We have measured the dependence upon target-foil temperature of the linear polarization fraction ($\frac{M}{I}$) of the $2s{}_{}{}^1{}_{}{}^{}S-3p{}_{}{}^1{}_{}{}^{}P$, 5016-Å transition in He i for ion energies between 60 and 180 keV. The thin carbon exciter foils were heated externally by Nichrome resistance elements. The measurements of Hight et al. are duplicated; the energy and current dependencies of $\frac{M}{I}$ are the same, assuming correspondence between beam heating and external heating. We also observe that $\gamma$, the number of secondary electrons produced per incident ion, decreases with increasing foil temperature. These two effects, in conjunction, offer a plausible explanation for the variation of polarization with beam-current density. The temperature of the foil is shown to depend on beam current to the one-fourth power, indicating that radiation is the primary energy-loss mechanism.

Production of core-excited autoionizing states of neutral Li having configurations of the form $1snl{n}^{\prime }{l}^{\prime }$ has been observed over the impact-energy range from 10-50 keV. Although the results for production of all such states is remarkably consistent with a quasimolecular-excitation model proposed by Stolterfoht and Leithäuser, production of individual lines in the observed spectra exhibits collision-velocity dependencies indicative of considerably more complex processes, including processes which appear to be inherently two electron in nature. Excitation functions are presented for the $\left(1s2\mathrm{}{s}^2\right){}_{}{}^2{}_{}{}^{}S$, $1s\left(2s2p{}_{}{}^3{}_{}{}^{}P\right){}_{}{}^2{}_{}{}^{}P$, $1s\left(2s2p{}_{}{}^1{}_{}{}^{}P\right){}_{}{}^2{}_{}{}^{}P$, and $\left(1s2\mathrm{}{p}^2\right){}_{}{}^2{}_{}{}^{}D$ core-excited states of Li and for total core excitation.

Absolute cross sections for the emission of ultraviolet resonance line radiations from Ar and Kr atoms resulting from Ar + Ar and Kr + Kr collisions are reported. The energy range covered extends from near the reaction thresholds to 150 eV in the center-of-mass system. The emission cross sections are found to have energy dependencies very similar to those exhibited by the total ionization cross sections for the same reactants. The techniques used to make the measurements are described and the results are discussed in terms of a current theoretical model of the interactions.

The hydrogenlike ions ${\mathrm{B}}^{4+}$, ${\mathrm{C}}^{5+}$, ${\mathrm{N}}^{6+}$, ${\mathrm{O}}^{7+}$, and ${\mathrm{F}}^{8+}$, and the heliumlike ion ${\mathrm{F}}^{7+}$ have been shown to exhibit resonant coherent excitation from the atomic level $n=1\mathrm{}$ to $n=2\mathrm{}$, caused by the periodic potential oscillations which occur as the ion moves in axial and nearly axial planar channels in thin crystals of Au and Ag. Various harmonics of the lattice-string periodicity are effective, at certain critical ion velocities, in reducing the number of one-electron ions which survive passage through the crystal without electron loss. Resonances, appearing as minima in the one-electron charge-state fraction versus velocity, have been found for several axial channels and for several different harmonics of the string frequencies. In some cases the resonances can be split by small crystal tilts which produce sidebands upon the string frequency. Certain harmonics have been shown to produce tilt-insensitive double minima which measure Stark splittings of the $n=2\mathrm{}$ levels.

Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the $s$-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the $l$-mixing cross section at a particular $n$ is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on $n$. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of $\mathrm{Na}\mathrm{}\left(\mathrm{nd}\right)+\mathrm{He}$, Ne, and Ar are treated as specific examples.

Qualitative features are discussed for the binding of three identical bosons interacting through pair potentials in two dimensions. Two special cases, known to yield pathologies in three dimensions, are examined using the Faddeev equation for the bound states. The Thomas effect does not occur: in the model which is treated, the trimer binding energy is finite for a zero-range force with a finite dimer energy. The Efimov effect can only occur under more restrictive conditions than in three dimensions: the number of bound trimer states is finite at the dimer threshold for a range of potential models. The trimer ground-state energy is determined as a function of the coupling constant for a simple model, and variational results for loosely bound Lennard-Jones trimers are shown to reflect a general trend found for the model.

