We have performed a 401-order perturbation calculation to resolve the controversy over the radius of convergence of the $\frac{1}{Z}$ expansion for the ground-state energy $E\left(\lambda \right)$ of heliumlike ions, where $\lambda =\frac{1}{Z}$ and $H\left(\lambda \right)=-\frac{1}{2}{\nabla }_1^2-\frac{1}{r_1}-\frac{1}{2}{\nabla }_2^2-\frac{1}{r_2}+\frac{\lambda }{r_{12}}$. Such high-order calculations followed by Neville-Richardson extrapolation of the ratios of the coefficients are necessary to study the asymptotic behavior of the perturbation series. We find (i) that ${\lambda }_c$, the critical value of $\lambda$ for which $H\left(\lambda \right)$ has a bound state with zero binding energy, is approximately 1.097 66, (ii) that ${\lambda }^{*}$, the radius of convergence of the perturbation series, is equal to ${\lambda }_c$, and (iii) that the nearest singularity of $E\left(\lambda \right)$ in the complex plane, which determines ${\lambda }^{*}$, is on the positive real axis at ${\lambda }_c$. Thus our results confirm Reinhardt's analysis Phys. Rev. A 15 802 1977 of this problem using the theory of dilatation analyticity (complex scaling). We also find that the perturbation series for $E\left(\lambda \right)$ is convergent at $\lambda ={\lambda }_c$. The same statements hold for the perturbation series for the square of the norm of the corresponding eigenfunction ${\parallel \psi \left(\lambda \right)\parallel }^2$. We find numerically that $E\left(\lambda \right)$ has a complicated branch-point singularity at $\lambda ={\lambda }_c$ of the same type as the function ${(1-\frac{\lambda }{{\lambda }^{*}})}^{-a}U(a,c;\frac{x}{(l-\frac{\lambda }{{\lambda }^{*}})})$, where $U$ is the irregular solution of the confluent hypergeometric equation, and that ${\parallel \psi \left(\lambda \right)\parallel }^2$ has a similar but even more complicated singularity at ${\lambda }^{*}$. We also discuss the $\frac{1}{Z}$ expansions for excited states of the helium isoelectronic sequence and for states of multielectron atomic ions. Byproducts of our calculation include the most accurate estimates so far of the nonrelativistic ground-state energies of the ${\mathrm{H}}^{-}$ ion and of the helium atom, as well as the most accurate upper bound ever obtained to the second-order energy coefficient $E_2$.

The method of point transformations enables us to generate an unknown wave function ${\Psi }_{\rho }$${(\mathrm{\{}\mathrm{r}}_k$}) from a given electron density ρ(r) based on a reference wave function ${\Psi }_0$${(\mathrm{\{}\mathrm{r}}_k$}) initially chosen for the system. The generated wave function ${\Psi }_{\rho }$${(\mathrm{\{}\mathrm{r}}_k$}) can be used to evaluate the energy $E_{\rho }$ associated with the given density ρ(r). This procedure constitutes a rigorous density-functional theory, if the density ρ(r) and reference function ${\Psi }_0$${(\mathrm{\{}\mathrm{r}}_k$}) are varied. Within the Hartree-Fock framework numerical applications are presented for the ground-state helium atom and its analogs both in position and momentum spaces. Simple position and momentum densities are reported that well reproduce the Hartree-Fock limit energy. A few calculations beyond the Hartree-Fock approximation are also given.

Accurate cross sections are obtained for the excitation and stripping of a muon from αμ in collisions with hydrogen atoms. This is done by calculating the excitation, ionization, and charge-transfer cross sections for the p-${\mathrm{He}}^{+}$ collision and scaling the results. An impact-parameter coupled-state method with a basis set of up to 51 Sturmian wave functions is used to obtain cross sections at center-of-mass energies ranging from 20 to 600 keV. Along with Stark, Auger, radiative, and stopping rates these cross sections are used to calculate the probability of stripping a muon from αμ by numerically solving a set of coupled differential equations that describe the kinetics of αμ as it travels through a mixture of ${\mathrm{D}}_2$ and ${\mathrm{T}}_2$. An effort has been made to minimize the uncertainty in the value of the stripping probability resulting in error bars of 9% and 11% at densities of 1.2 and 0.05 times liquid-hydrogen density, respectively. X-ray yields belonging to K and L series transitions among αμ states have also been computed. The present results are compared with recent theoretical and experimental data.

