Cross sections have been calculated for the Penning ionization of ground-state sodium atoms in collisions with metastable He(2 ${}_{}{}^1{}_{}{}^{}$,3S) atoms for the range of center-of-mass energies 0.01 eV ≤E≤1.0 eV. The cross sections were calculated with use of optical-model potentials. The real parts of the relevant potential-energy curves were determined by carrying out a configuration-interaction (CI) calculation on the NaHe molecule. The potentials were adjusted to yield the correct asymptotic van der Waals form. The imaginary parts of the potentials correspond to autoionization rates and were obtained from a Stieltjes moment analysis of a discrete ($L^2$) representation of the $e^{\mathrm{-}}$+${\mathrm{NaHe}}^{+}$ continuum, as represented by diffuse molecular orbitals generated by the CI procedure. The calculated cross section for He(2 ${}_{}{}^3{}_{}{}^{}S$) on Na at E=0.04 eV is in good agreement with stationary-afterglow measurements at room temperature. The singlet-to-triplet ratio of cross sections is in good agreement with that measured by beam techniques. Elastic differential cross sections for He(2 ${}_{}{}^1{}_{}{}^{}S$) scattered from Na have also been calculated. Satisfactory agreement is obtained with recent crossed-beam measurements.

Accurate measurements of the 1000-eV noncoplanar symmetric (e,2e) reaction on argon are reported. Cross-section calculations are carried out with use of both the plane-wave and distorted-wave impulse approximations. The distorted-wave impulse approximation describes accurately both the 3p and 3s angular correlations and their relative cross sections. The plane-wave impulse approximation overestimates the 3s cross section relative to the 3p and underestimates cross sections at large angles. The 3s spectroscopic factors are assigned up to a separation energy of 55 eV and the distorted-wave impulse calculation verifies that all the 3s strength has been found.

Optical-optical double-resonance photofragment spectroscopy of molecular ions is, for the first time, performed with a Doppler-limited resolution of 0.003 ${\mathrm{cm}}^{\mathrm{-}1}$. The high resolution allows the observation of perturbations in the b${\mathrm{}}^4$${\Sigma }_g^{\mathrm{-}}$ state arising from a vibrationally excited level in the d${\mathrm{}}^4$${\Sigma }_g^{+}$ state lying only 29 ${\mathrm{cm}}^{\mathrm{-}1}$ below the predissociation limit. The matrix element for the interaction between the b and d states is obtained from a perturbation analysis and is used to estimate the contribution of the d state to the predissociation of the b state. Precise effective Hamiltonians are reported for the a${\mathrm{}}^4$${\Pi }_u$(v’’=4,5) and b${\mathrm{}}^4$${\Sigma }_g^{\mathrm{-}}$(v’=4) states.

A beam-foil study of the lithium spectrum above 5000 Å has been undertaken. Four new observations of core-excited doublet transitions are reported. All of these transitions have autoionizing states as the final state. The autoionization width of the (1s2s ${}^3$S)3d ${}^2$D has been measured, yielding a value of 0.89±0.04 meV. A comparison with calculations of the term energies and the width is presented.

Relativistic computations of $L_1$-MM, $L_2$-MM, and $L_3$-MM Auger spectra have been carried out in the intermediate coupling with configuration interaction for a final two-hole state and j-j coupling for an initial state. Results for ten elements with 18≤Z≤92 are listed and compared with experimental data. Good agreement with the scarce experimental data is attained. The effect of correlation is shown to shift some of the Auger energies by as much as ∼15 eV. The effect of final-ionic-state configuration interaction is found to increase the $L_3$-$M_1$$M_1$ rate by a factor of ∼2 for Z≤45. Intermediate coupling is necessary to analyze the L-MM Auger spectra for 30≤Z≤80. As in the case of K-$M_1$$M_4$,5 transition calculated $L_1$-$M_3$$M_3$${(\mathrm{}}^3$$P_2$) and $L_3$-$M_1$$M_4$,5 intensities as functions of Z are found to peak sharply in the neighborhood of Z=63 due to the strong level-crossing interaction. This interaction is found to increase the $L_1$-$M_3$$M_3$${(\mathrm{}}^3$$P_2$) intensity at Z=60 by a factor of 50.