The sign of the rotational $g$ factor of acetylene has been directly measured to be positive with respect to the deuteron moment, thus resolving a disagreement between two earlier reported measurements. Corrections to a calculation of the susceptibility of acetylene which used the wrong sign for $g_J$ have been computed. The signs of the $g$ factors for a number of spherical top molecules, C${\mathrm{F}}_4$, Si${\mathrm{F}}_4$, Ge${\mathrm{F}}_4$, and S${\mathrm{F}}_6$, were also measured to be negative, confirming the results of earlier but less-direct experiments.

We obtain the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators. We next review a new method for obtaining the coherent states for arbitrary potentials, it being based on the classical motion of a particle. We apply this method to the Morse oscillator. After demonstrating that in the appropriate limit our results reduce to those for the harmonic oscillator, we obtain analytic insights into published numerical results on uncertainty products for Morse-oscillator wave packets.

Bands of this highly forbidden transition have been observed thus far in absorption only. In fact, emission of the $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ system is not to be expected from vibrational levels above $W\left(0\right)\mathrm{}$, since these levels are more rapidly depleted by $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}\to B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ transitions. For $W\left(0\right)\mathrm{}$, however, the ${\nu }^3$ factor so heavily favors the $W\to X$ that a progression of partially developed emission bands is to be expected in the 2000-Å region (when collisional deactivation is low.) These emissions are also favored by the circumstance that the $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$ is the ${\mathrm{N}}_2$ state most readily excited by low-energy electrons so that the $v=0\mathrm{}$ level may attain a very large population. The present measurements consist of intercomparisons of absorption bands recorded photographically in the 1500-Å region to yield $f$ numbers for several bands of the $W\leftarrow X$ system of ${\mathrm{N}}_2$. From these, transition probabilities for absorption and emission between the various levels of the $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$ and the ground state $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ have been calculated. For the $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$ $v=0\mathrm{}$ level, however, the calculation of transition probabilities for emission and of a lifetime becomes a rather complicated procedure as a result of the competitive relationship between $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ and $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}\to B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ for this one level. It turns out that the forbidden vacuum ultraviolet emission becomes more probable than the permitted emission which falls in the infrared beyond 100 μm. The predominance of the ultraviolet is not clearcut, however, with one of the three spin components more directed to the infrared and with a $J$-dependent branching ratio all across the band. Thus the measured lifetime for the $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$ $v=0\mathrm{}$ must be given as an intricately averaged value for just two of the spin components. It is found to be 4 sec, a lifetime which can be realized only in low-collision environments. Parameters are favorable for lasing to the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ $v=0\mathrm{}$ level.

A configuration-interaction calculation with a carefully optimized orbital basis gives an upper bound $E_u=-2.178040\mathrm{}$ a.u. (He) for the nonrelativistic energy $E_{\mathrm{nr}}$ of the $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{}^0{}_{}{}^{}$ metastable state of the He negative ion. Extensive studies of patterns of convergence for the energy show that $E_{\mathrm{nr}}=-2.178074\mathrm{}\left(10\right)\mathrm{}$, which together with Pekeris' accurate $E_{\mathrm{nr}}$ $\mathrm{He}\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}S$ yields a nonrelativistic electron affinity $A_{\mathrm{nr}}=77.4\mathrm{}\left(3\right)\mathrm{}$ meV. It is argued that the true electron affinity should not differ from $A_{\mathrm{nr}}$ by more than ±0.2 meV. Good agreement with the less-precise experimental values is obtained. The present results, by allowing a recalibration of the experiments, will permit a significant increase in the accuracy of future experimental determinations of electron affinities below 300 meV.

A new transformation for the Coulomb problem is introduced and its significance is discussed. Coulomb wave functions in the $\overrightarrow{\mathrm{u}}$ representation are derived. Examples of the application of the transformation are given.

