Monte Carlo calculations have been made of electron-photon cascades in thick tungsten targets bombarded by electrons with energies up to 60 MeV. The following information has been obtained: (1) the bremsstrahlung efficiency, (2) the angular distribution of the emitted bremsstrahlung intensity, (3) the spectra of the bremsstrahlung emitted in various directions, (4) the transmission of primary and secondary electrons through the target, (5) energy deposition as function of the depth in the target, (6) the differential photon track length distribution inside the target, and (7) the yield of photoneutrons. The paper also includes various comparisons with experimental data.

We have developed a semiempirical description of the ground-state band of even quasirotational nuclei, based on the picture of anharmonic vibrations, which agrees surprisingly well with experiment. Comparison with previous empirical and semiempirical formulas is presented.

The ($p,n$) reaction cross sections were measured to ±4% for 3- to 5.5-MeV protons on ${}_{}{}^{117,119,120,122,124}{}_{}{}^{}\mathrm{Sn}$ and on natural Sn and In. Analyses with a conventional optical-model potential were made in the energy regions where the ($p,n$) cross sections are nearly equal to the total absorption cross sections. These analyses show that the energv dependence in the real well is about three times greater for 5- to 10-MeV protons than it is for 10- to 61-MeV protons. The best-fit potential for 3- to 5.5-MeV protons on the Sn isotopes has a surface absorptive layer about half as thick as at 10 MeV. The In strength functions are fitted by increasing both the width and depth of the imaginary part of this potential by about 25%. The $Q$ value for ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}\mathrm{}(p,n)\mathrm{}{}_{}{}^{120}{}_{}{}^{}\mathrm{Sb}$ was found to be -3465 ± 7 keV.

Levels in ${}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$ have been studied through the reactions ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}\mathrm{}(d,p)\mathrm{}{}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}\mathrm{}(d,t)\mathrm{}{}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$, using 12-MeV deuterons, and via thermal-neutron capture in ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$. Over 40 states below 1.5 MeV are populated in the charged-particle reactions. These data, coupled with the $\approx 150$ capture $\gamma$ rays observed, lead to a level scheme that includes the following spectroscopic assignments (rotational band-head energy in keV, followed by the Nilsson single-particle state believed to be dominant): 0.0, ${\mathrm{½}}^{-}$[521], with associated rotational band to spin ${\frac{11}{2}}^{-}$, 92.2, ${\frac{5}{2}}^{-}\mathrm{}\left[512\right]\mathrm{}$, with band to ${\frac{11}{2}}^{-}$; 243.7, ${\frac{7}{2}}^{+}\mathrm{}\left[633\right]\mathrm{}$, with band to ${\frac{13}{2}}^{+}$; 562.1, ${\mathrm{½}}^{-}$[510], with band to ${\frac{7}{2}}^{-}$; 714.5, ${\frac{3}{2}}^{-}\mathrm{}\left[521\right]\mathrm{}$, with band to ${\frac{11}{2}}^{-}$; 823, ${\frac{7}{2}}^{-}$ [514], with band to ${\frac{9}{2}}^{-}$; 850, ${\frac{5}{2}}^{-}\mathrm{}\left[523\right]\mathrm{}$, with band to ${\frac{11}{2}}^{-}$; and 1081.8, ${\frac{3}{2}}^{-}\mathrm{}\left[512\right]\mathrm{}$, with band to ${\frac{7}{2}}^{-}$. In addition, a level at 860.2 keV is assigned as the head of a $K^{\pi }={\frac{3}{2}}^{+}$ band that is mainly the ($K-2\mathrm{}$) $\gamma$-vibrational state associated with ${\frac{7}{2}}^{+}\mathrm{}\left[633\right]\mathrm{}$. The data suggest that the 562.1-, 714.5-, and 1081.8-keV bands also have significant vibrational admixtures. Several features of the level scheme, including certain $\gamma$-ray branching ratios, are interpreted in terms of Coriolis mixing. The neutron separation energy for ${}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$ is determined as 6003.1 ± 0.3 keV, and the $Q$ value for the ${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}\mathrm{}(d,t)\mathrm{}{}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$ reaction is found to be -950 ± 30 keV.

