Wave functions, which include interelectron coordinates explicitly, are calculated for the four lowest ${}_{}{}^2{}_{}{}^{}S$ and four lowest ${}_{}{}^2{}_{}{}^{}P$ states of Lii. These wave functions are used to calculate oscillator strengths, including upper and lower bounds, for the 16 lines arising from allowed transitions among these four ${}_{}{}^2{}_{}{}^{}S$ and four ${}_{}{}^2{}_{}{}^{}P$ states. The results of this study are oscillator strengths for the $1s^2\mathrm{ns}{}_{}{}^2{}_{}{}^{}S\to 1s^2\mathrm{mp}{}_{}{}^2{}_{}{}^{}P$ Lii transitions for which $n$, $m=2, 3, 4, 5$ with rigorous upper and lower bounds which in the best case ($1s^{2}2s{}_{}{}^2{}_{}{}^{}S\to 1s^{2}2p{}_{}{}^2{}_{}{}^{}P$) are 3.5%.

Measurement of $v=1-0\mathrm{}$, $P$-branch 3.4-μm DF absorption spectra is made for DF mixed with foreign gases at a temperature of 23-25°C. A cw DF laser is used as a light source, and laser intensity transmitted by the gas mixture is measured in order to determine the absorption. From the measured absorption, the ratio of cross sections $\frac{Q_{\mathrm{AB}}}{Q_{\mathrm{AA}}}$ is determined, where $Q_{\mathrm{AB}}$ is the cross section for collision of DF $\mathrm{}(=A)\mathrm{}$ with a foreign gas $\mathrm{}(=B)\mathrm{}$ and $Q_{\mathrm{AA}}$ is for DF self-collisions. Results are obtained for the single line $v=1-0\mathrm{}$, $P\left(8\right)\mathrm{}$ in the case of ${\mathrm{D}}_2$, He, ${\mathrm{N}}_2$, C${\mathrm{F}}_4$, and S${\mathrm{F}}_6$ and for the lines $v=1-0\mathrm{}$, $P(5-10)\mathrm{}$ in the case of HF.

Raman spectra of low-pressure methane gas both at room temperature and near condensation have been studied in the frequency range from 0 to 50 ${\mathrm{cm}}^{-1\mathrm{}}$. The spectra include two contributions: One is due to collision-induced scattering (CIS) and the other to an unresolved dimer rotational band. The latter component is most prominent at low temperatures. Both the dimer band and CIS spectrum have been computed for a Lennard-Jones interaction and point-dipole polarizability. At large frequency shifts (> 20 ${\mathrm{cm}}^{-1\mathrm{}}$) it is sufficient to use classical collision dynamics to compute the CIS spectrum, but at lower shifts it is necessary to use quantum theory and add the dimer contribution to obtain good agreement with the experimental spectrum. From analysis of the spectra we determine that the fractional depolarized scattering from dimers is 10% at 300°K and 43% at 115°K. The shape of the far wing (20-50 ${\mathrm{cm}}^{-1\mathrm{}}$) provides a sensitive means of testing the form of the induced polarizability anisotropy. For methane, excellent agreement with experiment is obtained for the point-dipole model.

Hartree-Fock equations for transition matrices are formulated as an extension of the ordinary theory of atomic spectra. These equations form a hierarchy which may be subjected to various truncations. Some of the truncations are identified as equivalent to different forms of many-body theories (random-phase approximation, time-dependent Hartree-Fock, many-body perturbation theory, etc.). Thereby we connect the modern many-body treatments more explicitly with the Condon-Shortley-Racah tradition of spectral theory and provide physical interpretations of various approximations. Spin and angular variables are factored out at the outset by angular-momentum techniques. The problem then takes the form of a system of integro-differential equations for radial wave functions, which affords conceptual and computational advantages. The correlations that are characteristically studied by many-body techniques are seen to be confined to short radial distances and could accordingly be treated by $R$-matrix procedures.

