Angular distributions of the neutron polarization for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},n){}_{}{}^{14}{}_{}{}^{}\mathrm{O}$ reaction have been measured at eight bombarding energies between 4.1 and 5.9 MeV. Large polarizations, both positive and negative valued, are observed over the whole energy range, with maximum values of +0.70 ± 0.06 at 5.7 MeV (90°) and -0.82 = 0.04 at 4.5 MeV (75°). As $E\left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)$ increases, the shapes of the polarization angular distributions shift continuously and smoothly toward forward angles. A similar energy dependence is noted by Marr et al. for the proton-polarization measurements for the analog reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},p_1){}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{*}{}_{}{}^{}$ (2.31-MeV state). The data for these two reactions bear much resemblance despite the difference of the $Q$ values and possible Coulomb distortions in the proton exit channel. Although energy dependence in polarization angular distributions is not considered a usual characteristic of a direct-reaction mechanism, the smooth and continuous nature of the variation does suggest that this mechanism may be of some importance here. Exploratory two-nucleon-transfer distorted-wave calculations show that this theory can predict an energy dependence of the polarization using reasonable optical-model parameters for this energy and mass range. However, the trend of the calculations is contrary to the data, and little agreement with the data is found.

Some of the low-lying excited states of ${\mathrm{F}}^{20}$ were studied using the ${\mathrm{O}}^{18}(t,n\gamma ){\mathrm{F}}^{20}$ reaction at a bombarding energy of $E_t=2.7\mathrm{}$ MeV. The methods of $n-\gamma$ and $\gamma -\gamma$ angular correlations were used to obtain information concerning the spins of the 823- and 656-keV states and the multipole mixing ratios of the subsequent electromagnetic deexcitations of these states. The mean lifetime of the 823-keV state was measured with the recoil-distance technique to be 79 ± 6 psec. The results of the experiment are discussed in terms of current nuclear models.

Owing to its importance in stellar helium burning, we have carefully remeasured the excitation energy of the second excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ with a tandem accelerator and a broad-range magnetic spectrograph. The excitation energy of this state is found to be 7655.9 ± 2.5 keV, in excellent agreement with two other recent measurements. This value lowers the calculated rate of the helium-burning process in stars by a factor of ≅3 from that previously assumed. A simultaneous measurement of the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ gives 4442.2 ± 1.5 keV. A comparison is made with recent $\gamma$-ray measurements of this state.

Expressions are developed for the virtual photon spectrum and for the bremsstrahlung cross section, using the distorted-wave method for relativistic electrons in a Coulomb field. Evaluation of the matrix elements is made in terms of generalized hypergeometric functions, and some numerical results are given for electrons of energy 10 and 100 MeV. Significant enhancement of the virtual radiation spectrum is found to result from the use of distorted waves as opposed to plane waves. Calculations of the contributions of $E1\mathrm{}$, $M1\mathrm{}$, $E2\mathrm{}$, and $E3\mathrm{}$ radiation to the bremsstrahlung cross section, $\frac{d^2\sigma }{d\omega d\Omega }$, are also made; enhancement, similar to that observed with the virtual spectrum, is found in this case also.

The classical $\alpha$-particle model has been consistently applied to all $4N$ nuclei in the $2s-1d$ shell. The ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ nucleus was found to be a $D_{2d}$ distorted tetrahedron in agreement with earlier investigations. Electron scattering form factors were predicted, but there are at present no experimental data for comparison. Most interesting results were obtained for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, where the experimental matrix elements, energy spectrum, and electron scattering form factors were found to definitely favor a $D_{2h}$ bitetrahedron over the $D_{4h}$ square bipyramid used in other papers. Recent experiments on ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ also slightly favor an oblate $D_{3d}$ structure over the previously considered $D_{5h}$ pentagonal bipyramid. No definite structures could be established for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, because of the large number of $\alpha$ particles involved. However, a unique structure was found for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. It consists of six $\alpha$ clusters arranged in an octahedron outside of a tetrahedral ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core.

The total cross section of protons for neutrons of mean energy 2535 keV was measured to be 2536 ± 4 mb. This measurement is the average of determinations with five different hydrocarbon samples. Special care was taken to measure neutron energy accurately throughout the experiment and to keep corrections for background and inscattering very small. The singlet effective range deduced from this measurement is 2.78 ± 0.07 fm and is consistent with values deduced from proton-proton scattering under the assumption of charge independence of nuclear forces.

