The result of a differential scattering experiment of ${\mathrm{H}}^{+}$ by Ne at 5.71-eV collision energy is compared to the differential cross section predicted by (a) a JWKB partial-wave calculation based on a potential model, (b) a similar calculation based on the ab initio Peyerimhoff calculated intermolecular potential for the Ne${\mathrm{H}}^{+}$ system, and (c) a new and more efficient calculational scheme developed by Remler involving Regge poles. The agreement of the Peyerimhoff prediction, (b), with the experimental data is very good. Differences between the Peyerimhoff potential and the final values of the parameters retrieved from the iterative calculation in (a), as well as implicit ambiguities of (a) in reproducing the features of a low-resolution experiment, are discussed in terms of semiclassical theory and the Remler-Regge method.

Electron collision-excitation rate coefficients have been determined experimentally for excited singlet and triplet ($(n=2,3, \mathrm{and} 4$) levels of the berylliumlike ions N IV, O V, Ne VII, and Si IX using various plasma cases produced in a $\theta$-pinch device. Line intensities of these ions were measured absolutely and converted into rate coefficients by knowledge of the pertinent plasma parameters. Electron density and temperature were obtained as function of radius and time from the spectrum of scattered laser light. The intercombination transition $2s2p{}_{}{}^3{}_{}{}^{}P\to 2s^2{}_{}{}^1{}_{}{}^{}S$ was observed, and its absolute intensity allowed determining the metastable triplet level population. The probable error of any individual rate coefficient is estimated to be a factor of 2.

Widths and shifts of several neon red lines were measured as functions of electron densities [(0.4-2.1) × ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$] and neutral neon densities [(0.3-2.2) × ${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$]. Conditions in a gas-driven shock tube were determined from pressure-temperature data and from the shapes of hydrogen Balmer lines. In each experiment, profiles of neon lines emitted by the plasma were compared directly with the line shapes obtained with a low-pressure neon lamp. Stark broadening and shift parameters were determined with accuracies of 20-30 and 20-25%, respectively. Measured broadening due to neon atoms should be reliable to 35-50%. Theoretical and experimental comparison data are presented.

A generalized impact-parameter method (not based upon perturbation theory) which is capable of describing the evolution of a collision system throughout the entire interaction region is developed. The method is then applied to the collision of a proton and a hydrogen atom at low (chemical) energies. The results obtained suggest that static calculations such as those using molecular potential-energy surfaces do not represent a very real picture of a dynamic process like a collision. Furthermore, the model does not assume linear trajectories for the atoms. This is shown from the calculations to be of importance in such low-energy collisions, the trajectories being far from linear. The model is capable of generalization to collisions in which more than two atoms are involved, such as the three-body reaction $A+BC\to AB+C$.

The cross sections for the decay of circular and of linear polarization in oriented $4{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ potassium atoms, induced in collision with inert-gas atoms, were determined in a series of fluorescence experiments. A modified Zeeman scanning method was used to populate selectively the $m_J$ sublevels of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ potassium atoms mixed with inert gases and placed in a strong magnetic field. Measurements of depolarization of the fluorescence, in relation to gas pressures, yielded the following depolarization cross sections: ${\sigma }_1$ (disorientation): K-He, 86 ${\mathrm{\AA }}^2$; K-Ne, 86 ${\mathrm{\AA }}^2$; K-Ar, 164 ${\mathrm{\AA }}^2$; K-Kr, 248 ${\mathrm{\AA }}^2$; K-Xe, 251 Å. ${\sigma }_2$ (disalignment): K-He, 127 Å; K-Ne, 120 ${\mathrm{\AA }}^2$; K-Ar, 240 ${\mathrm{\AA }}^2$, K-Kr, 301 ${\mathrm{\AA }}^2$, K-Xe, 336 ${\mathrm{\AA }}^2$. The experimental values are in satisfactory agreement with the calculations of Nikitin and Ovchinnikova.

This work reports the first attempt at multiphoton ionization of molecules of iodine, heavy water, and carbon tetrachloride. Despite the occurrence of many different ions, only ${\mathrm{I}}^{+}$, ${\mathrm{D}}^{+}$, and C$\mathrm{Cl}_3^{}{}_{}{}^{+}$, respectively, were observed quantitatively using the technique of multiphoton ionization of atoms. "Saturation" was observed.

