A Doppler-tuned ${\mathrm{CO}}_2$ laser was used to excite n=10 to n=27 Rydberg-Rydberg transitions in a fast beam of atomic nitrogen. The fine structure of n=10, L=3–8 Rydberg levels is partially resolved in the spectrum, giving experimental information about nitrogen Rydberg levels with L≳4. The observed fine structure is well described by an effective potential whose empirical coefficients are adjusted to fit the data, giving estimates of the quadrupole moment and dipole polarizabilities of ${\mathrm{N}}^{+}$. For the highest-L n=27 levels studied, the spectrum shows evidence of a transition to a new coupling regime where the ${\mathrm{N}}^{+}$ hyperfine structure is larger than the Rydberg fine structure. © 1996 The American Physical Society.

The 3d photoabsorption spectra of Br, ${\mathrm{Br}}^{+}$, and ${\mathrm{Br}}^{2+}$ have been recorded photographically in the 60–90 eV region using the dual-laser-produced plasma technique. In each case intense 3d→4p transitions were observed while 3d→np (n≳4) features were also obtained in the spectrum of neutral bromine. The transitions were classified with the aid of multiconfiguration Hartree-Fock calculations. The excited states are predicted to decay by direct autoionization involving 4s or 4p electrons and the rates for the different processes and resulting linewidths were also calculated. From these data theoretical cross sections for the observed features were also computed. © 1996 The American Physical Society.

Resonance broadening in atomic xenon has been studied by using laser-induced fluorescence of two excited-state electronic transitions. The impact theory result for resonance broadening is verified to be accurate and the onset of the breakdown of the theory is chronicled. The spectral broadening of the 6s[3/2${]}_1^{\mathit{o}}$${(}^3$${\mathit{P}}_1$)→6p[1/2${]}_0$ (828-nm) transition by the resonant interaction of its lower level with ground-state xenon was investigated for densities of 4×${10}^{21}$–2×${10}^{24}$ atoms ${\mathrm{m}}^{\mathrm{-}3}$. The predominantly Doppler-broadened 6s[3/2${]}_2^{\mathit{o}}$${(}^3$${\mathit{P}}_2$)→6p[3/2${]}_2$ (823-nm) transition was analyzed for similar conditions, primarily to establish the kinetic temperature of the neutral xenon. Tunable narrow-linewidth semiconductor diode lasers were used to probe the excited states, which were produced by a direct-current glow discharge. The intricate hyperfine structure of the measured profiles was taken into account by summing constituent Voigt profiles to construct model line shapes. The 6s[3/2${]}_1^{\mathit{o}}$→6p[1/2${]}_0$ broadening constant at low densities and at 311 K was found to be 6.04(±0.66)×${10}^{\mathrm{-}21}$ MHz ${\mathrm{m}}^3$ ${\mathrm{atom}}^{\mathrm{-}1}$. This result is in agreement with the value predicted by the impact theory for resonance broadening. The 6s[3/2${]}_1^{\mathit{o}}$→6p[1/2${]}_0$ Lorentzian width extrapolated to zero density, 43±15 MHz, is in accord with the natural linewidth. At densities above 6×${10}^{23}$ atoms ${\mathrm{m}}^{\mathrm{-}3}$ the recorded line shapes of this transition exhibited an asymmetry, providing clear evidence of the breakdown of the impact approximation. The measured Lorentzian broadening for the 6s[3/2${]}_2^{\mathit{o}}$→6p[3/2${]}_2$ transition was 8.3(±1.8)×${10}^{\mathrm{-}22}$ MHz ${\mathrm{m}}^3$ ${\mathrm{atom}}^{\mathrm{-}1}$ at 311 K. © 1996 The American Physical Society.