The squares of the dipole and quadrupole matrix elements for the free-to-bound transitions of hydrogen up to bound states ‖n=20,l=19〉 are derived in closed analytic form as a function of the kinetic energy of the free electron. Coulomb wave functions are used for the free as well as the bound states and, thus, the results are good for any electron energy. Several interesting effects are found. First, the transition probabilities are maximum for recombination into specific intermediate-angular-momentum states at low energies (w<1 eV) and where the free-state angular momentum is greater than that of the bound state. Further, that specific intermediate-angular-momentum state depends on the kinetic energy of the free electron. This behavior is in contrast to the ‘‘normal’’ behavior of the transition strengths where recombination into s states is greatest and decreases with increasing angular momentum. Second, the quadrupole matrix elements vanish for certain velocities of the free electron. These ‘‘zeros’’ produce minima in the corresponding quadrupole cross sections. Finally, the calculated partial cross sections for recombination into high-angular-momentum states are greater when quadrupole transitions are included.

We have studied in detail the ionization and population of high-lying atomic states which occur in cesium vapor excited at the second resonance transition, 6S-7P. We have developed a simple model which qualitatively explains the laser-power dependences of level populations and electron densities which we observed. Measurements of spatial dependences of fluorescence point out the critical role of radiation trapping in these phenomena. Similar observations on rubidium demonstrate the same type of behavior when the first (5S-5P) or second (5S-6P) resonance is excited. At higher densities and temperatures we found that the fluorescence was dominated by diffuse molecular bands. Some of these bands probably consist of transitions to the repulsive ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state. Additionally four bands observed at 817.5, 826.6, 835.3, and 839.6 nm are tentatively identified as the cesium analog of the ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$${\to }^3$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$ satellite bands which have previously been observed in the blue wing of the first resonance doublet of the lighter alkali metals.

Kircz, Morgenstern, and Nienhuis [Phys. Rev. Lett. 48, 610 (1982)] have measured the cross section for the associative ionization of partially oriented pairs of excited [(3p) ${}_{}{}^2{}_{}{}^{}P_{3/2}^{}{}_{}{}^{}$] sodium atoms. Here, we extract information from these data about the identities of the participating adiabatic Born-Oppenheimer states of ${\mathrm{Na}}_2$. It is definitely established that more than one of these states is involved. The greatest contributor is the X ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state with the dominant molecular-orbital configuration ${\sigma }_g^2$ (at small internuclear separations). It is highly probable that only one other state (either the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ or ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{\mathrm{-}}{}_{}{}^{}$ state with the dominant molecular-orbital configuration ${\pi }_u^2$) is involved, but a small contribution from one state ${(}^1$${\Pi }_u$ or ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$) with the configuration ${\sigma }_g$${\pi }_u$ cannot be unequivocally dismissed.

We describe the first comprehensive measurements of the energy distribution, branching ratios, and angular distributions of electrons ejected from Ba i [6$p_{1/2}$ ${}_{\mathrm{}(3/2)\mathrm{}}{}^{}{}_{}{}^{}\mathrm{ns}_{1/2}^{}{}_{}{}^{}$${]}_{\mathrm{J}=1\mathrm{}}$ states in their autoionization to the Ba ii 6s, 5d, and 6p ion states. These measurements are made using a stepwise laser excitation scheme, which results in excitation of only the bound part of the autoionizing states. Furthermore, the laser excitation of these autoionizing states through the spherically symmetric Ba i 6sns ${}^1$$S_0$ intermediate states results in simplified electron angular distributions. We find that the Ba i [6$p_{1/2}$ ${}_{\mathrm{}(3/2)\mathrm{}}{}^{}{}_{}{}^{}\mathrm{ns}_{1/2}^{}{}_{}{}^{}$${]}_{J=1\mathrm{}}$ states autoionize predominantly to an excited state of the ${\mathrm{Ba}}^{+}$ ion. The interaction between the Ba i [6$p_{1/2}$${\mathrm{ns}}_{1/2}$${]}_{J=1\mathrm{}}$ and the Ba i [6$p_{3/2}$${\mathrm{ns}}_{1/2}$${]}_{J=1\mathrm{}}$ series manifests itself in the sharp variation in the electron asymmetry parameter β near the neighborhood of the interaction. We also present a simple analysis of our results incorporating the multichannel quantum-defect theory.