A calculation of the expectation value of the mass-polarization operator $〈{\overrightarrow{\mathrm{p}}}_1·{\overrightarrow{\mathrm{p}}}_2〉$ for the two-electron atom is made using the $Z^{-1\mathrm{}}$ perturbation expansion in order to determine the usefulness of this approach in calculating two-particle correlations in atoms. Evaluation of the first-order contribution to $〈{\overrightarrow{\mathrm{p}}}_1·{\overrightarrow{\mathrm{p}}}_2〉$ yields a value in good agreement both with an earlier value determined by another method and with the value which may be deduced from calculations using very accurate wave functions. An interesting feature of the calculation is the finding that the summations are dominated by contributions from matrix elements which involve continuum states, with more than 85% of the total coming from these contributions. The second-order contribution is then obtained by demonstrating that both first- and second-order contributions are included in the first-order formula if accurate uncorrelated wave functions for the ground state are used in the matrix elements, rather than the bare hydrogenic orbitals. After observing that most of the greater accuracy of such wave functions arises from inclusion of electronic screening, the first-order calculation is repeated using simple screened hydrogenic orbitals in the matrix elements. The values of $〈{\overrightarrow{\mathrm{p}}}_1·{\overrightarrow{\mathrm{p}}}_2〉$ obtained by means of this simple calculation for various $Z$ values agree quite well with those calculated by Hart and Herzberg using accurate 20-term wave functions. The conclusion which is drawn from this calculation is that this method appears to be relatively simple and quite promising for calculating certain types of correlation effects, such as those resulting from double excitation or ionization of valence or inner-shell electrons. As examples of this, qualitative estimates are made of the behavior of the double photoionization cross sections of the remainder of the He isoelectronic sequence ($Z\ge 3$) and of other closed-shell atoms.

Analytical techniques are developed for constructing $n\mathrm{th}$-order (i.e., $n$-electron) tensor matrices pertaining to transitions of an $N$-electron atom between two of its stationary states. These matrices serve to calculate the transition amplitude for the atom under the influence of an external field acting on $n$ electrons (typically $n=1\mathrm{}$). Their calculation requires, in turn, the solution of a truncated hierarchy of Schrödinger equations introduced in the preceding paper. The techniques presented here are applied to construct the matrices and their Schrödinger equation for the example of Ar atoms treated in the preceding paper.

Autoionization transition rates have been calculated for a representative selection of spectroscopic terms of multiply excited argon atoms. The states selected consist of two highly excited electrons in the Rydberg states ($n=4, 5$) together with one or two vacancies in the valence shell ($n=3\mathrm{}$) and a single vacancy in the inner shell ($n=2\mathrm{}$). Configuration mixing was found to be important. The eigenvalues and eigenstates were found by the truncated diagonalization method (i.e., $\mathrm{QHQ}$ is diagonalized). The effect of term splitting was included by calculating the contributions of the quadrupole terms in the interelectron repulsive potentials. The applicability of the $\mathrm{msnp}\pm$ classification scheme suggested by Cooper, Fano, and Prats for helium was investigated for the outer electrons. Among the doubly excited outer-shell states found here are pairs of states which predominantly have the characteristics of $45sp+$ and $45sp-$ levels. However, states of the less-ionized system show less ± character because the shielding of the nucleus by the core electrons removes the degeneracy in energy of $4s5p$ and $5s4p$ levels, so there is less mixing when there is more shielding. The lifetimes of the valence-electron ($n=3\mathrm{}$) shell decay range from ∼${10}^{-15\mathrm{}}$ to ∼${10}^{-13\mathrm{}}$ sec. The lifetimes of the highly excited electrons separate into two widely disparate ranges: from ∼${10}^{-17\mathrm{}}$ to ∼${10}^{-16\mathrm{}}$ sec and from ∼${10}^{-13\mathrm{}}$ to ∼${10}^{-11\mathrm{}}$ sec. The outer-shell states that have lifetimes shorter than the inner shell are those from which it is energetically possible for an electron to fall to a $4s$, $4p$, or $3d$ subshell, while the longer lifetimes are for states which can decay only to the $n=3\mathrm{}$ core.

