Coefficients $E_k$ in the $Z$-expansion series for $E\left(Z\right)\mathrm{}$, where $E\left(Z\right)\mathrm{}$ is the nonrelativistic total energy and $Z$ the nuclear charge, are tabulated for singly excited $n\left({}_{}{}^{1,3}{}_{}{}^{}S\right)$ and $n\left({}_{}{}^{1,3}{}_{}{}^{}P\right)$ states of two-electron ions, $n=2-5$. These results were obtained largely from an analysis of variational $E\left(Z\right)\mathrm{}$ values given by Accad, Pekeris, and Schiff but were taken in some cases from variational-perturbation calculations of other authors. The $Z$-expansion estimates of nonrelativistic term values for ions with $Z\ge 11$ have been compared with the corresponding results of Ermolaev and Jones, and agreement within 1 or 2 parts in ${10}^7$ was found for most states.

The development of the transcorrelated Hamiltonian method (THM) by Boys and Handy seemed to imply that the determination of atomic and molecular wave functions and energies with full electronic correlation can be done with calculations which involve at worst only pseudo-six-dimensional integrals. We show that the THM equations of Boys and Handy are in fact only the first of a hierarchy of equations obtainable by developing the true variational energy in terms of a certain expansion parameter; at this level of approximation only pseudo-six-dimensional integrals appear. The successively higher-order THM equations are shown to bring in the successively more complex integrals and include more subtle correlation corrections. The scope and limits of THM and various convergence aspects of the solutions of THM as well as inclusion of configuration interaction are examined. The formal ideas developed in the paper are tested in detail by the application of THM to the non-trivial but well-understood test case of the uniform electron gas. The analysis clearly unravels the type of particle correlations captured by THM in first order and shows that the full optimization of a trial wave function containing an infinitely flexible correlation factor leads to solutions closely resembling those of the random phase approximation. Finally we indicate briefly how correlated variational equations which are free of the non-Hermiticity difficulties of THM and which incorporate infinite-order summation characteristics and yet involve only a given order of difficulty in the integrals could be generated using elementary techniques. An application of this to the electron gas affords a useful comparison with THM.

Numerical data are obtained for the electron bremsstrahlung energy spectrum resulting from incident electrons of kinetic energy 1-500 keV, under the assumption that the process is described as a single-electron transition in a relativistic self-consistent screened potential, using partial-wave expansions. Comparisons with simpler analytical approximations show that these are at best of qualitative validity in this energy range. Our data are used to construct more complete tables of the spectrum by interpolation.

Electron capture cross sections (${\sigma }_{10}$) and stripping or loss cross sections (${\sigma }_{01}, {\sigma }_{12}, {\sigma }_{02}$) have been measured for 50- to 600-keV ${\mathrm{Tl}}^{0(+)\mathrm{}}$ and ${\mathrm{K}}^{0(+)\mathrm{}}$ passing through ${\mathrm{H}}_2$ gas. Equilibrium fractions were measured by increasing the ${\mathrm{H}}_2$ target gas density until the fraction was independent of the initial charge state. All capture and loss cross sections increased in this energy range. The equilibrium fractions were dependent only on the particle velocity and were independent of the incident-particle electronic structure.

Absolute excitation cross sections for charge transfer in 11-eV (lab) collisions between $\mathrm{He}_2^{}{}_{}{}^{+}$ ions and ${\mathrm{N}}_2$, CO, ${\mathrm{O}}_2$, and NO molecules have been determined by observing photons from the decay of excited ions formed in the collisions. The magnitudes of these cross sections are unusually large (greater than ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$) when the electron exchange process is resonant or nearly resonant. Vibrational state distributions of the product ions were also determined to be consistent with a vertical transition (Franck-Condon) model. Explanations for the large cross sections and observed state distributions are proposed.

We have determined the ratio of doubly to singly charged ions for He, Ne, and Ar caused by the impact of electrons with 2 keV energy. Special attention was given to the examination of the reliability of the apparatus with respect to its handling of differently charged ions. The results do not confirm the data of Van der Wiel et al., but they are in good agreement with those of Schram et al.