The cross section for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(p,2p)\mathrm{}$ reaction at an incident kinetic energy of 460 MeV is calculated in the framework of a model which takes account of nucleon-nucleon correlations and of the coupling to continuum channels of the residual nucleus.

The two intrinsic Hartree-Fock (HF) states, one characterized by isospin $T=T_z=\frac{1}{2}\mathrm{}(N-Z)\mathrm{}$ and the other containing an admixture of $T=T_z$ and $T=T_z+1\mathrm{}$, lie energetically very close in the case of light $\mathrm{odd}-Z-\mathrm{odd}-N$ nuclei. As a result, the low-lying $T=T_z$ states of these nuclei have substantial "band mixing." The HF projection formalism is employed to investigate the effect of band mixing on the properties of nuclear states in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ by explicitly treating all the nucleons. The results of our calculations are in fair agreement with the experimental data.

A variational method of calculating correlated intrinsic wave functions for deformed nuclei is formulated. The configuration amplitudes and the single-particle orbitals which define such wave functions obey a system of equations, which is solved self-consistently by an iterative procedure for the doubly even $N=Z$ nuclei in the $\mathrm{sd}$ shell. The correlations under study are of the 2p-2h type. Compared with the independent-particle Hartree-Fock picture, the present solutions show a greater stability in terms of binding energy and shape symmetry.

Excitation functions for the reactions ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured in the energy range 3.75 to 10.75 MeV and 5.5 to 10.5 MeV, respectively. These data have been compared with those for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p,p^{\prime }){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p,\alpha ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ reactions which also proceed through the same ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ intermediate system. The results of this comparison support the hypothesis of $\alpha$-like cluster resonances in the outgoing reaction channel.

Excitation functions and angular distributions for ($p,\alpha$) reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured from 19- to 45-MeV incident energy. The mean slope of the integrated cross sections for all the above reactions and for ($p,\alpha$) reactions on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ is the same, when plotted as a function of the intermediate-system excitation energy, and is of the type ${[{\left(E_p\right)}_{\mathrm{c}.\mathrm{m}.\mathrm{}}+B_p]}^{-3.75\mathrm{}}$. For the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ targets, the differential and integrated cross sections, which have been measured in energy steps of the order of some hundred keV, show a marked resonant structure with modulations having widths and spacings of the order of 1 MeV. Angular distributions, although presenting a well-developed diffraction pattern especially at forward angles, vary very rapidly with energy, particularly below 30 MeV. The analysis of excitation functions performed with a distorted-wave Born-approximation point triton pickup calculation gives ambiguous results. A statistical Hauser-Feshbach calculation gives too steep a slope which agrees with experimental data only when direct transitions are hindered. The analysis of the excitation functions, performed in the framework of the pre-equilibrium decay model, gives satisfactory results. This could indicate that $\alpha$ emission from light nuclei cannot be treated as a simple direct effect.

The spin-flip probability for scattering protons inelastically to produce the first excited $2^{+}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ has been measured at proton energies of 15.9 and 17.5 MeV using the deexcitation $\gamma$ rays emitted perpendicular to the scattering plane. The carbon results agree with previous measurements in the same proton energy region. The measured inelastic spin-flip probability on sulfur is higher than that reported for any other nucleus, exceeding a peak value of 0.5. A collective distorted-wave Born-approximation analysis employing the full Thomas spin-orbit interaction was carried out. Poor fits are obtained for the spin-flip-probability data when the depth and range of the spin-orbit optical potential are determined from elastic polarization data.

The problem of collective nuclear rotations is discussed in terms of a kinematic transformation to an intrinsic body-fixed coordinate system. Some results are obtained that are equivalent to the classical case. By use of approximate projection operators, an algorithm for calculating successively higher terms in the expansion of the rotational parameter ($\frac{1}{2}$ the inverse inertial moment) is developed. The first-order term is just the Skyrme formula, with the proviso that it be evaluated with respect to the "nonrotational" part of the Hamiltonian.