The $K\alpha$ x-ray satellite intensities were measured with proton impact at a scaled velocity (relative to that of the $L$-shell electron) $V_L=2.1\mathrm{}$ for $Z=13-20\mathrm{}$ and $V_L=1.0\mathrm{}$ for $Z=20-26\mathrm{}$. The intensity ratios $\frac{I_{K,1L}}{I_{K,0L}}$ are found to be well characterized by multiple-Coulomb ionization predictions. Taking into account the fluorescence yields, the comparisons of the measured intensity ratio with the corresponding ratio of theoretical vacancy cross sections yield a set of empirical vacancy-rearrangement correction factors. Theoretical estimates of these factors based on the atomic transition rates of McGuire are in reasonable over-all agreement with the extracted values.

The photoionization cross sections of the $3d$, $3p$, and $3s$ subshells of Zn i are calculated from threshold to 1000 eV. Electron-correlation effects are included using a low-order perturbation expansion obtained from many-body perturbation theory. The $3d\to \mathrm{kf}$ cross section is also calculated in the exact single-channel random-phase approximation with exchange. Autoionizing resonances due to the $3p^5\mathrm{ns}$ and $3p^5\mathrm{nd}$ configurations are included in the $3d\to \mathrm{kf}$ cross section, and the effect of core relaxation is considered. The effect of single-channel and multichannel correlations is included in all subshell cross sections.

Doppler and collision broadening were studied on six $2p^{5}5s-2p^{5}3p$ transitions of Nei. Line-broadening parameters were extracted using the method of least squares in the computer analysis of spontaneous emission profiles transmitted through a scanning plane-parallel Fabry-Perot interferometer. ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$-${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ Lorentz broadening parameters are tabulated, and their temperature dependence summarized.

Total photon cross sections are measured, using the transmission method in the heavy elements U, Th, Pb, and Au at energies 30.9, 35.9, and 55.4 keV, to study the photoelectric interaction below the $K$ edges of these elements. A krypton-filled proportional counter with a 512-channel analyzer is used as the detector of photons. The photoelectric cross sections, obtained by subtracting the small scattering contributions from the total cross section, are compared with theoretical predictions of Scofield and of Storm and Israel. General agreement is obtained, except for U and Th at 30.9 keV where the present experimental values show a slight preference to the calculations of Storm and Israel rather than the theoretical ones used by Scofield.

Systematic measurements have been made on the $K{\beta }_{1,3}$ emission lines of the transition elements $21\le Z\le 29$. Each element was studied in the metallic state and also in one of its oxidized states. The energy separation $\Delta E$ between the $3p_{\frac{1}{2}}$ and the $3p_{\frac{3}{2}}$ levels in these elements varies from about 3.4 eV for ${}_{}{}^{29}{}_{}{}^{}\mathrm{Cu}$ to about 2.0 eV for ${}_{}{}^{21}{}_{}{}^{}\mathrm{Sc}$, and therefore the $K{\beta }_{1,3}$ complex almost appears as a single emission line under the present experimental conditions. The exchange interaction between the $3d$ and the $3p$ electrons in these elements causes some of the electrons in the $3p$ state to move to lower energy levels; transitions from these levels appear as emission bands at the low-energy side of the $K{\beta }_{1,3}$ complex. A computer program was devised to unfold the complex structures and provide values for the mean energy separation $\Delta E$ and the relative transition probabilities of the constituent lines. For all the elements studied, the effect of oxidation seems to enhance the relative intensity of the low-energy emission band, without significantly altering the value of $\Delta E$. Comparison of the present experimental results with theoretical values derived on the basis of a simple exchange interaction exhibits good agreement on the value of the mean energy separation $\Delta E$, but shows large discrepancies in the relative transition probabilities.