Delayed-coincidence techniques have provided measurements of $\overline{Q}\left(r_0\right)$ for ${\mathrm{O}}^{+}$ -Xe collisions in the energy range 50-210 keV; here $r_0$ represents the distance of closest approach of the colliding particles, and $\overline{Q}$ is the average energy transferred to inelastic processes. At fixed $r_0$ the $\overline{Q}$ values increase with bombarding energy. The $\overline{Q}$ values generally increase as $r_0$ decreases although they remain constant over some regions of $r_0$ within the range (0.05-0.25 Å) covered by the experiment. The $r_0$ regions in which $\overline{Q}$ increases appear to be correlated with regions in which the differential cross sections for beam-particle scattering fail to vary according to the predictions of the exponentially screened Coulomb potential. Simple interpretations of the data attribute these results to the effects of electronic shell interpenetrations during the collisions. Supplementing the $\overline{Q}$ and cross-section data are determinations of average ionic charge states after collision and calculations of inelastic energy-loss cross sections deduced from the $\overline{Q}$ results.

The atomic-beam magnetic-resonance technique has been used to measure the magnetic-dipole hyperfine-interaction constants $A$ for the 8613-${\mathrm{cm}}^{-1\mathrm{}}$ ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ metastable atomic state of ${\mathrm{Sn}}^{117,119}$. The results are $A({\mathrm{Sn}}^{117},{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{})=-1269.\mathrm{}650\left(3\right)\mathrm{}$ MHz and $A({\mathrm{Sn}}^{119},{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{})=-1328.\mathrm{}745\left(4\right)\mathrm{}$ MHz. These results, together with the previous measurements of $A$ for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states, are considered (a) nonrelativistically, (b) relativistically, with Casimir correction factors, and (c) with relativistic Hartree-Fock radial wave functions. Procedure (c) is shown to be relatively successful in accounting for the hfs observations, and leads to a predicted mixing coefficient for the states ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ which is within 13% of the mutually consistent values found (i) by consideration of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ energy separation and (ii) from the precisely measured $g_J$ values for the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ states.

Energy considerations in the central-field approximation to the one-electron problem are used to derive a theoretical expression, namely, $Z_1\mathrm{}\left(l\right)\mathrm{}>~\left(\frac{1}{6}\right) {\mathrm{}(2l+1)\mathrm{}}^3$, for the atomic number $Z_1\mathrm{}\left(l\right)\mathrm{}$ at which a given atomic $l$ subshell first begins to become occupied. The lowest integral values of $Z_1\mathrm{}\left(l\right)\mathrm{}$ satisfying this relation for $l=0, 1, 2$, and 3 are found to be in exact agreement with the corresponding empirical values, i.e., $Z_1=1, 5, 21$, and 58, respectively. In the domain of the superheavy elements ($100\lesssim Z\lesssim 200$) and beyond, this relation gives $Z_1\mathrm{}\left(l\right)=122\mathrm{}$, 222, and 367 for $l=4, 5$, and 6, respectively. The first member of this latter triad is in close accord with a recent estimate of $Z_1\mathrm{}\left(4\right)=125\mathrm{}$, cited by Seaborg. Comparison is made with the work of others in this field. To the writer's knowledge, this is the first calculation, without arbitrary introduction or adjustment of parameters, to yield results in complete accord with experiment.

The vibrational and rotational excitations seen in photoelectron spectroscopy are shown to have intensities proportional to $k^2{\left(\frac{m}{M}\right)}^2[\alpha +(\beta -\alpha \left){sin}^2\Theta \right]$, where $\overrightarrow{\mathrm{k}}$ is the wave vector of the incident radiation, $m$ is the mass of the excited nucleus, $M$ is the total mass of the molecule, and $\Theta$ is the angle between the wave vector of the ejected electron and the polarization direction of the radiation. The $\alpha$ and $\beta$ are absolute squares of the nuclear transition matrix elements. This angular dependence is similar in form to the dependence of the photoelectric cross section which is $\alpha +(\beta -\alpha ){cos}^2\Theta$, where $\alpha$ and $\beta$ are the absolute squares of the transition matrix elements for the photoejection of an electron.

