Differential cross sections for the elastic scattering of 1.33-MeV photons from lead and uranium have been measured at angles ranging from 12 to 60°, using a lithium-drifted germanium detector. Available calculations of the various elastic scattering amplitudes are briefly reviewed and an argument is presented to establish the relative phases between the two polarization components of the real scattering amplitudes. Those relative phases and the relative phases among the amplitudes of the various scattering processes permit the addition of the amplitudes to calculate theoretical cross sections. Discrepancies exist between the measured and theoretical cross sections. Suggestions by several authors for resolving these discrepancies are discussed and the need for further theoretical work is indicated.

The locations of 48 energy levels in ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ have been deduced from $\gamma$-ray singles, conversion-electron, and $\gamma -\gamma$ coincidence measurements on the $\mathrm{E}\mathrm{C}-{\beta }^{+}$ decay of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Ta}$. Over $300\gamma$-ray transitions have been observed in the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Ta}$ decay spectrum, and about 140 of these have been definitely assigned to the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ level scheme on the basis of 75 $\gamma -\gamma$ coincidence spectra. Spin and parity assignments are proposed for 27 levels besides the ground-state rotationalband members. Less extensive $\gamma$-ray singles data from ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ and ${}_{}{}^{176m}{}_{}{}^{}\mathrm{Lu}$ decay have also been obtained; these are found to be consistent with the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ level structure proposed on the basis of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Ta}$ decay data. Two $0^{+}$ excitations in ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ identified at 1150 and 1293 keV are found to display quite different decay properties. Evidence for the existence of a series of low-spin four-quasiparticle states near 3 MeV is cited. The ${}_{}{}^{176}{}_{}{}^{}\mathrm{Hf}$ level structure is compared with available theoretical calculations, and a preliminary interpretation of several unusual features of the level scheme is presented.

We have used the atomic-beam magnetic-resonance method to determine the ground-state nuclear spin, the electronic ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground-state hyperfine-structure (hfs) separations $\Delta \nu$, and the nuclear magnetic moments of 45-min ${}_{}{}^{125}{}_{}{}^{}\mathrm{Cs}$ and 13-day ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$. A more accurate value of the hfs separation of 6.2-hr ${}_{}{}^{127}{}_{}{}^{}\mathrm{Cs}$ was obtained by combining resonances reported previously with those reported in this work. The collected results are:

The errors quoted for the $\Delta \nu$'s are twice the standard deviations of least-squares fits to the experimental data. The magnetic dipole moments were obtained from the $\Delta \nu$'s by the Fermi-Segrè formula; an error of ∼1% is taken to include possible hfs anomalies.

35 chain yields from thermal-neutron-induced fission of ${}_{}{}^{242m}{}_{}{}^{}\mathrm{Am}$ were measured by a recoil-catcher method, using ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ fission as a standard. Fractional cumulative yields of five krypton and of six xenon nuclides were measured by an emanation method. The results are in agreement with known trends.

${}_{}{}^{246}{}_{}{}^{}\mathrm{Pu}$ produced by multiple neutron capture during an underground explosion was recovered and subjected to extensive chemical separations. $\gamma$ rays in the decay sequence ${}_{}{}^{246}{}_{}{}^{}\mathrm{Pu}\left({\beta }^{-}\right)-{}_{}{}^{246m}{}_{}{}^{}\mathrm{Am}\left({\beta }^{-}\right){}_{}{}^{246}{}_{}{}^{}\mathrm{Cm}$ were investigated by use of several Ge(Li) detectors. In all, 158 $\gamma$ rays were observed, up to 2.2 MeV. Of these, 114 were ascribed to the decay of ${}_{}{}^{246m}{}_{}{}^{}\mathrm{Am}$. A decay scheme was deduced, including 37 levels. Bands in ${}_{}{}^{246}{}_{}{}^{}\mathrm{Cm}$ have been identified with the following bandhead energies: $\mathrm{g}.\mathrm{s}.\mathrm{}{K}^{\pi }=0^{+}$; 841.70 keV $K^{\pi }=2^{-}$, octupole; 1078.90 keV $K^{\pi }=1^{-}$, octupole; 1124.42 keV $K^{\pi }=2^{+}$, $\gamma$; 1249.81 keV $K^{\pi }=(0^{-}, \mathrm{octupole})$; 1348.89 keV $K^{\pi }=1^{-}$; 1452.06 keV $K^{\pi }=\left(1^{+}\right)$; 1593.80 keV $K^{\pi }=2^{\mathrm{}(-)\mathrm{}}$; 1604.31 keV $K^{\pi }=1^{-}$.