High-order multireference perturbation theory is applied to the ${}_{}{}^1{}_{}{}^{}$S states of the beryllium atom using a reference (model) space composed of the |1${\mathit{s}}^2$2${\mathit{s}}^2$〉 and the |1${\mathit{s}}^2$2${\mathit{p}}^2$〉 configuration-state functions (CSF’s), a system that is known to yield divergent expansions using Mo/ller-Plesset and Epstein-Nesbet partitioning methods. Computations of the eigenvalues are made through 40th order using forced degeneracy (FD) partitioning and the recently introduced optimization (OPT) partitioning. The former forces the 2s and 2p orbitals to be degenerate in zeroth order, while the latter chooses optimal zeroth-order energies of the (few) most important states. Our methodology employs simple models for understanding and suggesting remedies for unsuitable choices of reference spaces and partitioning methods. By examining a two-state model composed of only the |1${\mathit{s}}^2$2${\mathit{p}}^2$〉 and |1${\mathit{s}}^2$2s3s〉 states of the beryllium atom, it is demonstrated that the full computation with 1323 CSF’s can converge only if the zeroth-order energy of the |1${\mathit{s}}^2$2s3s〉 Rydberg state from the orthogonal space lies below the zeroth-order energy of the |1${\mathit{s}}^2$2${\mathit{p}}^2$〉 CSF from the reference space. Thus convergence in this case requires a zeroth-order spectral overlap between the orthogonal and reference spaces. The FD partitioning is not capable of generating this type of spectral overlap and thus yields a divergent expansion. However, the expansion is actually asymptotically convergent, with divergent behavior not displayed until the 11th order because the |1${\mathit{s}}^2$2s3s〉 Rydberg state is only weakly coupled with the |1${\mathit{s}}^2$2${\mathit{p}}^2$〉 CSF and because these states are energetically well separated in zeroth order. The OPT partitioning chooses the correct zeroth-order energy ordering and thus yields a convergent expansion that is also very accurate in low orders compared to the exact solution within the basis. © 1996 The American Physical Society.

Integral and differential cross sections for the Ps-formation channel for ${\mathit{e}}^{+}$–alkali-metal-atom collisions are calculated, with considerable success, by means of a model optical potential. The atomic targets discussed here are Li, Na, and K. The potential is obtained without empirical parameters via a global modeling of the dynamical polarization potential and of the short-range correlation forces, with the use of generalized damping functions. The absorption part of the potential is obtained by means of a dispersion relation. We present here a full account of this simple and promising technique. © 1996 The American Physical Society.

An accurate numerical finite-element method (FEM) solution of the three-body Coulomb problem with two equal masses is presented. The application of the FEM to systems with mass ratios ranging from 1836 to 1/1836 yields upper bounds for energy eigenvalues to a precision in the range of ${10}^{\mathrm{-}11}$–${10}^{\mathrm{-}9}$ a.u. Expectation values for different operators are computed and discussed. © 1996 The American Physical Society.

Using the multiconfiguration Hartree-Fock code by Cowan, Auger transition energies and radiative and nonradiative decay rates were calculated for doubly excited 3${\mathit{lnl}}^{\prime }$ and 4${\mathit{lnl}}^{\prime }$ (n≥4) states in ${\mathrm{Ne}}^{8+}$. The results are compared with previous theoretical results. The Auger yields for a given n are averaged over individual states. It is found that the average Auger yields for the configurations 3${\mathit{lnl}}^{\prime }$ (n=4–9) decrease slowly with increasing n while they are close to unity for the configurations 4${\mathit{lnl}}^{\prime }$ (n=4–7). © 1996 The American Physical Society.

