Prompt high-energy $\gamma$ rays resulting from neutron capture at thermal energies and in the resonances of ${\mathrm{Sb}}^{121}$ and ${\mathrm{Sb}}^{123}$ have been studied with the high flux beam reactor fast chopper using high-resolution Ge(Li) detectors. The binding energy $B_n$ of the last neutron in ${\mathrm{Sb}}^{122}$ and ${\mathrm{Sb}}^{124}$ has been determined to be 6807 ± 2 and 6468 ± 2 keV, respectively. Based on prompt capture $\gamma$-ray data, we have assigned a spin of 4 to the 21.6-eV resonance of ${\mathrm{Sb}}^{123}$. Energy levels populated by the neutron-capture $\gamma$ rays are given up to an excitation energy of 2475 keV in ${\mathrm{Sb}}^{122}$ and up to 2221 keV in ${\mathrm{Sb}}^{124}$. These data are compared with the existing ($d,p$) data on ${\mathrm{Sb}}^{121}$ and ${\mathrm{Sb}}^{123}$. We have also studied the low-energy (<511 keV) $\gamma$ rays originating in neutron capture in the different resonances. For ${\mathrm{Sb}}^{121}$, the observed spectra are found to fall into two classes, each having its own characteristic intensity distribution depending on the spin of the capturing state. By comparing these spectra with those originating from the 6.24-eV resonance ($3^{+}$) and the 15.4-eV resonance ($2^{+}$), we have assigned the following spins to the resonances in ${\mathrm{Sb}}^{121}$: 29.7 eV (3), 53.5 eV (2), 64.5 eV (3), 73.8 eV (2), 111.4 eV (2), and 126.8 eV (3). Similar, but more tentative, spin assignments are made for resonances in ${\mathrm{Sb}}^{123}$.

The low-energy spectra have also been used to measure the half-life of the 61.6-keV isomeric state in ${\mathrm{Sb}}^{122}$ by a new method. This experimental procedure is described. The half-life of the isomeric state is found to be 2.3 ± 0.6 μsec.

The intensities of the high-energy $\gamma$ rays in the 2.1-day decay of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Np}$ to ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ are measured using a high-resolution Ge(Li) detector (full width at half maximum of 1.7 keV at 1333 keV). The branching ratios for the transitions from the $\gamma$-vibrational band are found to be consistent with values of (26.5 ± 7.8) × ${10}^{-3\mathrm{}}$ for $z$, the band-mixing parameter for the ground-state rotational and $\gamma$-vibrational bands, and $\approx -7\mathrm{}\times {10}^{-3\mathrm{}}$ for $z_{\beta \gamma }$, the parameter for the mixing of $\beta$- and $\gamma$-vibrational bands.

The ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}(\gamma ,n)$ cross section was measured from threshold to 24 MeV with a photon beam produced by the in-flight annihilation of positrons. The photon beam resolution was determined to be 1.2% (full width at half maximum) by elastically scattering the $\gamma$ rays from the 15.1-MeV level in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The ($\gamma ,n$) cross section was found to have a maximum value of ∼348 mb and an integrated value up to 24 MeV of 1.72 ± 0.16 MeV b. Within the statistics and the photon resolution of the measurement, the results indicate that there is no structure in the cross section, with the possible exception of a weak bump at approximately 17.5 MeV. The results are compared with previous measurements and with theory; the latter comparison indicates that the widths of states in the dynamic collective theory should be considerably broader than those which have been typically used.

The spins of the four lowest neutron resonances in ${\mathrm{Er}}^{167}$ have been determined by measuring the transmission of polarized neutrons through a sample of polarized erbium nuclei. The determination of the spins depends solely on the transmission effect and is independent of any assumption about the sign of the nuclear magnetic moment or the direction of the effective field at the target nuclei. The spins were found to be $J=I+\frac{1}{2}=4\mathrm{}$ for the 0.460-eV resonance and $J=I-\frac{1}{2}=3\mathrm{}$ for the resonances at 0.584, 6.10, and 9.6 eV. The nuclear polarization of the sample, obtained as function of the sample temperature at a fixed energy, was fitted to a theoretical curve, using the magnetic and electric hyperfine splitting constants as fitting parameters. The values found for the magnetic and electric hfs constants are, respectively, $\frac{A}{k}=-0.085\mathrm{}\pm 0.0005$°K and $\frac{P}{k}=-0.005\mathrm{}\pm 0.001$°K. Taking the nuclear magnetic moment of ${\mathrm{Er}}^{167}$ to be $-0.56\mathrm{}{\mu }_N$, the corresponding effective magnetic field at the nucleus is 7.26 × ${10}^6$Oe.