A novel theory of the electric dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, or DT) is formulated, such that electrical asymmetry and the resulting dipole moment arise as purely electronic properties within a suitable Born-Oppenheimer approximation, and nonadiabatic (rovibronic) perturbations play no part in the theory. It is shown thereby that a much simpler and more direct explanation for these dipole moments can be given than that invoking non- adiabatic perturbations: The dipole moment arises from isotopic variation of the local effective electronic reduced mass and its effects on binding energies and sizes of orbitals. It is an odd function of the isotopic splitting parameter ${\alpha }_0$=(1/2)λm/μ, where λ=($M_A$-$M_B$)/($M_A$+$M_B$) is the nuclear mass asymmetry for nuclei A,B and (m/μ) is the electron-nuclear mass ratio (for HD, this parameter is 1.36×${10}^{\mathrm{-}4}$). A canonical transformation exhibiting these effects (in the form of an asymmetric effective potential) is the basis for the new formulation. Since ${\alpha }_0$ is small the resulting dipole moment function is essentially linear in ${\alpha }_0$, and hence the dipole moment functions for HT and DT may be computed by rescaling the results for HD. Since the problem is purely electronic in the new formulation, variational and convergence studies are easy to carry out. In this and the following paper we formulate the new theory in detail and carry out variation-perturbation calculations of the HD dipole moment. The results are in good agreement with theoretical results obtained by nonadiabatic perturbation theory and demonstrate that this approach to isotopically induced dipole moments is valid.

A formalism is developed for the angular distribution of two electrons in an Auger cascade. The formalism is applied to a coincidence measurement on the $L_1$-$L_2$,3${\mathrm{M}}_{\mathrm{i}}$-$M_i$$M_J$Mk cascades in argon. The motivation for this study is the possibility of using such a cascade measurement in ${}^1$${}_{67}^{63}$Ho to detect a nonzero neutrino mass. The cascade calculation in Ho is currently sufficiently unmanageable that a simpler calculation in Yb was performed. The latter calculation indicates that the angular anisotropy is on the order of 25% when reasonable assumptions on experimental detector parameters are made. This is comparable to the angular anisotropy calculated for a similar transition in Ar with similar experimental detector parameters.

The noniterative eigenchannel R-matrix method is used to study the properties of the valence electrons in Be and Mg ${}_{}{}^1{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ states. Our results detail the evolution of electron correlations as a function of energy. Besides obtaining an improved quantitative description of doubly excited states in these atoms, we verify the conclusion of an earlier hyperspherical-coordinate study that the wave functions are exact analogs of the sp+ and sp- states of helium and ${\mathrm{H}}^{\mathrm{-}}$. .AE

By analyzing the measured spin-relaxation transients of ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ nuclear spins and alkali-metal-atomic spins in mixtures of alkali-metal-atom vapors, Xe gas, and larger amounts of ${\mathrm{N}}_2$ gas, we have determined the three-body formation rates and the spin-transfer probabilities for alkali- metal–noble-gas van der Waals molecules. Three parameters, in addition to the spin quantum numbers of the alkali-metal and noble-gas nuclei, are needed to predict the spin-transfer rates. These parameters, which we have determined from experimental measurements, are x=γN/α, the ratio of the spin-rotation interaction γN to the spin-exchange interaction α; $p_0$, the third-body pressure for which the molecular breakup rate ${\tau }^{\mathrm{-}1}$ is equal to the spin-rotation frequency γN/h; and Z, the three-body rate constant for forming van der Waals molecules.

