X-ray photoelectron spectroscopy (XPS) is used to measure splittings of metal-atom electron binding energies in both inorganic solids and gases. These splittings are due to the various possible multiplet states formed by coupling a hole in a metal-atom subshell to an unfilled valence subshell. Splittings are observed in various solids containing $3d$-series atoms. In particular, the $3s$ binding energy is split into a doublet with as much as 7.0-eV separation between the two components. The instrumental resolution is ∼ 1.0 eV. $3s$ splittings are exhibited by inorganic compounds containing Mn and Fe, as well as by Fe metal, Co metal, and Ni metal. Theoretical predictions are in good agreement with experiment, provided that the effects of covalency in chemical bonding are taken into account. For Fe metal, the $3s$ splitting is identical both above and below the Curie point. The $3p$ binding energies of these solids also appear to show multiplet effects, but the interpretation of these results is less straight-forward. The $2p$ binding energies in Mn${\mathrm{F}}_2$ are broadened by at least 1.3 eV, and this is shown to be consistent with multiplet splitting. XPS results for gaseous monatomic Eu also indicate the presence of multiplet splittings. The two components in the $4d$ photoelectron spectrum are found to have an intensity ratio in disagreement with observed ratios for neighboring atoms with filled valence subshells. Also, the width of the $4f$ photoelectron peak above the instrumental contribution can be explained in terms of multiplet effects.

The $\frac{K{\alpha }_2}{K{\alpha }_1}$ transition probabilities have been measured for 22 elements ranging in atomic number from ${}_{21}{}^{}{}_{}{}^{}\mathrm{Sc}$ to ${}_{50}{}^{}{}_{}{}^{}\mathrm{Sn}$, with an estimated error of about 2%. This has been accomplished by bombarding the elements with an electron beam of constant energy, and studying the x-ray emission spectrum. The measured ratios rise gently above the classical limit as the atomic number increases, in contrast to the dip below this limit previously reported for $30\le Z\le 40$. For $Z\ge 30$, the experimental results are in excellent agreement with recent calculations based on the relativistic Hartree-Slater potential. For $Z\le 30$, although experimental results agree with theoretical calculations to within experimental error, they tend to be lower.

The observed behavior of the shift of the third- and higher-member lines (up to the 25th member) of the Cs principal series produced under various pressures (up to a relative density of ∼6) of all rare gases is described. A comparison of the shifts of various lines was made. The red shifts of Cs(3) and Cs(4) are nearly the same for Ar, Kr, and Xe when the relative density (rd) is below 0.6 and become increasingly different when the rd is increased. For He and Ne, the blue shift of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ component of Cs(3) is greater than that of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ component, while for Cs(4) the shift is greater, although the difference in shift of the two doublet components is much reduced. The slopes of the plots of the asymptotic values of shifts for high-member lines versus rd are 5.85, 0.366, -10.04, -19.6, and -35.0 ${\mathrm{cm}}^{-1\mathrm{}}$/rd for He, Ne, Ar, Kr, and Xe, respectively.

The diamagnetic susceptibilities of all free atoms up to $Z=103\mathrm{}$ are calculated within the nonrelativistic and relativistic numerical Hartree-Fock approximations. Relativistic calculations are also performed for certain ions. The use of Dirac self-consistent wave functions leads to lower calculated susceptibilities. This effect becomes appreciable at very large atomic numbers; e.g., in uranium a decrease of 12.3% below the nonrelativistic value is found. For the case of the rare gases, the Hartree-Fock diamagnetic susceptibilities are found to lie above the experimental values. This is attributed to the omitted effects of electron correlation. For the noble and divalent metals, the calculated atomic-core diamagnetic susceptibilities lie above the experimental metallic values, since we have not included the paramagnetism of the conduction electrons.

