The paper by Wang and Davis deals with a number of distinct aspects of laser-induced air breakdown. In this comment, each of these is discussed in detail and it is clearly demonstrated that many of their results, presented as new, form the subject of a number of earlier publications by the authors and others.

The spin-optimized self-consistent-field procedure is generalized for atoms. This new method is flexible, can allow for the angular correlation, and is applicable to the lowest state of any given symmetry type.

The frequency shift $\Delta \nu$ due to vacuum polarization by electron pairs and hadrons is calculated for the hyperfine interval of the ${\mu }^{+}{\mu }^{-}$ bound system. These corrections contribute at the part-per-thousand level and lead to a total triplet-singlet splitting of $\nu +\Delta \nu =4.220\mathrm{}\times {10}^7$ MHz.

The normalized two-time intensity-fluctuation functions are calculated for the spontaneous-emission radiation from a system of $N$ two-level atoms. The radiated field, when the system decays from the excited state to the ground state, does not look like a Gaussian or a coherent field.

The full nonlinear governing equations for the quasistochastic model, which describes the motion of a Brownian charge carrier in an external electric field, are solved for the stationary current response. We find that the nonlinear response is identical to the linear response obtained earlier by Lebowitz and Rubin.

Average $L$- and $M$-shell-vacancy distributions produced in the deexcitation of atoms that have been singly ionized in the $K$ shell or one of the $L$ subshells are derived from a comprehensive set of available experimental and theoretical data on radiative- and Auger-transition rates. The data are supplemented by new calculations in $j-j$ coupling from nonrelativistic screened hydrogenic wave functions of the following radiationless transition rates: $K-LL$, $K-LM$, and $K-LN$ for selected elements with $20\le Z\le 81$, and $L_i-MM$, $L_i-MX$, and $L_i-XY$ for $26\le Z\le 93$. Experimental and theoretical data on Auger- and radiative-transition probabilities are critically compared. Auger-electron intensity ratios and $\frac{K{\alpha }_2}{K{\alpha }_1}$ and $\frac{K\beta }{K\alpha }$ x-ray intensity ratios from a best fit to experimental data are tabulated for even atomic numbers from 20 to 94. The probability, per initial $K$ vacancy, of vacancy production in each $L_i$ subshell is derived from experimental data and tabulated for $20\le Z\le 94$; components due to Auger and x-ray transitions are listed separately. These probabilities agree well with purely theoretical vacancy distributions also derived here. The probability of $M$-shell-vacancy production in the decay of $K$ and $L_i$ vacancies is derived from theory and tabulated for selected atoms with $16\le Z\le 93$.

The energies of the $K{\alpha }_1$, $K{\alpha }_2$, $K{\beta }_1$, and $K{\beta }_3$ x rays of Cm, Bk, Cf, and Es, arising in the decay of suitable parent radioactivities, have been measured with a high-resolution Ge(Li) photon detector. The $K$-shell binding energies of Cm, Bk, and Cf have been determined using previously published values for the $L_{\mathrm{II}}$-, $L_{\mathrm{III}}$-, $M_{\mathrm{II}}$-, and $M_{\mathrm{III}}$-shell binding energies. The relative transition probabilities ($K{\alpha }_1=1000\mathrm{}$) of the $K$-series lines have been determined for Cm, Bk, Cf, and Es. The measured energies and relative transition probatilities agree well with recent theoretical predictions.

Positions of satellite bands near the atomic lines of alkali metals in the presence of heavy noble gases together with the assumption of a Lennard-Jones (6-12) interaction potential and knowledge of the attractive force constant $C_6$ are used to determine the repulsive force constant $C_{12}$ for excited states of the alkali atoms. The formula commonly used for $C_6$ is modified and leads to an improved agreement of the calculated values for this constant with experimental measurements. The constant $C_{12}$, derived from satellite-band measurements, is found to rapidly increase with excitation of the alkali atom and to be nearly independent of the noblegas. The values of $C_{12}$ found for 82 excited states of Li, Na, K, Rb, and Cs in the presence of Kr and Xe are represented by a simple power law in the effective principal quantum number of the excited state. The expression appears to have general utility when one atom is a noble gas and the other has one or two excited electrons.

The absorption spectrum of water vapor, in addition to giving information about the structure and properties of the water molecule, is of practical importance because of the effects of water vapor on the propagation of electromagnetic radiation. However, precise measurements of only 6 ground-vibrational-state transitions of ${\mathrm{H}}_2^{16}$O have been reported in the microwave region. We report the measurement of nine new rotational transitions of ${\mathrm{H}}_2^{16}$O and the remeasurement to higher accuracy of the four previously known submillimeter lines. The frequencies of the newly observed transitions are (in Mc/sec) ${10}_{2,9}$←$9_{3,6}$, 321225.644; $7_{5,3}$←$6_{6,0}$, 437346.667; $6_{4,3}$←$5_{5,0}$, 439150.812; $7_{5,2}$←$6_{6,1}$, 443018.295; $6_{4,2}$←$5_{5,1}$, 470888.947; $5_{3,3}$←$4_{4,0}$, 474689.127; $6_{2,4}$←$7_{1,7}$, 488491.133; $5_{3,2}$←$4_{4,1}$, 620700.807; and $2_{1,1}$←$2_{0,2}$, 752033.227. These transitions have been measured with a submillimeter-wave spectrometer which employs a klystron-driven crystal harmonic generator and a 1.6°K InSb photoconducting detector. With this work, the lines contributing the major portion of the atmospheric absorption of water vapor in the region up to 800 Gc/sec have been precisely measured.