The magnetic moment of the 2761-keV $8^{+}$ state in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$ has been measured as $\mu =(11.2\mathrm{}\pm 0.6){\mu }_N (g=1.40\mathrm{}\pm 0.07)$ using the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(\alpha ,2n){}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$ reaction and a time-differential technique. This result, which is consistent with a $|{\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}^2,8^{+}〉$ wave function, gives evidence for an enhanced $g_l$. The measurement also yielded a mean lifetime for the $8^{+}$ state of $\tau =275\mathrm{}\pm 10$ nsec. The lifetimes of the 2527-keV $5^{-}$ and 2613-keV $6^{+}$ states were measured by $p-\gamma$ and $\gamma -\gamma$ delayed-coincidence methods, respectively. A mean life of $\tau =2.24\mathrm{}\pm 0.06$ nsec was obtained for the $5^{-}$ state and the mean life of the $6^{+}$ state was found to be $\tau =2.22\mathrm{}\pm 0.07$ nsec. The observed $B(E2:8^{+}\to 6^{+})$ and $B(E2:6^{+}\to 4^{+})$ are consistent with ${\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}^2$ proton configurations for the $4^{+}$, $6^{+}$, and $8^{+}$ states. The lifetimes of the $6^{+}$ and $5^{-}$ states imply that the $6^{+}\to 5^{-}$ and $5^{-}\to 4^{+} E1\mathrm{}$ transitions in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$ are hindered relative to the Weisskopf estimates by 2 × ${10}^4$ and 7 × ${10}^4$, respectively. These results are consistent with pure proton configurations of ${\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}^2$ for the $4^{+}$ and $6^{+}$ states and ($2p_{\frac{1}{2}},1\mathrm{}{g}_{\frac{9}{2}}$) for the $5^{-}$ state.

The reaction ${\mathrm{Nb}}^{93}\mathrm{}(d,t)\mathrm{}{\mathrm{Nb}}^{92}$ has been studied with a deuteron beam of 17 MeV. Reaction tritons were momentum-analyzed by the Enge split-pole spectrograph and detected by position-sensitive counters as well as nuclear emulsions placed along the focal plane of the spectrograph. The experimental energy resolution was ∼8 keV full width at half-maximum. Up to 3 MeV in excitation, approximately 50 states of ${\mathrm{Nb}}^{92}$ have been identified including the 6 previously known low-lying states. Angular distributions for 40 of these triton groups were obtained and $l$-transfer values for the neutron pickup to the corresponding states in ${\mathrm{Nb}}^{92}$ were assigned by comparison with distorted-wave calculations. A previous classification of the lowest six positive-parity states as belonging to the ($1g_{\frac{9}{2}}^{ \pi }2d_{\frac{5}{2}}^{ \nu }$) multiplet is confirmed. As there are ambiguities in the assignment of spins to some members of this multiplet on the basis of spectroscopic strengths alone, the electromagnetic-decay properties of the lowlying positive-parity states of ${\mathrm{Nb}}^{92}$ have been studied via the ${\mathrm{Nb}}^{93}(d,t\gamma ){\mathrm{Nb}}^{92}$ reaction. On the basis of the resulting decay scheme, spin assignments are made to the previously identified ($1g_{\frac{9}{2}}^{ \pi }2d_{\frac{5}{2}}^{ \nu }$) multiplet of states. The 286-, 357-, 480-, and 500-keV states are assigned $J^{\pi }$ values of $3^{+}$, $5^{+}$, $4^{+}$, and $6^{+}$, respectively.

The angular distribution of the fission products formed in the reaction of 126-MeV ${\mathrm{C}}^{12}$ ions with ${\mathrm{Gd}}^{158}$ and 137-MeV ${\mathrm{O}}^{16}$ ions with ${\mathrm{Sm}}^{154}$, both of which give ${\mathrm{Yb}}^{170}$ compound nuclei at an excitation of 107 MeV, have been measured. It is found that the angular distribution in the ${\mathrm{C}}^{12}$-ion entrance channel is proportional to $\frac{1}{sin\theta }$ from about 25 to 155° in the center-of-mass system, while the corresponding range is about 15 to 165° for the ${\mathrm{O}}^{16}$-ion entrance channel. The total fission cross sections are 20 ± 2 and 39 ± 4 mb for the two entrance channels, respectively.