The possible solutions of open-shell restricted self-consistent-field equations for a doublet are studied for Li and Na atoms, according to the values of the parameters implied in those equations. A similar behavior, characterized by the presence of several variational solutions is observed in both atoms. Some of these solutions can be assigned to excited configurations. Excitation energies are in good agreement with experimental data. Doublet stability for the solutions obtained has been studied, discussing the saddle-point character present in those solutions associated to excited configurations.

Kinoshita has pointed out that the famous Hylleraas expansion, $\psi =\Sigma A_{l,m,n}{s}^l{u}^m{t}^n$, is unable to furnish a formal solution to the Schrödinger equation for the two-electron atom. He further noted that the source of the difficulty is the arbitrary restriction of the indices $l$ and $m$ to positive values. The Kinoshita variables $s=s$, $p=\frac{u}{s}$, and $q=\frac{t}{u}$ alleviate this difficulty, and a Kinoshita expansion $\psi =\Sigma C_{l,m,n}{s}^l{p}^m{q}^n$ seems capable of furnishing formal solutions. It is shown here for $S$ states that $C_{l,m,n}=0\mathrm{}$ for all $C_{l,m,n}$ with $n>m$. This result is equivalent to the statement that negative powers of $u$ are not needed. This result, when applied to the $1{}_{}{}^1{}_{}{}^{}S$ ground state, allows the determination of all coefficients of the form $C_{2,2\mu +1,n}$. The implied infinite series are summed and explicit closed-form expressions are found which involve a novel logarithmic term. Conditions which must be imposed on that part of $\psi$ constructed from $C_{2,2\mu ,n}$ are discussed.

The $k$-ordering properties of the spectra of atoms and ions consisting of a single valence electron outside a core of closed shells ($k=n+l$) have been introduced and discussed extensively in three previous papers, together with the constant $l$ sequences within each group of levels having the same value of $k$ ($k$ bands). Here we have extended the discussion of the $k$ ordering by a closer consideration of the three spectra: Gai, Rbi, and Sri. Thus it has been found that 119 additional atomic enegy levels exhibit perfect $k$ ordering, and the resulting total number of levels included among the 42 spectra considered becomes 1274. A correlation has been shown to exist between the occurrence of inverted fine structure and the limiting angular momentum $l_1$ for $k$ ordering, and the limiting ionicity ${\delta }_1$. We have discussed the probable existence of a basic symmetry characterized by the quantum number $k$, which is partially broken by the "$l$-dependent interaction", giving rise to a multiplet of levels with different $l$ values, such that $l\lesssim l_1$, and $n=k-l$ (semi-fine-structure). The overwhelming evidence (1274 levels) in favor of perfect $k$ ordering for $l\lesssim l_1$ and $\delta \lesssim {\delta }_1$ can probably be used in future analyses of atomic and ionic spectra, in order to assist in the assignment of $n$ and/or $l$ values to the observed energy levels $E_{\mathrm{nl}}$.

Electron-transfer cross sections for the reactions of ${\mathrm{Xe}}^{+}$ ($n=1-4\mathrm{}$) with Xe atoms have been determined as a function of projectile-ion kinetic energy in the range 15 keV-1.6 MeV. For ${\mathrm{Xe}}^{n+}$ ($n=2, 3, 4$), cross sections for sequential transfer of two or more electrons in single-ion-atom collisions have been obtained. These cross sections decrease with increasing number of electrons transferred. The observed insensitivity of cross sections to projectile kinetic energy in the range investigated follows the condition that the linear velocity of the ion is less than the orbital velocity of a valence electron in the slow-moving target atom. Attenuation cross sections for reactions of ${\mathrm{Xe}}^{n+}$ ($n=2, 3, 4$) follow approximately a $Z_{\oplus }^2$ charge dependence. A simple classical model based on Coulomb forces yields cross sections with a reasonable fit to the experimental data.

