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.

Magnetic hyperfine structure in muonic x rays is calculated for several models of the nuclear magnetism and compared to experimental values for ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$, ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. The results are excellent for the realistic models in most cases, and all but one of the nine cases agree within better than two standard deviations with the experiments. For the realistic models, the hyperfine energy is substantially reduced (by about 30% in most cases) from its point-nucleus value. In these models, the single-particle magnetism distribution is modified by the addition of configurations resulting from various residual nuclear interactions, the interaction strength being adjusted in each case to produce the experimental value for the magnetic moment.

It is observed that the proton separation energies $S_p$ for even-even nuclei do not vary linearly with proton number in a strict sense. $S_p$ values for even-even isotones with the same $j$, the angular momemtum of the last proton orbit, lie on a straight line. The systematics of nucleon separation energies are explained on the basis of the shell model for nuclei. It is assumed that the central potential well in which nucleons are supposed to move remains constant for a group of neighboring isotones with the last proton orbit characterized by the same $j$. This is also taken to be valid for isotopes with the last neutron orbit characterized by the same $j$. Furthermore, the interaction between the extracore neutrons, extracore protons, and their mutual interactions are simulated by average effective two-body interaction matrix elements.

The differential cross sections for the reaction ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\mathrm{}(p,t)\mathrm{}$ leading to states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ were measured at a proton energy of 50 MeV. The angular distributions were analyzed in the distorted-wave Born approximation (DWBA) and the transferred angular momentum was extracted. This led to the following energy-level sequence in ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$: ground state, $0^{+}$; 1.83 MeV, $2^{+}$; 3.36 MeV, $4^{+}$; 3.58 MeV, $0^{+}$ and $2^{+}$; 4.46 MeV, $1^{-}$; 5.12 MeV, and 6.34 MeV. A comparison was made with the predictions of DWBA calculations for the relative cross section, using various wave functions for both initial and final nuclei. It is concluded that only the wave functions which include the $1p_{\frac{1}{2}}$ and $1d_{\frac{3}{2}}$ configurations give satisfactory agreement with the data. The calculation of the form factor is also discussed, and its effect on the cross section is found to be large. On the whole, better agreement is achieved when using the same binding energy instead of the same well depth for all configurations.

We measure the differential cross sections for scattering of neutrons from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at or near four narrow resonances. The energy spread of the incident neutrons ranges from 5 to 13 keV full width at half maximum. We detect scattered neutrons as a function of angle with a stilbene crystal. Using phase shifts from previous work, we analyze the differential data and make resonant parameter assignments as follows (in order: excitation energy of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ in keV, $J$ value, parity, and c.m. resonant width in keV: $5867 (\frac{3}{2}+,6.6)$, $7164 (\frac{5}{2}-,1.4)$, $7377 (\frac{5}{2}+,0.5)$, and $7380 (\frac{5}{2}-,1.1)$. In table form, we review level assignments of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ up to 7380-keV excitation energy and give estimates of reduced widths in single-particle units.

We compute the effect of short-range correlations on the displacement energy (energy difference between the analog and the parent state) to first order in perturbation theory, using the plane-wave approximation for intermediate states. Both the contributions of the Coulomb interaction and of a charge-dependent component of the nuclear two-body interaction are taken into account.

The low-energy theorem is derived for nucleon-nucleon bremsstrahlung. We assume that the two nucleons interact through a potential which can be any model, nonlocal as well as local. For those potentials which depend explicitly upon momentum and/or angular momentum operators, the gauge terms arising from these operators are included in the derivation. These gauge terms are always important in the study of the off-energy-shell effects of the two-nucleon interaction, and for the $\mathrm{np}\gamma$ process they are essential in the derivation of the low-energy theorem. It is found that the gauge terms are canceled precisely by parts of the terms which represent the photons emitted by the internal nucleon lines.

The 90° excitation functions of the $\gamma$-ray transitions in the $\mathrm{Ge}(n,n^{\prime }\gamma )$ reactions have been measured at incident neutron energies from 0.5 to 2.55 MeV. Angular distributions at $E_n=1.75, 2.13, \mathrm{and} 2.55$ MeV have also been measured. The $\gamma$-ray production cross sections and the neutron inelastic scattering cross sections have been obtained at these neutron energies. Theoretical model calculations have been performed and are in good agreement with the experimental results. The Wolfenstein-Hauser-Feshbach formalism was used for the calculations. The low-lying decay schemes of the four even-$A$ Ge isotopes determined in this work are in good agreement with previous investigations. Branching ratios, as well as mixing ratios, of the $\gamma$-ray decay from the second $2^{+}$ state for all the four even-$A$ Ge isotopes have been obtained. The 1698-keV level of ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ has been confirmed and its decays to the first and second $2^{+}$ states have been established. The branching ratio and mixing ratios have been determined. A spin of 3 is tentatively assigned to that level for the first time in this work. In addition, a test of the fluctuation corrections to the statistical model at the mass region near $A=70\mathrm{}$ has been made. The corrections attempted worsen the agreement between theory and experiment.

The ${}_{}{}^{64,66,68}{}_{}{}^{}\mathrm{Zn} \mathrm{}(d,n)\mathrm{} {}_{}{}^{65,67,69}{}_{}{}^{}\mathrm{Ga}$ reactions have been studied by the neutron time-of-flight method. Absolute differential cross sections have been measured and have been analyzed in terms of the distorted-wave Born approximation. Spin and parity assignments for several levels are proposed on the basis of $l$ values and transition strengths. The experimental results for ${}_{}{}^{67,69}{}_{}{}^{}\mathrm{Ga}$ are compared with existing theoretical calculations. Only limited agreement is found.

Energy levels in ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$ were located by means of the ($p,n$) reaction. Neutron spectra were measured with approximately 10-keV energy resolution by the time-of-flight method with flight paths of 7.9 and 9.2 m. Several sets of close-lying levels were resolved, and many new levels were found in ${}_{}{}^{53}{}_{}{}^{}\mathrm{Mn}$ up to an excitation energy of 4 MeV. In ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$, a total of 36 levels were observed in the first 2.5 MeV of excitation, and in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Zn}$, a total of 11 levels up to 1.5-MeV excitation energy. In ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$, 66 levels were observed in the first 2.7 MeV of excitation energy; 16 new levels were found in the region between 2.26 and 2.73 MeV.