A new and more accurate numerical solution has been obtained to the differential equation which determines the first-order quantum-mechanical corrections to the Thomas-Fermi model of the atom. When used to calculate the diamagnetic susceptibility and atomic polarizability of the inert gases, it leads to a substantial improvement over the Thomas-Fermi model alone, and hence lends support to the validity of the quantum-mechanical corrections.

The problem of obtaining field isotope shifts for light elements is discussed, and it is shown to be possible, in principle, to extract this information solely from an optical-isotope-shift experiment. We attempted such an experiment with the even-even calcium isotopes: Ca 40, 42, 44, and 48. We found that an accuracy of ∼${10}^{-5\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ in the measurements would be required to effect the separation. Lacking that accuracy, we considered the conditions under which optical-isotope-shift measurements may be combined with those of other isotope-shift experiments. The even-even calcium isotopes fulfill these conditions, allowing the desired separation of optical mass- and field-effect isotope shifts to be accomplished by drawing on the results of muonic x-ray and electron-scattering experiments. The optical field-effect shifts thereby found are shown to corroborate the picture of the calcium nuclei derived from those experiments. A correlation between the relative isotope shift and the binding energy per nucleon, proposed by Gerstenkorn, is shown to apply to the calcium isotope shifts.

The atomic-beam magnetic-resonance method has been used to measure $g_J=1.\mathrm{}16052\pm 0.00014$ for the atomic ground state of fermium I. An intermediate-coupling calculation with parameters extrapolated from lower actinides, and with corrections for diamagnetic and relativistic effects, yielded the value $g_J=1.\mathrm{}1606$. The agreement between the measured and calculated values of $g_J$ establishes the fermium ground state as the ${}_{}{}^3{}_{}{}^{}H_6^{}{}_{}{}^{}$ level of the $5f^{12}7s^2$ configuration. The neutral fermium atoms were obtained by heating Fm${\mathrm{F}}_3$ and its Ho${\mathrm{F}}_3$ carrier in the presence of ZrC and tungsten.

The neon $K$ emission spectrum, excited by direct electron bombardment of the neon gas, has been obtained with photon counting on a single-crystal potassium-acid-phthalate (KAP) planar spectrometer. The measured relative integrated intensity of the ${\alpha }^{\prime }{\alpha }_3{\alpha }_4$ and ${\alpha }_5{\alpha }_6$ satellite groups was found to be larger than theoretical prediction, but in accord with the trend of previous comparisons for $K$ satellites of neonlike ions in solids. A comparison of the present results for electron excitation and the preliminary results by O. Keski-Rahkonen and T. Åberg for photon excitation indicates that the relative integrated intensity of the neon $K$ satellites is independent of excitation mode at the excess excitation energies employed. A weak increase of intensity on the low-energy side of $K{\alpha }_{1,2}$ in the (803-809)-eV region was recorded and can be attributed to a radiative Auger transition.

Many-body perturbation theory is used to calculate a value of (- 76.48±0.07) a. u. for the total energy of the ${\mathrm{H}}_2$O molecule. This value is obtained with a basis set of bound and continuum orbitals of angular momentum $s$, $p$, $d$, $f$, and $g$, computed in a potential appropriate to neutral oxygen. Diagrams involving the net interaction with passive unexcited states, minus the single-particle potential, and the hydrogen nuclei are evaluated through third order, and estimates of higher-order diagrams are made. Both pair and three-body correlation-energy diagrams are included in this calculation.

Parameter analyses of $f^{n}d$ configurations of rare-earth ions generally result in mean errors in excess of 200 ${\mathrm{cm}}^{-1\mathrm{}}$ when conventional Slater operators only are used. We introduce tensor operators whose mathematical structure is similar to those of the Slater angular functions $f_k$ and $g_k$, except that intermediate values of $k$ are allowed. We may therefore assume that, for the $\mathrm{fd}$ and $f^{13}d$ configurations, if we parametrize four new operators $f_1$, $f_3$, $g_2$, and $g_4$, we will get a complete description of the ten $\mathrm{LS}$ terms. The orthogonality properties of the $6-j$ symbols insure that the new operators are independent of the previous ones. We find a reduction of the mean error to less than 10 ${\mathrm{cm}}^{-1\mathrm{}}$ for Pr IV and Ce III, and to about 30-60 ${\mathrm{cm}}^{-1\mathrm{}}$ for La II, Yb III, and Th III. The effects of spin-spin and spin-other-orbit interactions are negligible.