It is shown how certain classes of problems dealing with the interaction of radiation with atoms can be formulated in terms of four-operator perturbation series. The case of an isolated atom coupled to a single-mode field is discussed in detail within the resolvent formalism. The process where no photon is effectively absorbed by the atom is described, to all orders, in terms of a series involving four operators which simultaneously increase and/or decrease the photon number and the orbital quantum number. This series is exactly summed and the summation technique is generalized to single-atom, two-field and to two-atom, single-field systems exhibiting zero, one, and two net photon absorptions or emissions. The theory is applied to induced emission of a single photon from a pair of two-level atoms coupled to a monomode radiation field. The energy diagrams, the time dependence of the probability, and the resonance curves are discussed for systems where (i) both atoms are in the upper state and (ii) atom 1 is in the upper state and atom 2 is in the lower state at t=0. In comparing these results to the ones obtained with a single atom, we find that the important intensity-dependent correlations give rise to trapping effects even when the atoms are initially in the upper state.

The zero-core-contribution model was used to calculate (1) the absolute total photodetachment cross sections as a function of photon energies and (2) the intensities for individual detachment channels for thirteen transition-metal anions at a fixed photon energy. A unique character of each transition-metal anion is that the photodetachment could occur involving either an ‘‘s’’ or a ‘‘d’’ outermost electron. A method for determining the relative weights of the s and the d detachment orbitals is presented. The intensities calculated for different channels are in excellent agreement with photoelectron-spectroscopy measurements, both for channels involving s-orbital detachment and d-orbital detachment. Total cross sections agree with the experimental results of Feldman et al.

Numerous KLL Auger transition energies for C ii, C iii, and C iv have been calculated using the saddle-point variational method and the unrestricted Hartree-Fock self-consistent-field technique. For Li-like C iv resonances, relativistic corrections are made. The theoretical energy for the C iv (1s2s2p${)}^4$$P^o$ state is calculated to high accuracy by means of a multiconfiguration-interaction wave function and by taking relativistic and mass polarization effects into account. The ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ channel energy is then used as a calibration point of the high-resolution carbon Auger spectra reported by Ro/dbro, Bruch, and Bisgaard. Generally, excellent agreement is found between our theoretical results and experimental data. A number of carbon Auger lines have been identified for the first time.

Stark broadening parameters for neutral-helium lines obtained using a semiclassical perturbation formalism are compared with critically selected experimental data. Our data are also compared with the results of Benett and Griem as well as with the semiclassical convergent calculations of Bassalo, Cattani, and Walder.

Angular distributions are reported for energy-resolved electrons obtained by resonance-enhanced multiphoton ionization of alkaline-earth atoms through excited intermediate valence states. The angular distributions are measured as functions of the independently variable polarizations of the exciting and ionizing laser beams. This report treats the following states, resonantly formed and photoionized: Ca(4s4p) ${}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$, Sr(5s5p) ${}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$, Sr(5s5p) ${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$, Ba(6s6p) ${}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$, and Ba(6s6p) ${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$. Systematic behavior in the resulting photoelectron angular distributions is explored. The effects of the hyperfine interaction are apparent.

This paper discusses the properties of a periodically dithered-ring-laser gyroscope in the approximation of a single phase-locking equation. We discuss both modulation of the input rotation, the phase of the backscattering, and its amplitude. The first two are found to be mathematically equivalent, and the last case is found to offer no advantages as compared with the undithered case. These conclusions are supported by a heuristic argument. The detailed mathematical treatment is based on Floquet theory, which allows us to obtain results by integrating over one dither period only. The locking condition can be determined from the Floquet exponent. For large input parameters the integration of the differential equation for the Floquet problem becomes numerically overwhelming, and the equivalent formulation in terms of an infinite matrix is utilized. This is evaluated using a method based on matrix continued fractions. In this way no restrictions on the parameters are necessary. The method is applied to the single-frequency dithering, and it is confirmed that the locking at zero rotation rate can be completely eliminated. The calculations also confirm the existence of higher-order lock-in zones, which are large just in those conditions which are optimal near zero rotation rate. Thus we conclude that with sinusoidal dither of one frequency it is not possible to avoid nonlinearities in the gyroscope response. In forthcoming publications we intend to discuss possible schemes to overcome this difficulty.

It is shown that the states produced from the vacuum by subharmonic- and harmonic-generation processes are nonclassical for all times. This is a consequence of the Manley-Rowe relations. The stability of the nonclassical nature of these states under small perturbations (such as noise) is also discussed.