The level-crossing technique has been used to measure the hyperfine structure of 47-day ${\mathrm{Hg}}^{203}$ and to remeasure the $g_J$ value of ${\mathrm{Hg}}^{199}$ in the $\mathrm{}\left(6s6p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ atomic state. The results, corrected for second-order perturbations arising from other fine-structure levels of the configuration, are $A=4991.\mathrm{}35\left(3\right)\mathrm{}$ MHz, $B=-249.\mathrm{}2\left(3\right)\mathrm{}$ MHz, $g_J=1.\mathrm{}486110\left(9\right)\mathrm{}$, and $\frac{A\left({\mathrm{Hg}}^{203}\right)}{A\left({\mathrm{Hg}}^{199}\right)}=0.\mathrm{}338301\left(2\right)\mathrm{}$. With these values, we calculate the nuclear moments $\mu =0.\mathrm{}856\left(9\right)\mathrm{}{\mu }_N$ and $Q=0.\mathrm{}46\left(4\right)\mathrm{}$ b. The value of $\mu$ includes a diamagnetic correction but not the calculated effect of the ${\mathrm{Hg}}^{199}$-${\mathrm{Hg}}^{203}$ hfs anomaly, ${}_{}{}^{203}{}_{}{}^{}\Delta _{}^{199}{}_{}{}^{}\approx -0.\mathrm{}91\%$. The error brackets for $\mu$ and the hfs interaction constants allow for a hfs anomaly of ±1%. The value of $Q$ does not include the Sternheimer correction. Formulas are given for the dependence on geometry and polarization of level-crossing signals, and a method of correction for asymmetric line shapes is described. The influence of variation, over a large range, of $\frac{B}{A}$ on the magnetic field positions of the level crossings for $J=1\mathrm{}$ has been studied. For $A=0\mathrm{}$ and neglecting the $g_I$ term in the Hamiltonian, the energy displacement from the "center of gravity" and the magnetic field position of the single level crossing are shown to be ${\sigma }_c=-\frac{A}{2}$, and $H_c=\frac{\mathrm{}(2I+1)\mathrm{}\left|A\right|\mathrm{}}{2{\mu }_B{g}_J}$, respectively.

Profiles of the overlapping fine-structure components of C II and N II vacuum ultraviolet resonance lines emitted from optically thick shock-heated layers consisting mostly of helium were measured on a shot-to-shot basis, using a $T$-type electromagnetic shock tube as a source. Plasma conditions were determined from spectroscopic measurements in the visible region. The analysis was based on a radiative transfer model for the resonance multiplets, assuming superimposed Lorentzian profiles with known oscillator strengths and the existence of local thermodynamic equilibrium. The resulting damping constants are interpreted as due mainly to elastic electron collisions and agree within factors of ∼ 1.0 and ∼ 1.5, respectively, with predictions based on a semiempirical method.

The mobilities of the ${\mathrm{He}}^{+}$ and $\mathrm{He}_2^{}{}_{}{}^{+}$ ions in helium were measured as a function of $\frac{E}{n}$ and gas temperature for $T=300-76\mathrm{}$ °K. At temperatures below 200 °K and at very low $\frac{E}{n}$, conversion of the $\mathrm{He}_2^{}{}_{}{}^{+}$ to $\mathrm{He}_3^{}{}_{}{}^{+}$ was observed to take place. Mobilities of $\mathrm{He}_3^{}{}_{}{}^{+}$ were determined at 115 and 76 °K. The zero-field mobility of ${\mathrm{He}}^{+}$ was found to increase with decreasing temperature and was in excellent agreement with the theoretical predictions of Dickinson. Both the $\mathrm{He}_2^{}{}_{}{}^{+}$ and $\mathrm{He}_3^{}{}_{}{}^{+}$ mobilities decreased with decreasing temperature. The $\mathrm{He}_2^{}{}_{}{}^{+}$ mobilities were all significantly lower than the Langevin polarization limit, and were lower even than the mobilities of the heavier $\mathrm{He}_3^{}{}_{}{}^{+}$ ion.

It is pointed out that the phenomenon of satellites of spectral lines is attributable to the breakdown of the Born-Oppenheimer approximation in the upper state of the collision-pair molecule owing to the proximity or crossing of molecular potential curves of the same symmetry. The Fano treatment of the configuration interaction between a single bound level and a continuum in conjunction with certain simple models for the potential curves yields an analytical expression for the intensity in the near wing of the spectral lines. The distant blue satellites may be shown to arise from the interaction with a second bound vibrational level. Combinations and variations of these two possibilities lead to cases typical of those which have been observed.

An analogy between the laser threshold region and a second-order phase transition is presented. The electric field acts as the order parameter for the laser while the atomic-population inversion plays the role of a temperature. The quantum-statistical theory of a laser including a symmetry-breaking external signal is discussed in order to establish a correspondence with the problem of a ferromagnet (treated in the molecular-field approximation) situated in an externally applied magnetic field. It is demonstrated that the results of the laser analysis may be discussed in terms of an energy function which is similar to the free energy of a thermodynamic system.