Using synchrotron radiation and a new two-grating grazing-incidence monochromator specially designed to remove higher-order components, the relative intensities of double-photoionization transitions have been measured in helium, neon, and argon between 70 and 200 eV by ion spectrometry. Extensive tests of a new ion spectrometer were undertaken to eliminate any charge discrimination for the ions. These new results resolve discrepancies existing between previous experimental data and favor, in general, the earliest results of Carlson for photon energies higher than 100 eV. For helium and neon they are in good qualitative agreement with theoretical calculations that include electron-electron correlations. In particular they agree very well with the many-body perturbation-theory approach of Chang and Poe in the case of neon.

Using a 40-cm curved muscovite mica spectrograph of the transmission (Cauchois) type, three new diagram lines at 1542.03 ± 0.01, 1537.94 ± 0.01, and 1535.80 ± 0.01 xu (${10}^{-3\mathrm{}}$ Å) have been reported in the $L$-emission spectrum of ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$. The first line corresponds to the electric dipole transition $L_3{O}_1\left({\beta }_7\right)$, and the other two correspond to the electric quadrupole transitions $L_1{M}_5\left({\beta }_9\right)$ and $L_3{O}_{2,3}$, respectively. A new nondiagram line (satellite) $L{\beta }_2^{\mathrm{II}}$ has been observed at 1551.90 ± 0.01 xu for the first time. On the basis of Wentzel's theory for the origin of high-frequency x-ray satellites, this line has been assigned to the transition $L_3{M}_3\to M_3{N}_5$. Apart from these newly observed lines, the presence of the electric dipole transitions $L_2{O}_4\left({\gamma }_6\right)$ and $L_3{O}_4\left({\beta }_5\right)$ and that of the nondiagram lines ${\alpha }^x$, ${\beta }_1^{\prime }$, ${\beta }_2^{\mathrm{I}}$, and ${\gamma }_1^{\prime }$, so far reported only by one worker, has been confirmed for the first time.

Experimental profiles of the hydrogen Balmer lines ($H_{\gamma }-H_{10}$) have been measured over the density range (2-8) × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and compared with theoretical profiles. Electron densities were measured using a multipass interferometer, while plasma homogeneity was demonstrated using a Langmuir probe. Electron temperatures were in the range 1-2.0 eV. The electron density as deduced from line profiles tended to be as much as 10% lower than that from the interferometer at higher densities. At lower densities, the two methods agreed to within experimental error. Evidence for asymmetries on the line wings was noted.

Muonic x-ray yields have been measured for Al, ${\mathrm{AlF}}_3$, ${\mathrm{AlCl}}_3$, ${\mathrm{AlI}}_3$, KCl, KBr, KI, Cd, ${\mathrm{CdF}}_2$, ${\mathrm{CdCl}}_2$, ${\mathrm{CdBr}}_2$, ${\mathrm{CdI}}_2$, Sn, ${\mathrm{SnCl}}_2$, ${\mathrm{SnCl}}_4$, Sb, ${\mathrm{SbF}}_3$, ${\mathrm{SbCl}}_3$, and ${\mathrm{SbCl}}_5$. The yields were normalized with the total intensity of the Lyman series. The capture ratios between Coulomb capture in the anion and the cation were determined for all compounds listed. These ratios are not well reproduced by the Fermi-Teller "$Z$ law." Chemical effects in the intensities were observed. All observed intensities were compared with cascade calculations assuming a modified statistical population of the levels with $n=20\mathrm{}$. In a number of cases this procedure does not yield a satisfactory reproduction of the experimental data.