Monochromatic photons obtained from thermal-neutron capture in iron were used for exciting nuclear levels in the energy region between 6 and 9 MeV. Angular distribution of the elastically scattered radiation was carried out for the determination of the spins of the resonance levels. Total and ground-state radiation widths of ten resonance levels in various isotopes were measured using self-absorption, temperature variation, and absolute scattering cross-section measurements. The parity of six resonance levels was measured using a Compton polarimeter, and strong $M1\mathrm{}$ transitions were found in ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; the character of four transitions was found to be $E1\mathrm{}$. The observed total radiation widths ${\Gamma }_{\gamma }$ of these bound levels were found to have the same magnitude as those of unbound levels obtained in neutron resonances, which indicate that ${\Gamma }_{\gamma }$ is continuous across the ($\gamma ,n$) threshold.

A four-parameter correlation experiment which measured neutron emission in "long-range alpha" (LRA) fission is described. The energies of both the fission fragments and of the $\alpha$ particle as well as the time of flight of the neutron were recorded. The experimental data were analyzed with the aid of a computer, and the method of analysis is described.

Some of the results of the present experiment have already been published. In this paper we discuss the pre-neutron-emission mass distribution of LRA fission as well as some properties of the neutrons as a function of $\alpha$-particle energy. In addition, the neutron kinetic energy as a function of fragment mass is given. The probability of $\alpha$-particle emission as a function of the fission-fragment mass ratio is also discussed.

Lane and Robson have given a stationary-principle formulation of an approximation theory for resonance reactions. They stated a paradox in the stationary principle, which is resolved here in support of the approximation method.

It is shown that the Tabakin potential apparently predicts a deuteron quadrupole moment which is smaller than that previously assumed by a factor of 3. This discrepancy arises from the original use of an inaccurate formula relating the quadrupole moment of the deuteron to the threshold slope of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ coupling parameter ${\epsilon }_1$. The new value indicates a corresponding Tabakin tensor force which is considerably weaker than is required. Also, the small $D$-wave spin-orbit splitting given by the Tabakin potential at 142 MeV is found to be different from the small experimental value.

The expansion developed previously for the derivation of the relation between the transmission coefficient and the ratio of the average width to the average spacing is reexamined. By rewriting the series in a more convenient form, not only is the objection raised against the expansion removed, but also an estimate of the smallness of the terms which are usually thrown out can be easily made.

In continuation of previous study of the impact-parameter representations of potential scattering amplitudes at large angles, we have numerically evaluated and compared various approximate forms of the impact phases along the trajectories parallel to the initial, final, and average momenta. The necessity of phase averaging in the symmetric forms of the amplitudes is pointed out. None of the presently available approximations seems to be sufficiently accurate to reliably replace the phase-shift analysis at large angles.

The distorted-wave Born approximation (DWBA) cross section is discussed for a reaction of the form $A(d,pn)A$ in which $n$ is not observed. We evaluate the slowly convergent oscillating radial integrals by contour integration in the complex radius plane. This avoids the computation of wave functions out to the large distances that the Huby-Mines technique requires. The present technique is also useful for stripping to very weakly bound states. We find that the DWBA angular distribution for stripping to a resonant $n$ state is closely reproduced by using a form factor for the resonant energy of $n$. The width of the resonance, rather than the spectroscopic factor, is found to be measured by the absolute magnitude of the cross section. The results of calculations with the present method are compared with the results of the Huby-Mines method for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(d,p)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ reaction leading to the resonant 5.08-MeV state of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$.