Time-independent and time-dependent theory of radiative and nonradiative resonant x-ray scattering (RXS) involving dissociative molecular states is presented. A strong space correlation between excitation and decay is found. This space correlation has a characteristic length equal to the path propagated during the lifetime of the core-excited state. It is shown that for internuclear distances beyond this characteristic length the RXS signal grows exponentially small. Additional untrivial properties of the RXS cross section for continuum-bound or bound-continuum decay transitions are predicted. Selection rules operate for continuum-bound transitions if the slope of the continuum potential is small; only transitions to vibrational states with odd quantum numbers are allowed in the harmonic approximation. We show that the main contribution to the RXS cross section is obtained at the dissociative limit if the lifetime of the core-excited state is sufficiently long. Emission transitions in the molecular region form the wing of the dissociative resonances. The spectral shape of this wing is in general oscillatory. The cross sections for both type of transitions are proportional to the square of the wave function of the vibrational state involved in the RXS process. The spectral shape copies the space distribution of the square of this wave function, and so, indirectly, maps the shape of the corresponding molecular potential. The zeros of the RXS cross section caused by the nodes of the vibrational wave function can be used to assign vibrational states. The spectral width of the RXS resonances involving dissociative molecular states strongly depends on the features of the interatomic potentials. In the general case the spectral shapes consist of a narrow part and a broad background, and will be determined by different limiting factors, such as the spectral photon shape, the Franck-Condon vibrational distribution, and the lifetime width for the core-excited states. The role of these limiting factors depends on the different combinations of dissociative and bound potentials for the ground state, the core-excited state, and the optically excited state. © 1996 The American Physical Society.

The adiabatic hyperspherical method is used to investigate the spectrum of the helium trimer and to explore effects on the spectrum of varying the helium masses as well as the interaction strength. When a realistic helium dimer potential is adopted, only two isotopic combinations are observed to have three-body bound states: ${}_{}{}^4{}_{}{}^{}\mathrm{He}_3^{}{}_{}{}^{}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}_2^3{}_{}{}^{}$He. By artificially adjusting the dimer potential, we also determine the range of interaction strengths for which halo states can result. The existence of Efimov states for both physical and unphysical systems is also examined. © 1996 American Institute of Physics.

The broadening and shifting of the Q branch of ${\mathrm{H}}_2$ diluted in ${\mathrm{N}}_2$ are studied at temperatures between 300 and 1200 K. (i) In order to account for the observed anomalies (asymmetric profiles and nonlinearity of the linewidth versus perturber concentration), the results are interpreted using a speed-dependent model in its general form. This model introduces the speed dependence of the shift and the broadening. In contrast with the previous ${\mathrm{H}}_2$–rare-gas studies, the high-temperature measurements prove the necessity to include speed-dependent broadening that was ignored in the previous studies. (ii) Concomitantly, we report as well pure ${\mathrm{H}}_2$ results including Raman frequencies for the Q(7–9) lines and broadening and shifting results at 800 and 1200 K. A consistent set of data is deduced for ${\mathrm{H}}_2$-${\mathrm{N}}_2$ up to 1200 K and the proposed model would be pertinent at higher temperatures for combustion applications. © 1996 The American Physical Society.

In the WKB approximation the ${\mathrm{\nabla }}^2$S term in Schrödinger’s equation is subordinate to the |∇S${\mathrm{|}}^2$ term. Here we study a modified WKB approximation in which the ${\mathrm{\nabla }}^2$S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground-state wave function, but unlike the WKB approximation it can be applied straightforwardly to problems having many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms, and to ${\mathrm{\phi }}^4$ field theory. We show that good numerical results for the bound-state energy can be obtained even when the initial guess for S is manifestly inaccurate. Our method supplies the wave function as well as the energy. © 1996 The American Physical Society.

Several years ago, a resonance-shift phenomenon was predicted to exist, termed the stochastic realization shift (SRS), which arises as a consequence of correlated amplitude and frequency variations in a resonant field. An interesting aspect of the phenomenon is that the sign of the SRS in weak and strong fields has been shown to differ. Here, we demonstrate that the SRS may be conveniently studied over a broad range of field strengths via magnetic resonance in an optically pumped alkali-metal vapor. Specifically, we study the SRS in the ground state 0-0 hyperfine transition of ${\mathrm{Rb}}^{87}$ for a field undergoing stochastic (yet correlated) amplitude-frequency fluctuations. Under our experimental conditions we find no evidence for a change in sign of the SRS as the field strength undergoes a transition from weak to strong. Further, our results show that in strong fields the magnitude of the SRS may be influenced by the field’s spatial variations. © 1996 The American Physical Society.

