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.

Proton inelastic scattering from ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ has been measured at 40 MeV. Angular distributions have been obtained from 10 to 80° for states up to 8 MeV of excitation in ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, and to 4.5 MeV in ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$. The cross sections for exciting the low-lying states that have relatively simple wave functions were analyzed in terms of a microscopic model, using realistic nucleon-nucleon forces. Core polarization is shown to be important, and it is seen that a strength obtained from the bound-state matrix elements of Kuo and Brown is adequate to describe the observed scattering. A macroscopic collective-model analysis of the data is also presented.

The low-lying states of the calcium isotopes ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ through ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ca}$ are discussed within the framework of the conventional shell model. An inert ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ core is assumed. Calculations are made in several basis-vector spaces involving active $0f_{\frac{7}{2}}$, $1p_{\frac{3}{2}}$, $0f_{\frac{5}{2}}$, $1p_{\frac{1}{2}}$, and $0g_{\frac{9}{2}}$ neutron orbits. In one set of calculations, we use a "realistic" effective interaction derived for this mass region by Kuo and Brown. The shell-model results suggest that, in this effective interaction, the interactions of $f_{\frac{7}{2}}$ neutrons with $p_{\frac{3}{2}}$, $p_{\frac{1}{2}}$, and $f_{\frac{5}{2}}$ neutrons are too strong. In other calculations, with a modified Kuo-Brown interaction, we find the calculated spectra for the low-lying states of the calcium isotopes are in agreement with observed spectra, with several significant exceptions. The exceptions are that the second $0^{+}$ and $2^{+}$ states observed in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ are not accounted for in the calculation. Calculated spectroscopic factors for $f_{\frac{7}{2}}$ transfers are in good agreement with experimental spectroscopic factors, and the observed centroids of the $p_{\frac{3}{2}}$ single-particle strengths are reasonably well reproduced. Our results also indicate that "core-excitation" effects are significant above about 2.5 MeV in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ through ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$.

The ground-state threshold for the reaction ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}\mathrm{}(p,n)\mathrm{}{}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$ has been measured to be 7.492 ±0.006 MeV. The absolute value of the total reaction cross section has been determined from threshold to 10.5-MeV bombarding energy. From the threshold energy, the mass excess of ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$ is calculated to be -27 281 ± 6 keV, which agrees within the error limits with positron end-point results but not with an earlier measurement of this threshold.

Angular correlations of $\gamma$ rays have been measured in coincidence with protons leading to states in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ at 0.61, 1.49, 1.51, 1.59 MeV, and one member of a doublet at 1.88 MeV. The measurements imply spin 1 for the 0.61-MeV state and for one member of the 1.88-MeV doublet. The best fit to the correlation for the 1.49-MeV state is obtained for spin 3, but other spins cannot be excluded. The 1.51-MeV state decays 100% to the isomeric $7^{+}$ state at 0.62 MeV. The 1.59-MeV state is measured to have spin 2. The relative populations of the $M=\pm 1$ and $M=0\mathrm{}$ magnetic substates are extracted from the data and compared with a simple direct-reaction model.

We have measured the hfs separation and nuclear magnetic moment of 6.2-day ${}_{}{}^{196}{}_{}{}^{}\mathrm{Au}$. The results we obtain are: $\Delta \nu \left({}_{}{}^{196}{}_{}{}^{}\mathrm{Au}\right)=21\mathrm{}347.2522\left(15\right)\mathrm{}$ MHz and ${\mu }_I({}_{}{}^{196}{}_{}{}^{}\mathrm{Au};\mathrm{uncorr})=+0.5823\mathrm{}\left(14\right)\mathrm{}{\mu }_N$. These values give the hfs anomaly with respect to ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{196}{}_{}{}^{}\Delta _{}^{197}{}_{}{}^{}=-8.02\mathrm{}\left(24\right)\%$. These measurements reconfirm the existence of large hfs anomalies in the gold isotopes. They also show that the ground-state nuclear structure of ${}_{}{}^{196}{}_{}{}^{}\mathrm{Au}$ is similar to that of ${}_{}{}^{198}{}_{}{}^{}\mathrm{Au}$.

