The covariant path integral with a quadratic Lagrangian in curved space will be evaluated using a Fourier-series analysis of smooth paths in Riemannian normal coordinates. The present treatment replaces an earlier one.

Misunderstandings concerning earlier work are clarified. The crucial role attributed to noncoincidence of the polarization states of the counterpropagating waves in a saturated gas laser is questioned.

Through analyses of the Monte Carlo data on strongly coupled fluids such as the classical one-component plasma, we demonstrate that the excess internal energy $U$ may be expressed to a good degree of accuracy by a lattice-model formula, $\frac{U}{N{k}_{B}T}=\alpha \Gamma +\frac{3}{2}$, near the crystallization point, where $\Gamma$ is the coupling constant and $\alpha$ takes on a value close to the Madelung constant of the corresponding crystalline lattice.

Five predicted but formerly unlocated energy levels in the $5p^{5}5d$ configuration of Cs II are reported. Transitions involving these new levels and previously known levels allow the classifications of 19 lines in the spectrum of Cs II which have been observed but not classified prior to this time.

The two-photon absorption initiated by two coherent beams is considered. It is shown that the resonance fringe variation, which appeared in the Doppler-free two-photon absorption of pulsed laser beams, can also be observed in absorption with a Doppler shift.

The asymptotic behavior of the coefficients $a_n$ in the expansion of the ground-state energy of the hydrogen molecular ion in terms of the inverse powers of the internuclear separation is found to be $a_n=-(n+1\mathrm{})!2^{-n}{e}^{-2\mathrm{}}[1+2\mathrm{}{n}^{-1\mathrm{}}-20\mathrm{}{n}^{-2\mathrm{}}-45\mathrm{}{n}^{-3\mathrm{}}+O(n^{-4\mathrm{}}\left)\right]$. The first two terms of this numerically obtained expression agree with the "asymptotic conjecture" involving the lowest excitation energy of $\mathrm{H}_2^{}{}_{}{}^{+}$

The wave functions for the hydrogen atom are determined in the momentum representation, using momentum variables $p_r$, $p_{\theta }$, $p_{\phi }$ which are associated with the spherical polar variables $r$, $t(=e^{i\pi cos\theta })$ and $v\left(e^{i\phi }\right)$. The functions may be written as $\left\{{\phi }_{n,l,m}\right(p_r,p_{\theta },p_{\phi })={\alpha }_{n,l}(p_r\left){\beta }_l^m\right(p_{\theta }\left)\delta \right(p_{\phi }+m),\}\left\{{\alpha }_{n,l}\right(p_r)={\left(\frac{n}{i{p}_0}\right)}^{3l+z}\Sigma \stackrel{n-l-1\mathrm{}}{k=0\mathrm{}}\left(\{n-l-1\mathrm{}\}\left\{k\right\}\right)\frac{2^{k-l+1\mathrm{}}}{\mathrm{}(2l+k+1)\mathrm{}(2l+k)\mathrm{}\cdots \mathrm{}(l+k+2\mathrm{})\mathrm{}}{\left(\frac{\frac{i{p}_0}{n}}{p_r-\frac{i{p}_0}{n}}\right)}^{l+k+2\mathrm{}},\}\left\{{\beta }_l^m\right(p_{\theta })=\Sigma \stackrel{E\left(\frac{l}{2}\right)}{j=E\left(\frac{m}{2}\right)}{a_j{p}_{\theta }}^{-\frac{\mathrm{}(m+1\mathrm{})\mathrm{}}{2}}{J}_{\frac{j-(m-1\mathrm{})\mathrm{}}{2}}\left(p_{\theta }\right),\}$ where $\delta$ is the Dirac delta function and $p_0=Z{a}_0^{-1\mathrm{}}$ ($a_0$ is the Bohr radius). $J_{\nu }\left(p_0\right)$ are Bessel functions of integer or half-integer order. The radial functions are shown to have poles up to order $n+1\mathrm{}$ at $p_r=i\frac{p_0}{n}$.

$g_J$-factor corrections for the ground states of the first-row atoms and sodium are calculated by use of spin-extended Hartree-Fock (SEHF) wave functions. The present results are compared with Hartree-Fock values and experimental $g_J$ factors. The theoretical SEHF $g_J$ factors show a deviation from the experimental ones which increase very regularly from lithium to fluorine. these discrepancies are believed to arise from the neglect of correlation effects, and they indicate that the previous success of the Hartree-Fock theory in the cases of oxygen and fluorine is fortuitous. Hartree-Fock values are also presented for the $g_J$-factor corrections of the ground states of the second-row atoms, and for potassium, rubidium, bromine, and iodine.