Previous investigators have shown how the Birkhoff-Gustavson normal form (BGNF) procedure can be used to develop an integrable Hamiltonian which approximates a nonintegrable Hamiltonian system. We discuss the symmetry properties of these approximate Hamiltonians and how a certain flexibility inherent to the BGNF procedure can be used to affect this symmetry. Because the BGNF procedure involves a transformation of the coordinates, the symmetry issue has been somewhat neglected due to its complexity. The techniques we demonstrate here with the Hénon-Heiles Hamiltonian are easily generalized for use in molecular Hamiltonians of arbitrary symmetry. © 1996 The American Physical Society.

The four-body corrected first Born approximation is used to investigate the single-electron transfer in fast collisions of hydrogenlike projectiles with helium atoms. The initial state of the target active electron is described by a Roothan-Hartree-Fock wave function. For an illustration, total cross sections are computed for electron capture from the ground state of He by fast H atom and ${\mathrm{He}}^{+}$ ion. The theoretical results are in good agreement with available experimental data. © 1996 The American Physical Society.

Electron-impact cross sections for the process ${\mathrm{H}}_2$(B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$,${\nu }_{\mathit{i}}$)+e→${\mathrm{H}}_2$(I${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathit{g}}$)+e have been calculated as a function of the collision energy and for different vibrational quantum numbers ${\nu }_{\mathit{i}}$ in the frame of impact-parameter method. Total and dissociative cross sections are compared with those referred to electronic transitions involving the ground electronic state of ${\mathrm{H}}_2$ (X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$→B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$→C${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathit{u}}$). Moreover, rate coefficients as a function of the vibrational state of the molecule are reported for different temperatures and for both B→I and X→B transitions, briefly discussing the role of these two processes in the ${\mathrm{H}}^{\mathrm{-}}$ negative-ion production. © 1996 The American Physical Society.

First Born approximation (FBA) and continuum-distorted-wave–eikonal-initial-state (CDW-EIS) approximation are used to calculate the cross section that is triply differential (TDCS) in the energy and angle of the emitted electron and scattered projectile for proton impact ionization of atomic hydrogen. The TDCS shows different prominent features, whose origin is examined on the basis of the results given by FBA calculations and reported for different physical effects. We discuss how these features are related to those present in the doubly differential cross section (DDCS). © 1996 The American Physical Society.

We report a detailed calculation of the contribution of excitation autoionization to the electron-impact ionization of ${\mathrm{Ar}}^{7+}$ by a distorted-wave Born approximation with exchange. Inner-shell excitations of the type 2${\mathit{s}}^2$2${\mathit{p}}^6$3s→2${\mathit{s}}^2$2${\mathit{p}}^5$3snl (n=3,4,5; l=0,1,2,3) and 2${\mathit{s}}^2$2${\mathit{p}}^6$3s→2s2${\mathit{p}}^6$3snl (n=3,4; l=0,1,2,3) are included. The level-to-level excitation cross sections and autoionization branching ratios are calculated in detail. The present results demonstrate that the use of unit branching ratios will overestimate the excitation-autoionization cross section by about 20–40 %. Furthermore, the calculation shows the largest contribution is from 2p→3p and 2p→3d excitations and the latter dominates the contribution of excitation autoionization to electron-impact ionization. The calculated results are also compared with recent experimental measurements and theoretical calculations. Being different from the results of Griffin, Bottcher, and Pindzola [Phys. Rev. A 45, 2929 (1992); 24, 2273 (1981)], our results for the branching ratio are closer to the measurement of Rachafi et al. [J. Phys. B 24, 1037 (1991)] and our values are smaller than the experimental one of Zhang et al. [Phys. Rev. A 45, 2929 (1992)], while the results for the unit branching ratio are very close to the calculation of Tayal [Phys. Rev. A 49, 2561 (1994)]. In addition, we find that the configuration interaction changes the autoionization branching ratios of individual levels, but has little effect on the total excitation-autoionization cross sections. © 1996 The American Physical Society.