Using the beam-gas method with gas-jet and doubly differentially pumped gas-cell targets, we have measured mean radiative lifetimes for several levels of ${\mathrm{Ar}}^{+}$. The levels and lifetimes in nanoseconds are as follows: for $4p{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}$, 8.28 ± 0.41; $4p{}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^o{}_{}{}^{}$, 8.40 ± 0.59; $4p{}_{}{}^4{}_{}{}^{}P_{\frac{1}{2}}^o{}_{}{}^{}$, 8.42 ± 0.42; $4p{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^o{}_{}{}^{}$, 9.23 ± 0.46; $4p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^o{}_{}{}^{}$, 9.19 ± 0.46; $4p^{\prime }{}_{}{}^2{}_{}{}^{}F_{\frac{7}{2}}^o{}_{}{}^{}$, 8.47 ± 0.42; $4p^{\prime }{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^o{}_{}{}^{}$, 4.50 ± 0.45; $4p^{\prime }{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^o{}_{}{}^{}$, 7.84 ± 0.39. The lifetimes of the $4p{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^o{}_{}{}^{}$ and $4p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^o{}_{}{}^{}$ laser levels are in excellent agreement (within 3%) with selective excitation measurements by Bennett, Kindlmann, Mercer, and Sunderland (1964-65).

We have selectively pumped the ${\mathrm{He}}_2(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}, v=0, J=5)\to {\mathrm{He}}_2(e{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}, v=0, J=6)$ transition of molecular helium with the light produced by a pulsed dye laser, and we have subsequently followed by fluorescence measurements on a nanosecond time scale both the relaxation of the electronic excitation energy and the energy redistribution among rotational sublevels of the $e{}_{}{}^3{}_{}{}^{}\Pi$ state. The radiative deexcitation rate of the upper electronic state is ${6.2\times 10}^7$ ${\sec }^{-1\mathrm{}}$; the corresponding two-body quenching rate by collisions with neutral helium atoms at 295°K is ${7.1\times 10}^{-11\mathrm{}}$ ${\mathrm{cm}}^3$${\sec }^{-1\mathrm{}}$. The total two-body rotational relaxation rate of the $J=6\mathrm{}$ level by collisions with neutrals is ${5.8\times 10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$${\sec }^{-1\mathrm{}}$. While collisions with $\Delta J=\pm 1$ account for more than 60% of total rotational transfer, it is necessary to include a substantial probability of multiquantum rotational transitions in order to explain the observed results.

The time dependence of the vacuum-uv emissions from xenon was studied at pressures ranging from 4 to 1000 Torr. Excitation of the atoms was provided by a low-intensity electron beam. Measurements were made at the wavelengths of the $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ resonance line, the 1500-Å (first) continuum, and the 1700-Å (second) continuum. Two- and three-body collision coefficients for the destruction of $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms and a three-body coefficient for $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ metastables were determined. A radiative lifetime of 99 nsec for the $1_u$ molecular state was measured at the wavelength of the second continuum. The pressure dependence of the decay constants at the three wavelengths leads to the following results: The collisional deexcitation rate for the transition $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ to $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ is ${9.1\times 10}^3$ ${\sec }^{-1\mathrm{}}$/Torr. The three-body coefficient for $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms is 46 ${\sec }^{-1\mathrm{}}$/${\mathrm{Torr}}^2$. The three-body destruction rate of $\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ metastables is 40 ${\sec }^{-1\mathrm{}}$/${\mathrm{Torr}}^2$. The estimated uncertainty in the results is ±10%.

Numerical results of angular electron pair-production cross sections are given for the $\gamma$-ray sources ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Tl}$. Cross sections are obtained analytically for a point-Coulomb potential, using an exact partial-wave formulation. Angular distributions are essentially unaffected in shape by the screening effects, as shown by Tseng and Pratt's calculations, so our curves can be useful to experimentalists. Moreover, they are computed at the tip region of the spectrum where screening effects are almost negligible.

The "mean frequency" technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the "mean frequency" lies near certain integers.

The photoionization cross section of HI was measured at 19 wavelength points from 910 to 609 Å with experimental uncertainties between 7 and 20%. An aerodynamic shock tube, equipped with explosively driven shutters, was used to produce fully dissociated hydrogen and neon gas mixtures for the photoabsorption measurements. A description of the new shock-tube facility and a discussion of the experimental techniques are presented. Since our results agree with well-established theory, the reliability of our apparatus and methods for making measurements of this kind has been demonstrated. The measurement is the first in a continuing program to measure the photoionization cross sections of HI, OI, CI, and NI.