We have measured total reaction cross sections for 30-, 40-, 49.5-, and 60.8-MeV protons incident on thin, separated isotopes covering the range from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Our results are consistent with previous data at 30 MeV, but disagree with earlier data at 60 MeV. We find a strong dependence of the reaction cross section on neutron excess for a series of Fe and Ni isotopes. Little, if any, such dependence is observed for the $N=28\mathrm{}$ isotones. The data are well represented by the relation ${\sigma }_{\mathrm{R}}=\pi {(r_0{A}^{\frac{1}{3}}+\overline{\lambda })}^2$ with $r_0=1.23\mathrm{}\pm 0.01$ F. When analyzed with the conventional optical model, our data require the volume absorption to increase and the surface absorption to decrease with increasing proton energy $E_p$. The analysis reveals a striking $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ dependence for the product $W_D{a}^{\prime }$. Using the Oak Ridge parameters for the real and spin-orbit potentials, we arrive at the following parametrization for the imaginary potential: volume absorption potential, $W_0=(1.2\mathrm{}\pm 0.09E_p)$ MeV; surface absorption potential, $W_D=[4.2-0.05\mathrm{}{E}_p+15.5\mathrm{}\frac{\mathrm{}(N-Z)\mathrm{}}{A}]$ MeV; imaginary diffusivity, $a^{\prime }=[0.74-0.008\mathrm{}{E}_p+1.0\mathrm{}\times \frac{\mathrm{}(N-Z)\mathrm{}}{A}]$ F.

The differential elastic cross sections for protons on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been obtained at energies between 9.8 and 21.7 MeV. A mass-identification system using an $E+\Delta E$ detector was employed for the measurements. Relative uncertainties are approximately ±2%. Absolute uncertainties are approximately ±5%.

An optical-model analysis of these data and the available polarization data in the same energy region have been performed. Reasonable fits were obtained by analyzing the data above and below 16.6 MeV separately. Significant differences in the imaginary and spin-orbit potentials were observed in these two regions.

The states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ below 7.5 MeV have been studied using the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ reactions at a bombarding energy of 18 MeV. Angular distributions of the reaction products have been compared with distorted-wave Born-approximation predictions. The resulting spectroscopic factors are compared with those calculated using the rotational model and with experimental spectroscopic factors from the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\mathrm{}(p,d)\mathrm{}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\mathrm{}(d,t)\mathrm{}$ reactions. The results suggest a $K^{\pi }=1^{-}$ $T=0\mathrm{}$ rotational band (2.21 MeV, $1^{-}$; 2.57 MeV, $2^{-}$; and 3.52 MeV, $3^{-}$) and a $K^{\pi }=2^{-}$, $T=0\mathrm{}$ band [4.58 MeV, $2^{-}$ ($0^{-}$, $1^{-}$, $3^{-}$) and 5.44 MeV, $3^{-}$ ($0^{-}$, $1^{-}$, $2^{-}$)] based on neutron pickup from the ${\frac{1}{2}}^{-}\mathrm{}\left[101\right]\mathrm{}$ Nilsson orbit. A comparison of the $l=1\mathrm{}$ ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ transition to the 5.95-MeV level in ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ with the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ results suggests that this state is the analog of the 5.14-MeV, $2^{-}$ state in ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ and that these levels correspond to the $K^{\pi }=2^{-}$, $T=1\mathrm{}$ band head based on nucleon pickup from the ${\frac{1}{2}}^{-}\mathrm{}\left[101\right]\mathrm{}$ Nilsson orbit. The results of the present study and a previous ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ study are discussed in terms of Nilsson configurations and associated rotational bands. It is found that the rotational model provides a reasonably adequate explanation for the observed spectroscopic factors of the negative-parity states up to 7.5 MeV and for the positive-parity states based on the ${\left({\frac{3}{2}}^{+}\mathrm{}\right[211\left]\right)}^2$ configuration if a deformation of $\delta \approx 0.5$ is assumed. The simple rotational model, however, is unable to account for the observed single-nucleon-transfer spectroscopic factors for the other positive-parity configurations.

The angular correlation between inelastically scattered $\alpha$ particles and the subsequent deexcitation $\gamma$ ray has been measured at an $\alpha$ energy of 42 MeV. Measurements have been carried out in the reaction plane for $\gamma$ rays resulting from the decay of the first excited ($2^{+}$) state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$. The results are reported in terms of the $\gamma$-ray symmetry angle, ${\theta }_0$, and the ratio $\frac{A}{B}$. Qualitatively the behavior of the symmetry angle is found to be the same for all four isotopes, rotating continuously at forward $\alpha$-scattering angles and oscillating about the plane-wave and adiabatic predictions at larger $\alpha$-scattering angles. For the three isotopes for which $\frac{A}{B}$ measurements were possible, the ratio was clearly not identically zero. Both the angular-correlation and cross-section data are compared with the results of distorted-wave-Born-approximation calculations using a wide range of optical-model parameters. The optical-model ambiguities encountered here are similar to those found in fitting cross-section data alone.