We have extended the theory of the high-frequency Stark effect in atomic spectra to treat cases of multiple interacting upper levels and of strong electric fields and resonances, where perturbation theory is inadequate. We have also included the effects of a static external magnetic field both in the perturbation theory and the more general treatment. Numerical calculations are presented for the 4922- and 4388-Å lines of He i for several field strengths and frequencies. The new theory is used to infer the frequency and strength of a microwave electric field applied to a steady-state helium discharge with no magnetic field; excellent agreement is obtained between the calculated and the observed spectra.

Accurate closed analytic expressions for certain properties of ${\mathrm{H}}^{-}$ that strongly depend on the long-range tail of its wave function are given. These properties are $〈{{\mathcal{r}}_1}^n+{{\mathcal{r}}_2}^n〉$, the static electric multipole polarizabilities, and the dynamic dipole polarizability. From the last, the ${\mathrm{H}}^{-}$ photodetachment cross section is calculated and the simple but accurate result obtained by Armstrong is recovered. The only assumption made is that the exact wave function can be replaced by its rigorous asymptotic form, for the purpose of calculating these properties. No model potentials or arbitrary cutoffs are introduced. The results for the dipole polarizabilities agree to better than 5% with the extensive recent calculations of Chung. For $〈{\mathcal{r}}_1^n+{\mathcal{r}}_2^n〉$, $n\ge 2$, the formula obtained agrees to within 0.5% with values obtained from large calculations. For all these quantities, the Hartree-Fock results are far inferior.

Early calculations by James and Coolidge and more recent work by Larsson have treated the lithium ground state by expansions containing correlation factors of the form ${{\mathcal{r}}_{\mathrm{ij}}}^p$. Similar calculations of the first two excited ${}_{}{}^2{}_{}{}^{}S$ states are reported herein. Expansions of 22 and 18 terms, respectively, led to calculated nonrelativistic energies (in a. u.) of - 7.3535 and - 7.3175, as compared to relativistically adjusted experimental values of - 7.3541 and - 7.3185. A brief discussion is given of feasibility of similar calculations for more complex atoms.

Many-body perturbation theory is used to calculate the dipole polarizability ${\alpha }_d$ of the neutral carbon atom in its ${}_{}{}^3{}_{}{}^{}P$ ground state. The result is 2.38 ${\mathrm{\AA }}^3$ in lowest order. When correlations are included by calculating higher-order terms in the perturbation expansion, we obtain the value 1.54 ${\mathrm{\AA }}^3$ for ${\alpha }_d$ averaged over $M_L$ values. A calculation of the coefficient of the $R^{-6\mathrm{}}$ term in the van der Waals interaction between two carbon atoms each in the ${}_{}{}^3{}_{}{}^{}P$ ground state is also reported.

The theory of the homogeneous interacting electron gas is used to derive a functional of the density for the form factor for incoherent scattering of x rays by a statistical atom. The results show a dramatic improvement over an early calculation of Heisenberg who used the Thomas-Fermi model. Detailed calculations of form factors are carried out for several elements (A, Cu, Ce, Na) and compared with the results of Hartree-Fock-Slater (HFS) self-consistent wave-function calculations. Whereas the Thomas-Fermi model gives incoherent cross sections which differ at low energies by orders of magnitude from those given by the HFS model, the theory of the homogeneous electron gas yields results which compare within 15% of the HFS results.

The external electromagnetic interactions of hydrogenic atoms, which exhibit global Galilean invariance but preserve the relativistic description of the electron, are investigated. The Hamiltonian for the free atom consists of the Breit Hamiltonian for a relativistic electron interacting with a nonrelativistic spinless proton. Approximate generators of the Galilean group are constructed in terms of individual-particle position, momentum, and spin operators in several unitarily equivalent representations. In one of these the Hamiltonian is separable in conventional relative and center-of-mass coordinates. This separability facilitates the treatment of a number of external-field problems. An effective Hamiltonian for the interaction of the atom with a constant external electric field is given and compared to that obtained by other authors. The low-energy theorem for Compton scattering from the composite system is explicitly verified including corrections due to atomic binding. This also gives an independent verification of recently obtained bound-state corrections to the atomic magnetic moment. Finally, an effective interaction of a charged Dirac particle with a hydrogenic atom is given in the representation in which the atomic Hamiltonian is separable.