Singly auto-ionizing (SAI) states of three-electron atoms below the first core excitation threshold are defined as eigenfunctions of an operator $\mathrm{QHQ}$. It is shown that a particular type of multiconfiguration calculation provides upper-energy-bound estimates of such states, subject to a certain definition of $Q$ (and the assumption that a certain set of equations has a solution). For SAI states with $L\ne 0$, $Q$ is the proper Feshbach operator which projects out all wave-function components which overlap the exact ground state of the two-electron core. For SAI states with $L=0\mathrm{}$, the bound is only established by adopting a modified, approximate $Q$ which projects out only those wave-function components which overlap the angle-independent part of the core ground state. It is proposed that doubly auto-ionizing (DAI) states be defined as eigenfunctions of $Q^{\prime }H{Q}^{\prime }$, where $Q^{\prime }$ is the projection operator which eliminates all wave-function components which overlap the known $1s$ hydrogenic ground state of the one-electron system. The explicit form of $P^{\prime }$ and $Q^{\prime }$ is given, and a brief summary is given of various upper-energy-bound computational methods for DAI states; these closely parallel methods discussed previously for SAI states of two-electron atoms.

Natural line shapes of the states ${\left(2\mathrm{}{s}^{2}2p\right)}^{2}P$ and ${\left(2s2p^2\right)}^{2}D$ of ${\mathrm{He}}^{-}$ are observed in the ionization-efficiency curve of He. The shape factor $q$ and bandwidth $\Gamma$ are determined. The energies of those states are measured, respectively, as 57.15±0.04 and 58.23±0.04 eV. Furthermore, doubly excited levels of He are detected in the ionization-efficiency curve of He as they autoionize and add a contribution to the ${\mathrm{He}}^{+}$ continuum. All nine energy states measured are in very good agreement with values reported using other techniques.

The semiclassical spectrum, defined by use of WKB wave functions, and the classical expression of the spectrum are interpreted in terms of Feynman amplitudes. The radiative electronic transition may be considered to occur instantaneously, and the different times at which it can occur define different "paths" from initial to final state. During a collision of the radiating atom with a perturbing atom, the electronic transition occurs preferably when the relative distance between the two atoms is such that their relative velocity is conserved in the transition (Franck-Condon principle). In a given collision, there are several such preferred transition times which define as many preferred paths. Interference between these paths can result in interference patterns in the spectrum. In general, an interference structure, associated with the repulsive part of the interatomic potential difference, will appear in the violet wing of the spectral line. This forms a highly plausible explanation for the violet satellites observed in the spectrum of various gas mixtures. Not much regarding the shape of the interference structure can, in general, be deduced outside of numerical computations; nevertheless, the general dependence of the position of the violet satellites on parameters such as temperature, reduced mass, and size of the repulsive core of the potential difference can be inferred in a rough manner, and qualitative agreement with experiment be obtained.

By recording the absolute number of $K$ x-ray quanta emitted from a thin graphite target bombarded with electrons of energy $E$ between 2 and 30 keV, the quantity ${\omega }_{K^{\circ }}{Q}_K\mathrm{}\left(E\right)\mathrm{}$ for carbon has been measured, where ${\omega }_K$ is the $K$-shell-fluorescence yield and $Q_K\mathrm{}\left(E\right)\mathrm{}$ the ionization cross section for the $K$ shell. $Q_K\mathrm{}\left(E\right)\mathrm{}$ was calculated with the formula of Gryzinski, and the fluorescence yield of carbon was obtained as ${\omega }_K=0.0035\mathrm{}$. This value is much higher than the two other experimental values, but in agreement with a semiempirical formula of Byrne and Howarth and in near agreement with a recent calculation of McGuire. It is shown that this formula and this calculation seem to be valid for elements with atomic numbers down to $Z\approx 6$.