The atomic-beam magnetic-resonance method has been used to measure the nuclear spin $I$ and the hyperfine structure constants $a$ and $b$ in the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ atomic state of 38-h ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ge}$ and 82-min ${}_{}{}^{75}{}_{}{}^{}\mathrm{Ge}$, and in the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ atomic state of ${}_{}{}^{75}{}_{}{}^{}\mathrm{Ge}$ and 11-day ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$. From these measurements, the nuclear moments ${\mu }_I$ and $Q$ are deduced. The results are: for ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ge}$, $I=\frac{5}{2}$, $a\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=\mp 23.40\left(3\right)\mathrm{}$ MHz, $b\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=\pm 8.28\left(8\right)\mathrm{}$ MHz, ${\mu }_I\left(\mathrm{uncorr}\right)=\pm 0.733\left(7\right)\mathrm{}{\mu }_N$, and $Q\left(\mathrm{uncorr}\right)=\pm 0.028\left(6\right)\mathrm{}$ b; for ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$, $a\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)=+360.53\mathrm{}\left(4\right)\mathrm{}$ MHz; and for ${}_{}{}^{75}{}_{}{}^{}\mathrm{Ge}$, $I=\frac{1}{2}$, $a\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=-81.06\mathrm{}\left(8\right)\mathrm{}$ MHz, $a\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)=+335.94\mathrm{}\left(9\right)\mathrm{}$ MHz, and ${\mu }_I\left(\mathrm{uncorr}\right)=+0.508\mathrm{}\left(5\right)\mathrm{}{\mu }_N$.

The level structure of ${}_{45}{}^{}{}_{}{}^{}\mathrm{Rh}_{}^{105}{}_{}{}^{}$, below 2 MeV in excitation, was studied by ${\mathrm{Ru}}^{104}({\mathrm{He}}^3,d){\mathrm{Rh}}^{105}$ at $E_{{\mathrm{He}}^3}=18\mathrm{}$ MeV, and by ${\mathrm{Pd}}^{108}(p,\alpha ){\mathrm{Rh}}^{105}$ at $E_p=15\mathrm{}$ MeV. An Enge split-pole spectrograph was used for high-resolution analysis of the reaction products. Particle detection for deuterons was achieved with nuclear emulsions, while position-sensitive "triode" counters were used for the $\alpha$ particles. Targets were kept thin enough to permit total experimental resolutions of 12-13 keV. Comparison of 17 measured (${\mathrm{He}}^3,d$) angular distributions with nonlocal, finite-range distorted-wave Born-approximation (DWBA) calculations indicated a predominance of $l=2\mathrm{}$ transfers, and yielded $J^{\pi }$ limits for the more strongly excited states. Differential ${\mathrm{Pd}}^{108}(p,\alpha ){\mathrm{Rh}}^{105}$ cross sections were obtained over the angular range of from 8 to 100° and complement the (${\mathrm{He}}^3,d$) measurements, frequently exciting levels not seen in proton stripping. DWBA triton-cluster transfer calculations reproduce the empirically observed $l=1\mathrm{} j$ dependence. A weaker, but detectable, $j$ dependence is predicted for $l=3\mathrm{}$. The observed ${\mathrm{Rh}}^{105}$ energy-level scheme is compared with weak-coupling-model expectations and the results of earlier $\beta$-decay studies.

$\alpha$-cluster knockout from ${\mathrm{Be}}^9$, ${\mathrm{C}}^{12}$, and ${\mathrm{O}}^{16}$ by 160-MeV protons was investigated. The outgoing proton and $\alpha$ particle were detected in coincidence and their momenta measured with good resolution. Knockout, sequential decay, and spallation reactions were observed. Proton and $\alpha$ detection angles were varied so as to test the plane-wave impulse-approximation (PWIA) model of the knockout reaction over a wide range of the effective $p$-cluster interaction. The method, apparatus, and carbon results are discussed in this paper. Measured values of the fully differential cross section ($\frac{d\sigma }{d{\Omega }_{\alpha }d{\Omega }_{p}d{T}_p}$) are given, and are shown to vary nearly as predicted by the PWIA. The errors due to finite detector sizes (finite momentum resolution) are discussed in some detail. The recoil correction to the usual PWIA expression for the cross section is derived. The branching ratio to the first excited state of the residual ${\mathrm{Be}}^8$ nucleus, as well as the effective number of $\alpha$ clusters in ${\mathrm{C}}^{12}$, are discussed and compared with theoretical predictions.