The $\gamma -\gamma$ perturbed angular correlation of the 236-50-keV cascade in ${}_{}{}^{223}{}_{}{}^{}\mathrm{Ra}$ has been investigated, yielding $g({\frac{3}{2}}^{-},50\mathrm{} \mathrm{keV})=+0.28\mathrm{}\pm 0.04$. The magnetic hyperfine fields experienced by Ra nuclei embedded in Ni, Co, and Fe lattices were found to be -30 ± 10, -80 ± 16, and -105 ± 20 kOe, respectively.

A study of the neutron-capture reaction mechanism for radiative capture of resonant-energy neutrons has been made for ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}(n,\gamma ){}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$. The statistical distribution of the partial radiation widths over 11 neutron resonances is inconsistent with a ${\chi }^2$ distribution with one degree of freedom. No correlations are observed between the $\gamma$-ray partial widths and the reduced neutron widths of either the capturing or final states. Neither is there any significant correlation among the individual $\gamma$-ray widths. Such facts indicate that neither channel capture nor doorway states contribute strongly to the neutron-capture process in the region above the neutron binding energy. However, there is a small but significant departure from a purely statistical compound-nuclear process. Final states unreported in previous experiments are observed. In addition, the spins of 11 resonances, as well as limitations on the spins of the low-lying final states are determined.

Photon scattering cross sections were measured with 70-keV resolution from 6 to 9 MeV in Sn, and from 8.5 to 12.5 MeV in Zr. A new method of analysis is used to infer relatively reliable total photon interaction cross sections. Both the elastic scattering and the total interaction cross sections vary more rapidly with energy than had been anticipated; the best identified localization of transition strength is between 11.4 and 11.8 MeV in Zr. The average total interaction cross sections are qualitatively similar to, but about 50% larger than, an extrapolation of the electric dipole giant resonance. The cross sections are large enough to imply that electric dipole interaction dominates at most energies. The relative probability of photon scattering and photoproton emission is very sensitive to correlations between proton widths and ground-state $\gamma$-ray widths. There is no evidence for width correlations associated with the additional strength concentrated near 11.5 MeV in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$.

We have calculated the effect of nuclear deformability on the cross section for interaction of heavy ions with uranium. Static calculations indicate that these effects should be large; dynamic calculations with liquid-drop parameters indicate that they should be smaller, but measurable with currently available heavy ions (argon incident on uranium). Dynamic calculations with parameters derived from spectroscopic measurements indicate that the effects should be quite small, in agreement with experiment. We have done both classical and quantum-mechanical calculations; the two methods give the same results. The quantum-mechanical calculations also give the probability of Coulomb excitation to the vibrational states of the target nucleus. We discuss the value of several approximations used to estimate total reaction cross sections.

The $\beta -\gamma$ angular correlation of the $(536\mathrm{}-\mathrm{K}\mathrm{e}\mathrm{V}-\beta )-(604\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V}-\gamma +612\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V}-\gamma )$ transition in ${\mathrm{Ir}}^{192}$ was measured and found to be zero. The $\gamma$-conversion-$e^{-}$ correlation of the 604-keV-316-keV transitions in ${\mathrm{Pt}}^{192}$ was used to estimate the $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratio of the 605-keV $\gamma$ ray, giving $\delta =3\mathrm{}$.