The probabilities of single and multiple Compton scattering and the angular distributions of scattered photons are analyzed in terms of the effects of sample geometry and details of the photon-electron interaction (form of the single-electron cross section). It is shown that the desired desired quantities may be calculated analytically if Thomson scattering and an appropriate geometry are assumed. Consideration of scattering using an isotropic cross section suggests that in most cases sample geometry is more important than the form of the cross section in determining the probability and angular distribution of single and multiple scattering.

We give experimental verification of the novel theory for wave propagation in a homogeneous random medium, which was developed in a previous paper to circumvent the difficulty of the multiple-scattering problem. The prediction of the presence of the two modes of wave propagation, that is, the traveling-wave mode which exists in the case when the power spectrum of the random medium vanishes at double the wave number, and the cutoff mode which exists in other cases as a standing wave with exponentially increasing or decreasing amplitude, is demonstrated by means of a computer simulation of the random media described by the three Gaussian processes with different spectral forms. The formation of the cutoff mode during the propagation is explained from another point of view in terms of the phase-space trajectory of a forced nonlinear oscillation, which is verified by an example of the simulated solution. The average and variance of the phase and log-amplitude of the cutoff mode are measured from the simulated data for various combinations of the parameter values describing the spectra, and are shown in figures to compare with the theoretical values. The agreement between the theory and the experiment is shown to be satisfactory in spite of the approximate theoretical formulas.

We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.

The low-lying levels in the eigenvalue spectrum of a nonresonant maser model are investigated at $T=0\mathrm{}°\mathrm{K}$ when the atom-photon coupling constant is strong enough to cause the appearance of the so-called superradiant phase transition in the thermodynamic properties of the system. The frequency of the field is assumed to be larger than the Larmor frequency of the pseudospins, and eigenfunctions and eigenvalues are found using a technique based on the theory of continuants. The eigenvalue spectrum turns out to consist of a set of slightly split doublets, and the corresponding eigenstates are such that the dynamical properties of the system in each doublet closely correspond to tunneling between equivalent energy configurations. The atoms are shown to be surrounded by a cloud of virtual photons which accompany them during the tunneling motion.

The potential for use of inner-shell vacancies produced by photoionization for creation of an x-ray laser is discussed. A detailed numerical model of the physical processes involved is described and applied to sulfur, one of the most favorable materials for production of x-ray lasing at energies substantially greater than 1 keV. At solid density an x-ray pumping power of 1.7×${10}^{16}$ W/${\mathrm{cm}}^2$ is required with a rise time of less than 5 fsec, while at very low densities the rise-time requirement relaxes to about 50 fsec. The difficulties of meeting these requirements with current technology are discussed briefly.

The effects of incoherent feeding and decay on a coherently driven two-level system are investigated using density-matrix techniques. A closed-form solution that includes the effects of relaxation and spontaneous emission between the two levels is obtained for cases in which the sample size is both small and large compared to the wavelength of the coherent field. The formalism developed herein is somewhat more general than the original approach of Bloch, Bloembergen, Purcell, Pound, and Redfield, insofar as it is applicable to cases where the trace of density matrix is not constant in time. As such, several new phenomena are predicted. Specifically, the steady-state solutions reveal that under appropriate conditions a significant off-resonance coherent component can be maintained indefinitely by the combination of driving field and incoherent feeding. We term this effect "kinetic coherence" and develop its formalism for both optical and radio-frequency fields.

A model for Raman and fluorescent scattering by molecules embedded in small particles is described. This takes into account the effect of the particle's geometrical and optical properties upon the unshifted field which excites the molecular transitions within the particle, and upon the shifted field. Formulas are given which relate the angular distribution of the scattered radiation to the nature of the molecular scatterers and to the size and refractive index of the particle. These results are relevant for current problems in cell biology and atmospheric physics.

Under certain stated conditions, the electron population can be inverted in a variety of targets by a combination of x-ray (e.g., originating in a storage ring) and low-energy photon (e.g., from a laser) pumping. Coherent (mainly soft) x rays could then be produced by stimulated emission.