Radiative corrections generate shifts in the Rydberg levels of "murium," the system composed of an electron bound by its image charge to a plane wall, which are proportional to the fine structure constant $\alpha$; if the wall is perfectly conducting and impenetrable the shift in the ground-state energy is 0.2%, extraordinarily large for a radiative correction. (The difference from the usual hydrogenic Lamb shift, which goes roughly as ${\alpha }^3$, originates in the fact that the vacuum fluctuation fields near the wall differ from those in free space, so that on renormalization the leading terms are not completely canceled.) The absolute shift is greatly reduced for a realistic wall.

The cross sections for the formation of excited ${\mathrm{Mg}}^{+}$ states in 20-500 keV ${\mathrm{Mg}}^{++}$-Mg collisions have been measured by optical spectrometry in order to test the validity of the model proposed by Horsdal-Pedersen et al. Phys. Rev. Lett. 41, 1541 (1978) to explain a pronounced structure in the experimental cross section for resonant double-charge transfer in ${\mathrm{Mg}}^{++}$-Mg collisions. The present ${\mathrm{Mg}}^{+}3p$-formation cross sections support the basic assumption in the model, that the interaction between two molecular states, separating into the atomic configurations ${\mathrm{Mg}}^{++}-\mathrm{M}\mathrm{g}3s^2$ and ${\mathrm{Mg}}^{+}3p-{\mathrm{Mg}}^{+}3s$ at large intermolecular distances, plays a dominant role in the collision. An extended version of the model is needed to account for the observed formation of ${\mathrm{Mg}}^{+}3d$ and ${\mathrm{Mg}}^{+}4s$ states, the population of the ${\mathrm{Mg}}^{+}3p$ state from the projectile and target, separately, and the polarization of the ${\mathrm{Mg}}^{+}(3p\to 3s)$ emission.

Measurements of the total charge-changing cross sections ${\sigma }_{-0\mathrm{}}$ and ${\sigma }_{-+}$, are reported for ${\mathrm{H}}^{-}$ ions with energies in the range 30-200 keV incident on Ne, Ar, Kr, Xe, Li, Na, K, Rb, and Cs gas or vapor targets. Measurements of ${\sigma }_{g+}$ and ${\sigma }_{g-}$ are reported for fast ground-state ${\mathrm{H}}^0$ atoms with energies of 30-200 keV incident on the same targets. Measurements are also reported on the fractional yields as a function of the target thickness for ${\mathrm{H}}^{-}$ ions with energies in the range 30-200 keV incident on a variety of targets. The neutral fraction increases, reaches a maximum value, $F_0^{max}$, and then decreases to the equilibrium fraction $F_0^{\infty }$ as the target thickness increases from 0 to a very large value. Measurements of $F_0^{max}$, $F_0^{\infty }$, and $F_{-}^{\infty }$ are reported for ${\mathrm{H}}^{-}$ ions incident on a variety of targets.

The saddle-point technique is applied to the helium atom below the ionization threshold and for ${}_{}{}^1{}_{}{}^{}P$ and ${}_{}{}^3{}_{}{}^{}P$ resonances in the elastic-, and inelastic-scattering energy region. The results generally support the assertion that the method gives the best square-integrable approximation within the inner-shell vacancy picture for excited or autoionizing states. For the resonance where the Feshbach shift is negative, the saddle-point method gives essentially the same result as that of the $\mathrm{QHQ}$ approximation. However, for resonances with a large positive Feshbach shift, the results of the new method are substantially better. For example, for the lowest ${}_{}{}^1{}_{}{}^{}P$ resonance in the inelastic-scattering region, we get 69.901 eV, the experimental result is 69.90 ± 0.04 eV by Madden and Codling, 69.92 ± 0.03 eV by Dhez and Ederer.

We have observed sharply resonant collisional energy transfer from electronic excitation of the Na $\mathrm{ns}(n=5-11\mathrm{})\mathrm{}$ states to vibrational excitation in C${\mathrm{H}}_4$ and C${\mathrm{D}}_4$ leading to resonant cross sections of ∼300 ${\mathrm{\cong }}^2$. However, not all energetically resonant transfers occur with large cross sections. The apparent selection rules for the process and the magnitude of the cross sections suggest that the process be described in terms of low-energy electron-molecule scattering.