The infrared vibration-rotation transitions ${\nu }_2\left[{}_{}{}^q{}_{}{}^{}Q_{-}^{}{}_{}{}^{}\mathrm{}\right(8,7\left)\right]$ of ${}_{}{}^{14}{}_{}{}^{}\mathrm{NH}_3^{}{}_{}{}^{}$ and ${\nu }_2\left[{}_{}{}^q{}_{}{}^{}Q_{-}^{}{}_{}{}^{}\mathrm{}\right(4,4\left)\right]$ of ${}_{}{}^{15}{}_{}{}^{}\mathrm{NH}_3^{}{}_{}{}^{}$ have been pumped by the $P\left(13\right)\mathrm{}$ and $P\left(15\right)\mathrm{}$ lines, respectively, of an ${\mathrm{N}}_2$O laser, and the resulting changes in the molecular populations of the rotational levels have been monitored by observing the microwave inversion lines. Large variations of the intensities of the monitored lines have been observed. In addition, small variations of neighboring inversion lines due to collision-induced transitions have also been found. The dependence of the efficiency of pumping on the frequency difference between the laser line and the N${\mathrm{H}}_3$ absorption line (which was varied by using a Stark field) and on the pressure of the sample was studied. The results can be explained by using Karplus and Schwinger's theory of saturation and by taking into account a "hole burning" on the Doppler profile of the absorption line.

The transfer of excitation in a dimer is treated as a resonance, using Feshbach's nuclear reaction formalism. The radiation field-matter interaction is treated simultaneously with the intermonomeric potential. This gives a unified point of view and allows one to see what the interference effects are. The Förster vibrational-relaxation mechanism and the Frenkel exciton are studied for the dimers, and explicit expressions for the decay probability are obtained.

The mean life of the metastable $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of the ${\mathrm{O}}^{6+}$ ion has been determined by measuring the decay length of the $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{} (\lambda 21.8)$ radiation emerging from a 20-MeV beam of highly stripped oxygen ions. The result is ${\tau }^{-1\mathrm{}}=(6.6\mathrm{}\pm 0.5)\times {10}^8$ ${\sec }^{-1\mathrm{}}$ which compares favorably with our earlier measurement of (6 ± 1) × ${10}^8$ ${\sec }^{-1\mathrm{}}$. Mixing of singlet levels above $n=2\mathrm{}$, a feature of some recent calculations of this lifetime, is needed to bring about overlap of theoretical and experimental results. Additional information concerning excitation of one- and two- electron ions in such beams is presented.

We attempt to overcome one of the shortcomings in the Thomas-Fermi and related theories for atoms by connecting a quantum-mechanical electron density for the region near the nucleus to a density given by a statistical model. The joining may be done in a nonarbitrary manner: All parameters are determined. It suffices to use a very crude and easily calculated approximation to the density to start with, so the calculation is quite easy. The resulting electron density is in much better agreement with reality than that from the unmodified theories.

A center-of-mass-transformed Hamiltonian is used to study the molecular structure of methane, ammonia, and water, where the protons as well as the electrons are described by Slater determinants of one-particle Slater functions. The matrix elements of the Hamiltonian are given for a wave function constructed from a product between a sum of Slater determinants for the electrons and a sum of Slater determinants for the protons. The ground states of the protons were the ${}_{}{}^5{}_{}{}^{}S$ multiplet of the $s{p}^3$ configuration at -39.137 64 hartrees for methane, the ${}_{}{}^4{}_{}{}^{}P$ multiplet of the $s{p}^2$ configuration at -55.445 22 hartrees for ammonia, and the ${}_{}{}^3{}_{}{}^{}P$ multiplet of the $\mathrm{sp}$ configuration at -75.500 05 hartrees for water. The energies of the other protonic multiplets of the above configurations are given also, as are the energies of the protonic multiplet of the $s^2{p}^2$ and $p^4$ configurations in methane, of the $s^{2}p$ and $p^3$ configurations in ammonia, and of the $s^2$ and $p^2$ configurations in water. The errors in the wave functions are discussed.