Fluorescence (${\omega }_2$), Auger ($a_2$), and Coster-Kronig ($f_{23}$) $L_{\mathrm{II}}$-subshell yields, and the total $L$ fluorescence yield (${\overline{\omega }}_L$), in uranium and radium have been determined from measurements on $L$ x rays emitted following $\alpha$ decay of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ and ${}_{}{}^{228}{}_{}{}^{}\mathrm{Th}$, respectively. $\alpha$ x-ray coincidence techniques employing a surface-barrier detector for the $\alpha$ particles and Si(Li) $L$ x-ray spectrometer and a NaI (Tl) scintillation counter, for the $L$ x-rays, were used. The experimental results are ${\omega }_2=0.423\mathrm{}\pm 0.023$, $a_2=0.522\mathrm{}\pm 0.056$, $f_{23}=0.07\mathrm{}\pm 0.05$, and ${\overline{\omega }}_L=0.442\mathrm{}\pm 0.012$ for uranium, and ${\omega }_2=0.415\mathrm{}\pm 0.027$, $a_2=0.571\mathrm{}\pm 0.084$, $f_{23}=0.01\mathrm{}\pm 0.7$, and ${\overline{\omega }}_L=0.404\mathrm{}\pm 0.024$ for radium.

The Hartree-Fock exchange and the statistical free-electron approximation are analyzed and compared for a number of atoms. The exchange energy is calculated in the two approximations—in both cases by using accurate Hartree-Fock orbitals—and split up into contributions from individual electronic shells and also into self-interaction and interelectronic parts. The results are conveniently expressed by the ratio of the various quantities in the two approximations. It is found that these parameters vary in a simple and regular way, which can be interpreted by means of an extended free-electron model. It is, e.g., found that the parameter of the total self-interaction is significantly larger than that of the total interelectronic exchange. This explains in a simple way the principal variation with the atomic number of the parameter in the so-called $X\alpha$ method. The analysis is only intended to yield some insight into the exchange phenomenon, and no new—local or nonlocal—exchange potential is suggested.

A magnetic-resonance technique has been used to make an accurate measurement of the $g_J$ values of the $5d{\left[\frac{7}{2}\right]}_4$, $5d{\left[\frac{7}{2}\right]}_3$, and $5d{\left[\frac{3}{2}\right]}_2$ states in xenon and of the hyperfine structure of the $5d{\left[\frac{7}{2}\right]}_4$ state in ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$. The $5d$ states are excited and aligned by unidirectional electron impact in a hot-cathode discharge tube containing Xe at a pressure of about 5 × ${10}^{-3\mathrm{}}$ Torr. Induced transitions between magnetic sublevels of the aligned $5d$ state are detected by monitoring the intensity of linearly polarized light emitted during the second step in the cascade $5d\to 6p\to 6s$. The $g_J$ values were measured by determining the Zeeman transition frequency of a particular $5d$ state in a magnetic field of about 20 G which had been locked to the Zeeman resonance in the $6s{\left[\frac{3}{2}\right]}_2$ metastable state. The results are $g_J=1.2506\mathrm{}\left(3\right)\mathrm{}$ for $5d{\left[\frac{7}{2}\right]}_4$, $g_J=1.0749\mathrm{}\left(4\right)\mathrm{}$ for $5d{\left[\frac{7}{2}\right]}_3$, and $g_J=1.3750\mathrm{}\left(3\right)\mathrm{}$ for $5d{\left[\frac{3}{2}\right]}_2$. The hyperfine structure was measured by placing the tube in a T${\mathrm{E}}_{102}$ microwave cavity and observing direct ($\Delta F=1\mathrm{}$) hyperfine transitions in a magnetic field of a few gauss. The result for ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ in the $5d{\left[\frac{7}{2}\right]}_4$ state is $a=-583.571\mathrm{}\left(2\right)\mathrm{}$ MHz. The error for both the $g_J$ values and the hyperfine structure arises from the magnetic field measurement and corresponds to about one-tenth of the linewidth. Our results are improvements of previous optical measurements.

The earlier work on the vibrational and structural studies has been given for the metal-carbon-oxygen bonds and the metal-metal bonds in dimanganese iron tetradecacarbonyl, ${\mathrm{}\left(\mathrm{manganese}\right)\mathrm{}}_2$iron${\mathrm{}\left(\mathrm{carbonyl}\right)\mathrm{}}_{14}$. The $\delta$-function potential model is developed and shown to be valuable in evaluating important quantities through the use of the variational method and the $\delta$-function electronic wave functions. It is then applied to calculations of bonding and nonbonding electron contributions to the parallel and perpendicular components of the bond polarizability, and the average molecular polarizability of both diatomic and polyatomic molecules. The $\delta$-function strengths, the values of the parameter $c$, and the atomic polarizabilities of all the atoms in dimanganese iron tetradecacarbonyl were calculated. The bond polarizabilities and contributions to their parallel and perpendicular components due to nonbonding electrons were calculated, and the average molecular polarizabilities were computed for both crystallographic versions of dimanganese iron tetradecacarbonyl.