Cross sections of ($n,2n$), ($n,p$), and ($n,\alpha$) reactions of medium-$Z$ nuclei at 14.4 MeV, calculated from the statistical model with the constant-nuclear-temperature approximation for level densities, are compared with experiment. Using effective thresholds for second- and third-emitted neutrons, obtained by adding 0.5 and 1 MeV to the ground-state thresholds, respectively, the agreement with experiment is about ±15, ±20, and ±30% for ($n,2n$), ($n,p$), and ($n,\alpha$) reactions, respectively. For ($n,\alpha$) reactions, it is necessary to add 1 MeV to the pairing energy for the shell closures at $N=50\mathrm{} \mathrm{and} 82$ to get satisfactory agreement. An average nuclear temperature of 1.5 MeV is used for all types of reactions and for all nuclei investigated. The exponential dependence on $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ for $n,p$ cross sections in Levkovskii's empirical formula is derived from the statistical model and a semiempirical mass equation. Empirical equations are obtained which depend only on $A$ and $Z$ for quick estimation of 14.4-MeV ($n,2n$) cross sections from $Z=28\mathrm{} \mathrm{to} 82$ and of [$\mathrm{}(n,np)+(n,pn)+(n,d)\mathrm{}$] cross sections of the lightest stable isotope of even-$Z$ elements in the region of $Z=28\mathrm{} \mathrm{to} 50$.

A value of 3.7 × ${10}^6$ yr (± 10%) for the half-life of ${\mathrm{Mn}}^{53}$ was determined by a direct method involving measurement of both the specific activity [(dis/min ${\mathrm{Mn}}^{53}$)/(μg Mn)] and the isotope ratio (${\mathrm{Mn}}^{53}$/${\mathrm{Mn}}^{55}$). The ${\mathrm{Mn}}^{53}$ specific activities were determined by neutron activation, and the ${\mathrm{Mn}}^{55}$/${\mathrm{Mn}}^{53}$ isotopic ratios by mass spectrometry. A surface-ionization method was applied using a rhenium single filament with the sample mounted in a silica-gel layer. This technique gave a stable and enhanced ion beam of ${\mathrm{Mn}}^{+}$. One source of ${\mathrm{Mn}}^{53}$ was an electroplated Cr target bombarded by 15-MeV $\alpha$ particles in a cyclotron. The other source of ${\mathrm{Mn}}^{53}$ was the Mn fractions extracted from iron meteorites by carrier-free processes. Activities of 10 dis/min ${\mathrm{Mn}}^{53}$ and 2000 dis/min ${\mathrm{Mn}}^{54}$ were obtained with about 2 μg of ${\mathrm{Mn}}^{55}$ from the Cr target. The isotopic ratio ${\mathrm{Mn}}^{55}$/${\mathrm{Mn}}^{53}$ was 750. Activities of about 1 (dis/min ${\mathrm{Mn}}^{53}$)/(μg Mn) and isotopic ratios ${\mathrm{Mn}}^{55}$/${\mathrm{Mn}}^{53}$ of 3000-4000 were obtained from the iron-meteorite extracts.

The differential cross sections for elastic and inelastic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ scattering from ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$ targets have been measured at 24 MeV. The first $2^{+}$ and the $3^{-}$ inelastic levels are strongly excited in comparison with the excitation of the second $2^{+}$ and $0^{+}$ levels. Assuming a priori a one-phonon-transfer process, the ground state and strongly excited $2^{+}$ and $3^{-}$ angular distributions have been calculated using a coupled-channel code. The optical-model parameters used were obtained from analysis of the elastic scattering. Different optical potentials were used in the calculations. The quality of the fits to the inelastic levels, as well as the dependence of the magnitude of the deformation parameters on the geometrical parameter of a given optical potential, are discussed. The deformation lengths deduced from these measurements are in good agreement with those derived from similar analysis using other projectiles.