The multipole character and $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios of all $\gamma$ transitions following the decay of ${\mathrm{Ag}}^{110m}$ to ${\mathrm{Cd}}^{110}$ have been determined by measuring the 1-2, 1-3, and 1-4 directional correlations, using two 30-cc coaxial Ge(Li) detectors in conjunction with a multichannel coincidence gating system. The analysis of the data clearly demonstrated the necessity for careful investigations of the effects of the Compton background on directional correlation measurements using Ge(Li) detectors. The directional correlation functions for mixed $\gamma -\gamma$ cascades are given in terms of explicitly defined reduced matrix elements and their ratios $\delta \left({\gamma }_n\right)$. The analysis of the 25 measured directional correlations yielded a consistent set of $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios for all mixed multipole transitions. The $\frac{E2\mathrm{}}{M1\mathrm{}}$ amplitude ratios $\delta \left({\gamma }_n\right)=\frac{〈I_{n+1\mathrm{}}\parallel {\overrightarrow{\mathrm{j}}}_N{\overrightarrow{\mathrm{A}}}_2^E\parallel I_n〉}{〈I_{n+1\mathrm{}}\parallel {\overrightarrow{\mathrm{j}}}_N{\overrightarrow{\mathrm{A}}}_1^M\parallel I_N〉}$ for the ${\mathrm{Cd}}^{110}$ $\gamma$ rays are (energies are in keV): $\delta \mathrm{}\left(447\right)=-0.45\mathrm{}\pm 0.20$, $\delta \mathrm{}\left(620\right)=-0.80\mathrm{}\pm 0.50$, $\delta \mathrm{}\left(678\right)=-0.25\mathrm{}\pm 0.20$, $\delta \mathrm{}\left(687\right)=-{1.1}_{-0.4\mathrm{}}^{+0.8\mathrm{}}$, $\delta \mathrm{}\left(707\right)=-1.0\mathrm{}\pm 0.3$, $\delta \mathrm{}\left(818\right)=-1.20\mathrm{}\pm 0.15$, $\delta \mathrm{}\left(1384\right)=-0.37\mathrm{}\pm 0.03$, and $\delta \mathrm{}\left(1505\right)=-0.55\mathrm{}\pm 0.10$. In terms of the multipole moments $〈I_{n+1\mathrm{}}\parallel \mathfrak{M}\left(\pi L\right)\parallel I_n〉$ of Bohr and Mottelson, the $\frac{E2\mathrm{}}{M1\mathrm{}}$ moment ratios $\Delta =\frac{〈I_{n+1\mathrm{}}\parallel \mathfrak{M}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\parallel I_n〉}{〈I_{n+1\mathrm{}}\parallel \mathfrak{M}\mathrm{}\left(M1\mathrm{}\right)\mathrm{}\parallel I_n〉}$ in natural units ($\hslash =m=c=1\mathrm{}$) are: $\Delta \mathrm{}\left(447\right)=-3.0\mathrm{}\pm 1.3$, $\Delta \mathrm{}\left(620\right)=-3.8\mathrm{}\pm 2.4$, $\Delta \mathrm{}\left(678\right)=-1.09\mathrm{}\pm 0.88$, $\Delta \mathrm{}\left(687\right)=-{4.7}_{-1.7\mathrm{}}^{+3.4\mathrm{}}$, $\Delta \mathrm{}\left(707\right)=-4.2\mathrm{}\pm 1.3$, $\Delta \mathrm{}\left(818\right)=-4.3\mathrm{}\pm 0.5$, $\Delta \mathrm{}\left(1384\right)=-0.79\mathrm{}\pm 0.06$, and $\Delta \mathrm{}\left(1505\right)=-1.08\mathrm{}\pm 0.20$.

The trajectories of the $\alpha$ particle and the two main fragments produced in ternary fission are calculated by computer on the basis of initial conditions determined by the statistical theory of fission. The angular and energy distributions of the three particles as functions of the mass ratio of the main fragments are deduced; they compare well with the experimental results of Fraenkel on spontaneous fission of ${\mathrm{Cf}}^{252}$. Calculations are repeated with varied initial conditions; the final results are insensitive to the initial velocities of the fragments and the initial position of the $\alpha$ particle, but are very sensitive to the initial velocity of the $\alpha$ particle. Based on this sensitivity, the experimental angular distribution strongly supports the view of the statistical theory that the fission process is a slow process. The initial positions of the fragments are related to the prompt-neutron distribution; the present results on angular and energy distributions are consistent with experimental results of prompt-neutron distribution.

The nuclear matrix element for the double $\beta$ decay ${\mathrm{Te}}^{130}$→${\mathrm{Xe}}^{130}$ is calculated with a specific Gamow-Teller force. A reasonable strength of this force is unable to give enough reduction in the rate to agree with the experimental half-life. The amount of isospin violation in the wave function owing to the difference of the neutron and proton single-particle energies is calculated. The number and isospin problems are discussed in connection with the use of the random-phase approximation in a $\beta$-decay calculation. It is shown that the $\beta$-decay operator has no spurious terms due to number or isospin dispersion.