Plastic scintillators were exposed in the external 920-MeV $\alpha$-particle beam at the 184-in. cyclotron at Lawrence Radiation Laboratory. The beam-flux monitor was Ilford 100-μ L4 pellicles. The cross section for ${\mathrm{C}}^{12}(\alpha ,\alpha n){\mathrm{C}}^{11}$ was found to be 49.4 ± 1.8 mb.

The generalized cranking model is used to study the corrections to the nuclear rotational spectra that cause it to deviate from the $I(I+1\mathrm{})\mathrm{}$ rule. The fourth-order cranking corrections and the Coriolis-antipairing effect are treated as modes of a generalized vibration in the same way as the centrifugal stretching. The new form helps to explain the success of various two-parameter formulas used to fit the experimental energy levels and shows that they are equivalent. The parameters of such formulas are calculated here microscopically in a good- $j$ basis, and they agree reasonably well with experiment.

Experimental $B\left(E2\mathrm{}\right)\mathrm{}$ values are tabulated for transitions in odd-mass spherical nuclei and compared with predictions of the pairing-plus-quadrupole model including up to two phonons. Of the well over 100 cases, agreement within a factor of 2 is obtained for $\approx \frac{2}{3}$, indicating the general validity of the theory and suggesting its use as a guide to yet unmeasured cases.

The three-body breakup reactions induced by 47-MeV protons on a gaseous ${\mathrm{He}}^4$ target have been investigated in a kinematically complete experiment. Protons were observed in coincidence with tritons or ${\mathrm{He}}^{3,}$s at several pairs of coplanar lab angles using two counter telescopes. Data were stored by an on-line computer which serially listed four linear signals from each event on magnetic tape. The proton spectra showed strong enhancements from neutron-proton and proton-proton final-state interactions, in agreement with the predictions of the Watson-Migdal theory. A Chew-Low-type extrapolation procedure was used to extract the $\mathrm{np}$ singlet scattering length, which was in fair agreement with the value from $\mathrm{np}$ free scattering. The triton and ${\mathrm{He}}^3$ spectra showed peaks due to sequential reaction processes via the continuum resonance states in the ${\mathrm{He}}^4$ system. These enhancements could be identified with previously observed ${\mathrm{He}}^4$ levels of known spin and parity assignments.

The $R$-matrix expansion for the ground-state energy of a many-fermion system is carried through fourth order. We evaluate this expansion for a potential modeled after the nucleon-nucleon one. The calculation is described in detail. We find that the "hole-line" approximation seems to underestimate the attraction so that a hard-core force may well be consistent with the experimental binding energy of large nuclei.

A thick-target method has been used to measure absolute differential cross sections for the reactions ${\mathrm{O}}^{16}\mathrm{}(d,n)\mathrm{}{\mathrm{F}}^{17}$ and ${\mathrm{O}}^{16}\mathrm{}(d,n)\mathrm{}{\mathrm{F}}^{{17}^{*}}$ (0.500 MeV) from 2.0 to 4.2 MeV. Excitation functions were taken at 20° intervals from 0-160° in the lab system. Satisfactory fits to the angular distributions required Legendre polynomials of order 6 or higher. The c.m. Legendre coefficients $A_0$ and $A_1$ are presented as a function of lab deuteron energy for the ground-state data. The total cross sections for production of ground-state and first-excited-state neutrons are also given as a function of energy.

The elastic scattering of the $\Lambda$ particle by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been studied in the 0.1- to 10.0-MeV energy range. The calculation was performed using baryon-baryon interactions composed of central potentials previously employed in binding-energy calculations of ${}_{\Lambda }{}^5{}_{}{}^{}\mathrm{He}$ and a derivative spin-orbit $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential. Phase shifts, total cross sections, angular distributions, and polarizations were computed as functions of energy for $l=0,1, \mathrm{and} 2$. The results are sensitive to the potential parameters, implying that even simple measurements would yield interesting information.

Realistic shell-model potentials are used to test Strutinsky's method. It is found that the results are strongly dependent on the shell-smearing parameter as well as the order of the curvature correction for smearing. No unambiguous values can be obtained for the shell correction, even with the effect of the continuum properly included. As a result, the Strutinsky theory should be regarded only as a recipe to be used in combination with Nilsson potentials.