.5%. By making reasonable assumptions, an upper limit of 0.2% was assigned to the time-reversal-noninvariant part of the reaction amplitudes.

States of ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ were studied with the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reaction at a bombarding energy of 21 MeV. The data were found to favor the assignments $J^{\pi }={\frac{7}{2}}^{+} \mathrm{and} {\frac{5}{2}}^{+}$ to the levels at 8.65 and 8.69 MeV, respectively. A distorted-wave analysis of the angular distributions for negative-parity states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ yielded spectroscopic factors whose relative values agreed well with the predictions of Cohen and Kurath, even though the excited-state energies were found to be in better agreement with the predictions of the unified rotational model.

A method of equivalent local potentials is applied to separable interactions which fit the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ two-nucleon phase shifts. The method of generating equivalent local potentials used in this paper is independent of the boundary conditions imposed on the solutions of the nonlocal equation; consequently, all solutions of the nonlocal equation lead to the same equivalent local potential. The uniqueness of the equivalent local potential obtained by the present method is considered to be useful for the purpose of understanding nonlocal interactions. The Yamaguchi, the one- and two-term Tabakin, and the case-IV Mongan potentials are studied. The equivalent local Yamaguchi potential is similar to low-energy local two-nucleon interactions which do not have short-range repulsion. The two-term Tabakin potential results in an equivalent local potential with short-range repulsion. The occurrence of spurious states in the one-term Tabakin potential is related to a class of zeros of this separable interaction in coordinate space. The case-IV Mongan potential results in an equivalent local potential with strong short-range attraction. Further study of this interaction revealed a spurious state at 19.6 BeV which causes the wave function to have an additional node at experimentally relevant energies. The paper is concluded with an examination of the problem of constructing separable interactions which have short-range repulsion. It is shown that such interactions have a pronounced tendency to produce spurious states.