We report measurements of the circular polarization of $\gamma$ rays from unpolarized sources of ${\mathrm{Hf}}^{181}$ and ${\mathrm{Yb}}^{475}$ of 100-1000-Ci strength, using a Compton polarimeter in a forward-scattering geometry. Our technique consisted of integrating the total detector current and digitizing the charge. Several aspects of this novel method are discussed, such as the role of the switching pattern in optimizing the signal-to-noise ratio. All possible causes of false asymmetries are investigated. Control experiments are carried out with ${\mathrm{Ru}}^{103}$ sources. The contribution to the observed circular polarization due to bremsstrahlung has been calculated, as well as determined experimentally. Our results for the circular polarization are $P_{\gamma }=(-3.9\mathrm{}\pm 1.2)\times {10}^{-6\mathrm{}}$ for the 482-keV transition in ${\mathrm{Ta}}^{181}$, and $P_{\gamma }=(6.3\mathrm{}\pm 1.0)\times {10}^{-5\mathrm{}}$ for the 396-keV transition in ${\mathrm{Lu}}^{175}$. These findings confirm the existence of a parity-nonconserving term in the nuclear Hamiltonian.

It was recently shown that in the photodisintegration of ${\mathrm{B}}^{11}$ certain expected $\gamma$ rays were missing. A partial explanation is offered here for the failure to observe these transitions. It is also pointed out that no conclusions about the strength of the $T=\frac{3}{2}$ giant resonance can be drawn from this experiment.

The value of $\overline{\nu }$ for ${}_{}{}^{246}{}_{}{}^{}\mathrm{Cm}$ was found to be 3.20 ± 0.22 in a B${\mathrm{F}}_3$ proportional counter calibrated with a ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ standard.

Differential cross sections for 16-Me V protons scattering from ${\mathrm{Sm}}^{154}$ and ${\mathrm{Sm}}^{148}$ were reanalyzed using the coupled-channel computer program JUPITOR-1 written by Tamura. The results of this analysis yield a better fit to the data using a value of ${\beta }_2=0.250\mathrm{}$ for ${\mathrm{Sm}}^{154}$ than with the value of 0.351 obtained from Coulomb excitation studies. The same optical-model paramters which were used for ${\mathrm{Sm}}^{154}$ yield a good fit for ${\mathrm{Sm}}^{148}$ with vibrational deformation parameters ${\beta }_2=0.120\mathrm{}$ and ${\beta }_3=0.150\mathrm{}$.

The fluctuation cross section is derived as a function of the reduced-width correlation co-efficient and also as a function of the channel cross correlation, with the resulting indication that the fluctuation cross section depends strongly on the channel cross correlation. The total average cross section is shown to be proportional to the quantity $2I+1$ only when the total level width is sufficiently large. Finally, the author suggests that only for experiments in the region of very large ${\Gamma }_{\mu }$ should the total cross sections be compared with the $2I+1$ rule. In order to get the above condition, low energy with a high $Q$ value are highly desirable.

It is shown that the anomalous magnetic moment of the electron contributes to the radiative correction to scattering by a charge, even at high energies, when the scattering angle is 180°. This effect increases the radiative correction slightly as compared with the usual Schwinger correction.

The $2^{+}$ levels in ${\mathrm{Be}}^8$ at 16.6 and 16.9 MeV were investigated using the ${\mathrm{B}}^{10}(d,\alpha ){\mathrm{Be}}^8$ reaction at several angles and bombarding energies from 4.0 to 12.0 MeV. A pattern of interference between these two levels was observed at all angles and energies except at a deuteron energy of 4.0 MeV. Fits were made to the $\alpha$-particle spectra using two different formulas for the differential cross section. The results are interpreted in terms of the isobaric spin purity of the levels and isobaric spin mixing in the reaction. The latter is found to vary from 4 to 99%. The effects of other $2^{+}$ levels on the 16.6- and 16.9-MeV levels are also discussed. Differential-cross-section ratios of the $1^{+}$ doublet at 17.6 and 18.1 MeV were simultaneously measured. This ratio depends upon deuteron bombarding energy in a way consistent with the change in isobaric spin mixing in the reaction. The $3^{+}$ doublet at 19.05 and 19.22 MeV was investigated. Only one particle group is observed. Various explanations in terms of interference in this region are discussed. The excitation energy and width of the higher $1^{+}$ level were found to be 18.146 ± 0.005 MeV and 138 ± 6 keV, respectively, based on an adopted value of 17.638 MeV for the excitation energy of the lower $1^{+}$ level.