Measurements are reported for $\gamma$-ray energies and intensities present in the $\beta$ decays of four nuclei ${\mathrm{Xe}}^{142}$, ${\mathrm{Cs}}^{142}$, ${\mathrm{Ba}}^{142}$, and ${\mathrm{La}}^{142}$. These nuclei are all members of the isobaric decay chain beginning with ${\mathrm{Xe}}^{142}$, which was made available by use of an on-line isotope separator developed for the study of gaseous fission products. Partial energy level schemes have been constructed for ${\mathrm{Cs}}^{142}$, ${\mathrm{Ba}}^{142}$, ${\mathrm{La}}^{142}$, and ${\mathrm{Ce}}^{142}$ with the aid of Ge(Li)-Ge(Li) coincidence data. Some spin-parity assignments were made and relative transition probabilities determined for levels in ${\mathrm{Ba}}^{142}$ and ${\mathrm{Ce}}^{142}$; comparative half-lives were calculated for the decays of ${\mathrm{Ba}}^{142}$ and ${\mathrm{La}}^{142}$. The energy level scheme of ${\mathrm{Ce}}^{142}$ suggests vibration-like excitations, but that of ${\mathrm{Ba}}^{142}$ supports the suggestion of a transition to deformation effects as the neutron number approaches $N=88\mathrm{}$.

Absolute differential cross sections of transitions to levels in the $N=82\mathrm{}$ nucleus ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ populated by the reaction ${}_{}{}^{138}{}_{}{}^{}\mathrm{La}\mathrm{}(d,p)\mathrm{}{}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ at 12-MeV bombarding energy have been measured with a magnetic spectrograph. The $Q$ value of the reaction is 6553 ± 3 keV. The reaction strongly populates the one-quasiproton ground state of ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ by $l=2\mathrm{}$ neutron transfer, which establishes positive parity for the ${}_{}{}^{138}{}_{}{}^{}\mathrm{La}$ ground state. Of the many known states in the region from 1200 to 2000 keV in ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, only the 1536.3-keV state is weakly populated. The reaction strongly populates a high density of three-quasiparticle states in ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, beginning at 3355-keV excitation energy, by $l=3\mathrm{}$ neutron transfer. The shell-model multiplet structure of ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ has been calculated using a modified surface $\delta$ interaction within a configuration space having ($1g_{\frac{7}{2}}$) and ($2d_{\frac{5}{2}}$) active proton orbitals and ($3s_{\frac{1}{2}}$), ($2d_{\frac{3}{2}}$), ($2f_{\frac{7}{2}}$), and ($3p_{\frac{3}{2}}$) active neutron orbitals. Comparisons between experimental and theoretical multiplet structure are presented.

The ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}(\alpha ,{\alpha }^{\prime })$ reaction at $E_{\alpha }=45.0\mathrm{}$ MeV and $\Delta E_{{\alpha }^{\prime }}\approx 35$ keV was studied to investigate the particle-vibration interaction in this $N=82\mathrm{}$ nuclide and to elucidate the ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ level structure in the 0-4-MeV region. The $\alpha$-particle angular distributions were measured in ≤2° steps over ranges of 7-80° for elastic scattering and 12-66° for inelastic scattering. A ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}(d,d^{\prime })$ spectrum at $E_d=28.7\mathrm{}$ MeV and with higher resolution (20 keV) was also recorded. These measurements, in combination with other high-resolution studies, establish the existence of approximately 50 levels with excitation energies of 1.1-3.0 MeV. Approximately 20 of these levels can be identified in the ($\alpha ,{\alpha }^{\prime }$) spectra and are interpreted as states with significant collective components. Although most of these levels are in either a positive-parity group between 1.1 and 1.9 MeV or a negative-parity group between 2.0 and 2.5 MeV, it is found that the assumption of a weak particle-vibration interaction based on the $2^{+}$ and $3^{-}$ core states of ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ and the $d_{\frac{5}{2}}$ ground state of ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ is inadequate to explain the results. Qualitative agreement is found with the results of recent shell-model studies which assumed nine active protons outside an inert $Z=50\mathrm{}$, $N=82\mathrm{}$ core. In addition, some evidence is found for the approximate validity of the $\Delta B=0\mathrm{}$ selection rule for inelastic scattering transitions which was recently proposed by Hecht and Adler.

Nuclear hyperfine interactions in the 145-keV state of ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ have been investigated by measurements on Mössbauer-scattered $\gamma$ rays. The magnetic moment of this level was determined to be ${2.78}_{-0.06\mathrm{}}^{+0.12\mathrm{}}{\mu }_N$, a value which is considerably larger than that predicted by Kisslinger and Sorensen. Renormalizing $g_l$ in their calculation to account for meson-exchange effects reduces the disagreement significantly. The magnetic field at the site of the Pr nucleus has been investigated for a number of compounds. The values 2.07 ± 0.08 and 0.86 ± 0.06 MOe were obtained for the fields at 4.2°K in Pr${\mathrm{B}}_6$ and Pr${\mathrm{O}}_2$, respectively. Although these are only about ½ the values expected for the internal fields in the corresponding free Pr ions, the temperature dependence closely followed a Brillouin function. Line broadening that persisted to temperatures well above the magnetic-ordering temperatures was observed for these compounds indicating the presence of a smaller residual hyperfine interaction. Isomer shifts have been observed for a number of Pr compounds. Based on isomer shifts between ionic trivalent and tetravalent compounds, the difference in the mean square charge radii of the excited and ground states is estimated: $〈r_e^{}{}_{}{}^2〉-〈r_g^{}{}_{}{}^2〉=(6.3\mathrm{}\pm 2.5)\times {10}^{-3\mathrm{}}$ ${\mathrm{fm}}^2$.