We report the first detailed studies of high-resolution Doppler-free two-photon absorption in molecular systems. The ${\nu }_3$ vibrational bands in ${}_{}{}^{12}{}_{}{}^{}\mathrm{CH}_3^{}{}_{}{}^{}$F are studied using two fixed-frequency infrared optical fields in combination with molecular Stark tuning. These measurements are used to formulate definite conclusions concerning the free-system properties and collisional interactions in the ${\nu }_3$ vibrational manifold. Specifically, the near coincidences of the $P14\mathrm{}$ and $P30\mathrm{}$ lines of two oppositely directed cw ${\mathrm{CO}}_2$ lasers at 9.6 μm with the $R{\mathrm{}(1,1)\mathrm{}}_{0\to {\nu }_3}$ and the $R{\mathrm{}(2,1)\mathrm{}}_{{\nu }_3\to 2{\nu }_3}$ lines in ${}_{}{}^{12}{}_{}{}^{}\mathrm{CH}_2^{}{}_{}{}^{}$F are used to determine the following properties: (1) precise transition energies for the $({\nu }_3,J,K)=(0,1,1)\mathrm{}\to \mathrm{}(2,3,1)\mathrm{}$ two-photon transition, (2) pressure-broadening coefficients, and (3) pressure-shift parameters. Finally, the influence of polarization on the properties of the two-photon signal amplitude is examined.

Detailed studies involving high-resolution Doppler-free two-photon spectroscopic measurements of the ${\nu }_2$ vibrational bands in ${}_{}{}^{14}{}_{}{}^{}\mathrm{NH}_3^{}{}_{}{}^{}$ are presented. Using the technique of combining fixed-frequency ir sources with molecular Stark tuning presented in the preceding paper, we have used two successive $Q(5,4)\mathrm{}$ vibrational-rotational transitions to study the spectroscopic and collisional properties of the ${\nu }_2$ vibrational manifold. We report (1) precise transition energies for the $({\nu }_2,J,K)=(0^{-},5,4)\to (2^{-},5,4)$ two-photon transition, (2) pressure-broadening and pressure-shift data, (3) optical Stark shift parameters, and (4) excited-state transition matrix elements. An observation of collisional narrowing arising from ${}_{}{}^{14}{}_{}{}^{}\mathrm{NH}_3^{}{}_{}{}^{}$-Ne collisions is also reported.

Atomic vapors of Ca, Sr, Ba, Zn, Cd, and Hg were studied by photoelectron spectroscopy in a special high-temperature cell using He I (and in some cases Ne I or He II) resonance radiation. In addition to strong lines obtained by photoemission from the nominal $n{s}^2+(n-1\mathrm{})\mathrm{}{d}^{10}n{s}^2$ configurations, weaker lines were observed that are attributed to admixtures of the configurations $n{p}^2$, $\mathrm{}(n-1\mathrm{})\mathrm{}{d}^2$, etc. (in group-IIA elements) or $n{p}^2$, in group-IIB elements, into the ground state. In the group-IIA cases, the satellite intensities are consistent with expectations based on multiconfiguration Hartree-Fock results. Photoelectron spectroscopy thus appears to provide incisive information about the details of electron correlations in these atoms. Intensity ratios of spinorbit partners fall near the multiplicity ratios in Zn and Cd, but deviate in Hg due to relativistic effects, in agreement with expectations based on earlier work.

The use of the random-phase approximation with exchange (RPAE) for calculating partial and total photoionization cross sections and photoelectron angular distributions for open-shell atoms is examined for atomic chlorine. Whereas the RPAE corrections in argon ($Z=18\mathrm{}$) are large, we find those in chlorine ($Z=17\mathrm{}$) to be much smaller due to geometric factors. Hartree-Fock calculations with and without core relaxation are also presented. Sizable deviations from the close-coupling results of Conneely are found.