Elastic and inelastic nuclear resonant scattering of monochromatic photons from ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$ has been studied using a 20-cc Ge(Li) detector. The $\gamma$ source was obtained from thermal-neutron capture in titanium. The scattering isotope was identified by using an isotopically enriched thallium target. The energy of the resonance level in ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$ was found to be 6.418 MeV. Assuming the high-energy lines to be primary transitions deexciting the resonance level, some 14 energy levels were found from the ground state up to 2.9 MeV, 4 of which may be identified with recently reported levels.

By measuring the angular distribution of the scattered radiation, the spin of the 6.418-MeV level was determined to be ½, and thus, based on the assumption of dipole transitions, the spins of several low-lying levels were found to be either ½ or $\frac{3}{2}$. The total radiative width of the resonance level was determined and found to be ${\Gamma }_{\gamma }=0.32\mathrm{}\pm 0.06$ eV and $\frac{{\Gamma }_0}{{\Gamma }_{\gamma }}=0.026\mathrm{}$. The spectral shape of scattered radiation was found to have a strong intensity bump at about 5 MeV; this is discussed in the light of similar bumps obtained in ($n,\gamma$) and ($d,p\gamma$) reactions on nuclei in the same mass region.

The energy distribution of the neutrons emitted in the fission of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ induced by 155-MeV protons was measured at 0 and 90° with respect to the fission fragment direction. The neutron velocity was measured by the time-of-flight method in coincidence with the measurement of the kinetic energy of the two fission fragments. The number of postfission neutrons as a function of the fragment mass and the energy distribution of the postfission neutrons were determined without reference to any theoretical model. The number of prefission neutrons was determined on the assumption of isotropic emission from the excited nucleus. With this assumption we find that 5.8±1.0 prefission neutrons are emitted from U and 6.9±1.0 from Bi. The number of postfission neutrons is 5.1±0.5 for U and 4.2±0.5 for Bi. We compare our experimental results with the results of calculations based on the usual model of a prompt intranuclear cascade followed by neutron evaporation-fission competition with several assumptions for $\frac{{\Gamma }_f}{{\Gamma }_n}$ (ratio of fission width to neutron emission width). We are unable to find a consistent set of parameters which would give good agreement between the calculated results, our experimental results, radiochemical results for spallation residues, and total fission cross-section measurements. Our experimental results indicate that $\frac{{\Gamma }_f}{{\Gamma }_n}$ decreases at high excitation energies. We find that the number of postfission neutrons increases rapidly with increasing fragment mass for both Bi and U. When our results for U are compared with low-energy fission data for this element, it is found that almost all the additional excitation energy available in high-energy fission is concentrated in the heavy fragment.

Simultaneous Mössbauer-effect spectra of the first excited states of ${\mathrm{W}}^{182}$, ${\mathrm{W}}^{184}$, and ${\mathrm{W}}^{186}$ were observed following Coulomb excitation by 6.0-MeV $\alpha$ particles. Tungsten nuclei were in tungsten metal targets at liquid-nitrogen temperature. An absorption spectrum of the first excited state of ${\mathrm{W}}^{183}$ was also observed. Taking the half-life of the first excited state of ${\mathrm{W}}^{182}$ to be 1.377±0.014 nsec, the half-lives of the first excited states of ${\mathrm{W}}^{184}$, ${\mathrm{W}}^{186}$, and ${\mathrm{W}}^{183}$ were determined to be 1.28±0.13, 1.38±0.12, and 0.174±0.006 nsec, respectively. Data were consistent with electric quadrupole interactions in the targets. The Debye temperature of tungsten metal at liquid-nitrogen temperature was determined to be 329±8°K.