We show that the results obtained by several authors for the internal scattering amplitude for bremsstrahlung can be derived in a unified way from an operator identity. This shows the mathematical connection between these various approaches and their essential equivalence. We show how the approaches of these authors are generalized to the case of momentum-dependent potentials.

An explicit proof is given of the effective orthogonality among the channel wave functions obtained from a set of coupled equations by showing that the nonorthogonal parts of the wave functions are physically redundant, thus providing a rigorous basis for the treatment of nuclear stripping and pickup reactions. An orthogonality-preserving procedure of the coupled-channel method is outlined.

Differential and integral cross sections for the disintegration of the deuteron by antineutrinos, both in the charge-exchange and the hypothetical charge-retention mode, are presented, together with the salient features of assumptions and calculations. The incident spectra used, those due to equilibrium and instantaneous fission, are also presented. For comparison, integral cross sections weighted by the lithium-8 spectrum are added. When weighted by the equilibrium fission spectrum, the values derived here of the integral cross sections in the two modes are ${\sigma }_{\mathrm{nn}}=0.272\mathrm{}\times {10}^{-44\mathrm{}}$ ${\mathrm{cm}}^2$ and ${\sigma }_{\mathrm{pn}}=0.655\mathrm{}\times {10}^{-44\mathrm{}}$ ${\mathrm{cm}}^2$, respectively.

The excitation spectrum of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ has been examined through measurements of charged-particle energy spectra from four nuclear reactions. Triton energies up to 22 MeV were used to induce the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(t,\alpha ){}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(t,p)\mathrm{}{}_{}{}^6{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(t,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{He}$ reactions. Deuterons of 16- and 22-MeV energy were used to induce the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{He}$ reaction. All of the energy spectra show peaks from the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ ground and first excited (1.80-MeV) states, but no other structure attributable to states of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ was observed. Differential cross-section data for the ground and first excited states were obtained for three of the reactions. The ($d,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) cross-section data were compared with the results of distorted-wave Born-approximation calculations and with data collected from the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ reaction. These comparisons were consistent with an assignment of $2^{+}$ for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ 1.80-MeV state.

Systematics of $n-p$ interaction energies $I_{\mathrm{np}}$, obtained from a linear combination of nuclear binding energies, are discussed. The calculated $I_{\mathrm{np}}$ values show evidence of shell effects. A closed expression, connecting $n-p$ interaction energies with nuclear size and spin, is given for even-even nuclei.

We show that it is possible to fit the low-energy spectrum in a truncated space using any one of a variety of pseudo-Hamiltonians together with a suitable choice of a set of orthonormal wave functions. Numerical examples are used for illustration.

The maximum-overlap orbitals first proposed by Brenig, in which the overlap between the true wave function and a Slater determinant is maximized, is shown to be equivalent to Löwdin's exact self-consistent-field theory. By defining an energy functional and varying it, some points in Löwdin's theory are clarified. The ground-state energy is expanded in perturbation theory, and it is pointed out that some diagrams could become divergent. In order to eliminate these diagrams, Bogoliubov's principle of compensation of dangerous diagrams (PCDD) is extended to finite fermion systems. In these systems, the PCDD states that the sum of all the diagrams leading from the vacuum to a single particle-hole state must be set equal to zero. This condition is the Brillouin-Brueckner condition, which is also obtained from the other methods. The form of the PCDD obtained here is different from another form that leads to Löwdin's natural orbitals, and the difference is discussed.

Differential cross sections have been measured for the mirror reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,n_0){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,p_0){}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ for incident energies between 13 and 16 MeV. A striking feature of the data is the existence of a pair of states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; One (17.63 MeV) appears to emit protons and not neutrons, the other (18.10 MeV) appears to emit neutrons and not protons. The total lab widths of these levels are ∼180 keV for the 17.63-MeV level and ∼250 keV for the 18.10-MeV level. The ($\alpha ,p$) angular distribution near the center of the 17.63-MeV state is similar to the ($\alpha ,n$) angular distribution near the center of the 18.10-MeV state. The results indicate large isospin mixing in the 18.10-MeV state. Evidence that the two states comprise an isospin-mixed doublet formed by strong mixing of a $T=0\mathrm{}$ and $T=1\mathrm{}$ state is presented.