We describe a set of experiments that investigate diffusion of barium 6s5d${\mathrm{}}^3$${\mathit{D}}_{\mathit{J}}$ metastable level and 6${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$ ground-state atoms through the noble gases: He, Ne, Ar, Kr, and Xe. The barium metastable levels were populated through optical pumping of the 6${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$→6s6p${\mathrm{}}^3$${\mathit{P}}_1^{\mathit{o}}$ intercombination transition with a pulsed laser, followed by spontaneous or stimulated emission into the 6s5d${\mathrm{}}^3$${\mathit{D}}_{1,2}$ levels. Collisional mixing then distributed population throughout the 6s5d${\mathrm{}}^3$${\mathit{D}}_{\mathit{J}}$ levels. A weak narrow-band cw laser was tuned to appropriate transitions to probe the spatial distribution of metastable level atoms, as well as the hole created in the ground-state spatial distribution, by the pulsed laser. Time-dependent absorption coefficients were obtained by measuring the transmission of the probe laser at several different pump-probe spatial separations. From these absorption data, spatial number density profiles were mapped out for various times following the firing of the pump laser. These density profiles were used to determine the diffusion coefficient for each state at a particular buffer-gas pressure and temperature. From these pressure- and temperature-dependent diffusion coefficients D, we determined the thermally averaged diffusion cross sections ${\mathrm{\sigma }}_{\mathit{D}}$(6s5d${\mathrm{}}^3$${\mathit{D}}_{\mathit{J}}$) and ${\mathrm{\sigma }}_{\mathit{D}}$(6${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$) for the metastable and ground-state atoms diffusing through the noble gases, respectively. We also report values for the scaled standard diffusion coefficients ${\mathit{D}}_0$. Our experimental values of the thermally averaged diffusion cross sections ${\mathrm{\sigma }}_{\mathit{D}}$(6s5d${\mathrm{}}^3$${\mathit{D}}_{\mathit{J}}$) and ${\mathrm{\sigma }}_{\mathit{D}}$(6${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$) for the barium-helium system are compared with values calculated from published, theoretical barium-helium potentials and the agreement is excellent. © 1996 The American Physical Society.

We have measured the contributions from high-n dielectronic satellite lines to the 1${\mathit{s}}^2$–1s3p${\mathrm{}}^1$${\mathit{P}}_1$ resonance line of heliumlike ${\mathrm{Ar}}^{16+}$. Using a high-resolution crystal spectrometer to analyze the x-ray emission of ions trapped and excited in an electron-beam ion trap, contributions from satellite levels of the type 1s3${\mathit{lnl}}^{\prime }$-1${\mathit{s}}^2$${\mathit{nl}}^{\prime }$, for n=3,4,5 and n≥6, have been recorded. The resonance strength of the n=3 satellites was measured to be (4.65±0.67)×${10}^{\mathrm{-}21}$ ${\mathrm{cm}}^2$ eV. The resonance strength of the n=4 satellites was determined to be larger than that of the n=3 satellites and that of the n=5 satellites was found to be nearly equal to the resonance strength of the n=3 satellites. The ${\mathit{n}}^{\mathrm{-}3}$ dependence of resonance strengths expected from the n scaling of the Auger rates is thus shown to not be valid for the satellites studied in our measurements. © 1996 The American Physical Society.

We calculate and discuss the differential cross sections for nonrelativistic electrons in a strong magnetic field scattered by free protons with and without the emission of a photon. The electrons are assumed to be in the lowest Landau state before and after scattering. Forward scattering is the dominant part of the cross section but leads only to a small energy change per scattering. Another relevant contribution occurs if a cyclotron photon is emitted during the scattering event. This resonant process can change the electron energy by a large amount. © 1996 The American Physical Society.