We report measured cross sections for the collisional production of highly charged low-velocity Ne recoil ions resulting from the bombardment of a thin Ne gas target by highly charged 1-MeV/amu C, N, O, and F projectiles. The measurements were made using time-of-flight techniques which allowed the simultaneous identification of the final charge state of both the low-velocity recoil ion and the high-velocity projectile for each collision event. For a given incident-projectile charge state, the recoil charge-state distribution is very dependent upon the final charge state of the projectile. Single- and double-electron capture events by incident bare nuclei and projectile $K$-shell ionization during the collision cause large shifts in the recoil charge-state distributions toward higher charge states. A previously proposed energy-deposition model is modified to include the effects of projectile charge-changing collisions during the collision for bare and hydrogenlike projectiles and is used to discuss the present experimental results.

The total quenching cross sections for $\mathrm{He}\left(n^{1,3}S\right)\left(2\mathrm{}\le n\le 11\right)$ states by thermal collisions [600(+ 200, - 100) K] with He, Ne, Ar, Kr, and Xe have been measured. The main quenching mechanism is attributed to Penning ionization for lower $n$, and collisional angular-momentum transfer for highly excited states. Measured cross sections are of the order of ${10}^{-15\mathrm{}}$ to ${10}^{-14\mathrm{}}$, ${\mathrm{cm}}^2$. The values for higher $n$ states are much smaller than the geometrical cross section; this is explained by a relatively large energy spread between the $S$ state and $l\ge 1$ states.

The quenching cross sections for the He $2S-9S$, $3{}_{}{}^1{}_{}{}^{}P$, and $n=5-9\mathrm{}$ manifold states by ${\mathrm{N}}_2$, and $n=6-9\mathrm{}$ manifold states by He, Ar, and Kr have been measured at 600 K. The cross section for $2 {}_{}{}^3{}_{}{}^{}S$ by ${\mathrm{N}}_2$ is 7.9(+1.2,-0.7) ${\mathrm{\AA }}^2$, and the values obtained for $\mathrm{nS}-{\mathrm{N}}_2 (n\ge 3)$ are 40-80 ${\mathrm{\AA }}^2$ and increase slowly with $n$ up to $n=5\mathrm{}$ then show a plateau or decrease slightly with $n$. The cross sections for the ${}_{}{}^1{}_{}{}^{}S$ are about 1.3 times those for the ${}_{}{}^3{}_{}{}^{}S$ for $n=3\mathrm{} \mathrm{and} 5$. The cross sections for the $n=5,8, \mathrm{and} 9$ manifold states by ${\mathrm{N}}_2$ are nearly the same in magnitude as those for $S$ states; however, those for rare-gas collisions are about one order smaller than those for ${\mathrm{N}}_2$ collisions. The main mechanism for the quenching of He Rydberg states ($n\ge 3$) by ${\mathrm{N}}_2$ is attributed to $n$-changing collisions due to excitation of molecular vibrations in ${\mathrm{N}}_2$.

Using the generalized oscillator strength formulation of the Bron approximation, proton ionization cross sections were calculated for a large sample of subshells of atoms throughout the periodic table. The results are presented in the form of scaled cross sections for all subshells up to the $6p$. Comparison with measurements shows reasonable agreement (better than a factor of 2), with some exceptions, for the proton energy range studied. The scaled cross sections presented herein are limited, in general, to proton energies greater than 184 times the subshell ionization energy.

A perturbation theory is presented which is suitable for the treatment of strong or resonant interactions in quantum systems described by time-independent Hamiltonians. The formulation is exact for finite-level systems and encompasses both nondegenerate and degenerate problems. The derivation is based on the partitioning of the levelshift operator, an operator which occurs naturally through the use of projection operators. The formulation is applied to the eigenvalue problem and to the calculation of the transition amplitude between states of the unperturbed system induced by a time-independent perturbation. The results are expressed in terms of Green's functions involving continued fractions which are truncated for finite-level systems.

Cross sections for the electron-impact excitation of the $n=2\mathrm{}$ states of the heliumlike ions Fe xxv and Kr xxxv are calculated in the relativistic distorted-wave approximation. Both bound-core orbitals and continuum-scattering orbitals are calculated using the Dirac Hamiltonian. The most significant relativistic effects result from the spinorbit mixing of the $2 {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and $2 {}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ excited states. We compare our results with previous calculations based on a perturbation-theory treatment of relativistic effects.