The kinetic-energy change in electron-capture collisions between ${\mathrm{N}}^{2+}$ and He or Ne in the collision energy range 0.2-2.4 keV has been observed with sufficient resolution to separate all possible final states. These processes were modeled in terms of both a curve-crossing and a noncrossing mechanism. The results suggest that the observed transitions occur at an intermediate internuclear separation, $\mathrm{}(3.5-8)\mathrm{}{a}_0$, and that the noncrossing mechanism is important when an appropriate crossing does not occur within this range.

Measured cross sections for electron capture by a variety of multiply charged ions in collisions with atomic and molecular hydrogen are presented. The data are primarily for He-like and Li-like ions of B, C, N, and O in the velocity range 0.4-1.0 × ${10}^8$ cm/sec. The electron-capture cross sections for these ions are typically 3 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ in the velocity range tested. Comparison is made between these data and a number of recent theoretical predictions. While no simple scaling rules apply to these low-velocity data, for initial charge $q\ge +4\mathrm{}$ the cross sections are essentially characterized by initial ionic charge rather than by projectile mass or electronic structure.

Total cross sections for electron capture have been measured for ${\mathrm{O}}^{q+}\left(1\mathrm{}\le q\le 8\right)$, ${\mathrm{Fe}}^{q+}\left(4\mathrm{}\le q\le 15\right)$, ${\mathrm{Mo}}^{q+}\left(4\mathrm{}\le q\le 18\right)$, ${\mathrm{Ta}}^{q+}\left(3\mathrm{}\le q\le 19\right)$, ${\mathrm{W}}^{q+}\left(6\mathrm{}\le q\le 15\right)$, and ${\mathrm{Au}}^{q+}\left(5\mathrm{}\le q\le 16\right)$ incident on H and ${\mathrm{H}}_2$ in the velocity range 2.2-6.2×${10}^8$ cm/s. Both the scaling of the capture cross sections with projectile charge and their velocity dependence are investigated and compared to current theoretical models. In the range of charge states and velocities investigated, the cross sections, in general, are observed to decrease uniformly with increasing projectile velocity and to increase monotonically with increasing projectile charge. The charge dependence of the cross sections becomes stronger with increasing projectile velocity. In the present range of velocities, the ratios of the cross sections measured on ${\mathrm{H}}_2$ and H targets decrease with increasing projectile charge, while increasing as a function of velocity. For the lighter projectiles Fe and Mo, localized deviations from the expected smooth increase of the capture cross sections with increasing projectile charge at constant velocity were observed in the vicinity of projectile charge states corresponding to closed-shell configurations. These observed "dips" are strongly correlated with variations in calculated ionic projectile radii. For the heavier projectiles Ta, W, and Au, oscillations superimposed on the expected monotonically increasing $q$ dependence were observed, having amplitude and phase that are only weakly dependent on projectile species. This oscillatory behavior is attributed to interference between the long-range Coulomb and short-range (screened) Coulomb interactions characterizing the collision.

The differential cross sections for collisional electron detachment of ${\mathrm{H}}^{-}$ ions by He, H, and ${\mathrm{H}}_2$ targets in the 100-keV-10-MeV energy region is investigated. The summation over all the final states which contribute to electron detachment is carried out in the closure approximation using the concept of the average energy loss at a fixed scattering angle. In the Born approximation, the differential cross section for electron-detachment collisions is strongly peaked in the forward direction. We have also studied nondetachment collisions in the Born approximation. One of the interesting features associated with nondetachment collisions is the zero in the differential cross section near the forward direction. Results for the total electron-detachment cross section are also presented and compared with experiment where measurements are available.

We have investigated the effect of target distortion on the electron-detachment differential cross sections for ${\mathrm{H}}^{-}$-ion collisions on He and H atoms in the 100-keV-100-MeV energy region. In the present paper we are concerned with the following process: ${\mathrm{H}}^{-}+M\to \mathrm{H}+e+M$ for the production of H atoms. The target denoted by $M$ is not excited and the H atom can be produced in any of its states. Semiclassical JWKB and eikonal approximations are used to treat the distortion of the target by the incident ${\mathrm{H}}^{-}$ ion. The results which are compared with the Born approximation indicate a significant difference at the forward direction.