A variational generalization of Brueckner's theory has been applied to the calculation of hyperfine parameters for the ${}_{}{}^2{}_{}{}^{}P$ ground state of atomic boron. The computational method makes use of a hierarchy of $n$th-order (or $n$-particle) variational Bethe-Goldstone equations defined in terms of configurational excitations of a Hartree-Fock reference state. Hyperfine parameters are computed as the sum of net increments defined at each level of the hierarchy. Orbital basis sets are extrapolated to practical completeness for each one- and two-particle net increment. Three-particle net increments are found to be small but not negligible. Computed magnetic hyperfine constants are within roughly 1% of experiment. The electric field gradient is computed, and its relative accuracy is estimated from that of the magnetic hyperfine constants. Combined with experimental quadrupole coupling constants, this implies values of the nuclear quadrupole moments $Q\left({\mathrm{B}}^{10}\right)=0.\mathrm{}08472\mathrm{}\left(56\right)\mathrm{}$ b and $Q\left({\mathrm{B}}^{11}\right)=0.\mathrm{}04065\mathrm{}\left(26\right)\mathrm{}$ b, with the indicated precision.

Measurements have been made of the hyperfine structure (hfs) constants and lifetimes of the first and second ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of the stable alkali atoms, except lithium, using the pure magnetic field level-crossing technique. The results for ${\mathrm{Na}}^{23}$ are

The results for ${\mathrm{K}}^{39}$ have been reported previously. For ${\mathrm{Rb}}^{85}$ and ${\mathrm{Cs}}^{133}$, hfs constants were obtained that agreed with, but were less accurate than, previous work. The measured life-times are

The error limits in these measurements are two standard deviations. The above results were obtained by fitting the observed level-crossing signal to a theoretical line shape computed from the Breit formula, using $a$, $b$, and $\tau$ as parameters.

The criteria for applicability of a full contact transformation are examined. Comments are made on the relation between the Rayleigh-Schrödinger and contact-transformation perturbation representations. The analysis is based upon the use of a Hermitian operator defined as a commutator with the zero-order Hamiltonian and upon the use of the Fock representation. The methods are developed in the context of the vibrational Hamiltonian.

The Holstein-Biberman integrodifferential equation for the transport of resonance radiation has been solved for a gas contained in a long cylindrical container. The solution involves the following assumptions: (i) The excited atoms are initially distributed uniformly along the axis of the cylinder; (ii) the pressure and temperature of the gas are such that the absorption coefficient has either a pure Doppler-broadened or a pure pressure-broadened profile; (iii) the radius of the cylinder corresponds to many optical depths at the frequency corresponding to the maximum of the absorption coefficient. It is also shown that steady-state solutions corresponding to a line source along the axis of the cylinder can be calculated by the same procedure. The geometry and the initial conditions considered here are of particular interest because the situation can be simulated experimentally. Hurst and Thonnard have pointed out that an approximate line of excited atoms can be produced by sending a well-collimated pulse of protons or electrons down the axis of a long cylinder containing the gas of interest. The present paper also considers the decay of resonance radiation from a steady state built up by a line source. The latter situation is even easier to arrange experimentally. All experimental work to date has concerned itself with situations where the initial distribution of excited atoms is not known, and theory and experiment can only be compared at times which are large enough so that the system has decayed to its lowest eigenmode.

The spin-polarized (SPHF) and unrestricted (UHF) Hartree-Fock equations are solved for the lowest ${}_{}{}^2{}_{}{}^{}P$ states of Li and B. The orbitals are not symmetry adapted with respect to ${\overrightarrow{\mathrm{l}}}^2$ in the UHF approximation for these states. The most important admixture, and the only one that has been taken into account here, is $d_0$ admixture into the $s$ orbitals. The UHF determinant is not an eigenfunction of ${\overrightarrow{\mathrm{L}}}^2$ and ${\overrightarrow{\mathrm{S}}}^2$. Various aspects of this fact are pointed out and discussed. The admixture of $d$ character into the orbitals will depend heavily on exchange. It will lead to substantial corrections to hyperfine-structure expectation values. The results agree well with Sternheimer's for the quadrupole terms for B and Li. For the spin dipolar term, the results agree with the first-order perturbation-theory results of Lyons et al. for Li and with the "polarization function" results of Schaefer et al. for B. Configuration interaction and second-order perturbation-theory results are also discussed in this connection.