Dielectronic recombination due to the 2s→2p excitation has been measured for metastable He-like ${\mathrm{C}}^{4+}$ and ${\mathrm{O}}^{6+}$ ions and for Li-like ${\mathrm{C}}^{3+}$ and ${\mathrm{O}}^{5+}$ ions. The measurements have been performed with a merged-beams technique. An energy resolution of 0.135 eV was obtained. The data for the Li-like ions are compared with distorted-wave calculations. For the low-lying resonances, good agreement is found between experiment and theory except for one resonance (2p4l) for ${\mathrm{C}}^{3+}$ that is very close to threshold. The contribution due to higher Rydberg states is in agreement with theory for external fields of 3 V/cm for ${\mathrm{C}}^{3+}$ and around 7 V/cm for ${\mathrm{O}}^{5+}$. The field present in the experiment is expected to be around 2 V/cm. Large and unexpected structures are observed in the He-like data. These have tentatively been explained in terms of interaction between different core configurations. For the metastable He-like ions extremely large cross sections of the order of ${10}^{\mathrm{-}15}$ to ${10}^{\mathrm{-}14}$ ${\mathrm{cm}}^2$ are found.

Results are presented for both inelastic and rearrangement scattering of positrons by hydrogen atoms for total angular momentum of zero. Sector adiabatic basis functions in hyperspherical coordinates are used to form a 43-coupled-channel scattering expansion for energies below the H(n=4) threshold. Partial cross sections out of $e^{+}$+H(1) into H(1), Ps(1), H(2), Ps(2), and H(3) are shown, as are those out of $p^{+}$+Ps(1) into H(2), Ps(2), and H(3). Considerable resonance structure is apparent in all of these cross sections.

From accurate spectroscopic constants one finds that the thermal dissociative-attachment process (DA) in DI should be exothermic only for rotational levels J>8 in v=0. We report herein measurement of an enhancement of DA with rotational temperature T in the range 298–468 K. The effect is easily accounted for by the increase in total fractional population of excited J levels in DI relative to HI. The effect affords a rotational analog to the use of vibrationally excited molecules (e.g., HCl) in a plasma to control electron conduction.

We have measured in coincidence the projectile-ion charge state, the target-recoil-ion charge state, and the energy of a free electron (cusp electron) emerging from the same collision with a velocity close to the beam velocity, for 1-MeV/u bare and one-electron oxygen and carbon projectiles colliding with neon targets. The most probable recoil-ion charge state of recoil ions not associated with cusp electrons is 1. Most cusp electrons accompany a projectile that does not change charge, and the most probable recoil-ion charge state in this case lies between 2 and 3. The recoil-ion charge-state distribution associated with a cusp electron and bound-state capture by the projectile is shifted towards even higher charge states. Cusp-electron production in conjunction with electron loss by the projectile is not associated with such a large shift. The probability of cusp-electron production given the production of a recoil ion increases with increasing recoil-ion charge state for projectiles that do not change charge and for projectiles that capture an electron, and decreases with increasing recoil-ion charge state for projectiles that lose an electron in the collision.

Electron-impact excitation of the x ${}_{}{}^1{}_{}{}^{}\Sigma _g^{\mathrm{-}}{}_{}{}^{}$, y ${}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$, and $o_3$ ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ Rydberg electronic states of the nitrogen molecule has been studied. We have measured the maximum electron-impact optical-emission cross sections of many vibrational bands of the y ${}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$→w ${}_{}{}^1{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$, y ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$→a’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{\mathrm{-}}{}_{}{}^{}$, and x ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{\mathrm{-}}{}_{}{}^{}$→a’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{\mathrm{-}}{}_{}{}^{}$ electronic transitions. The maximum values of the optical-emission cross sections of these band systems are typically less than or on the order of ${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$. The dependence of the emission cross sections of selected bands on electron energy has been studied. The excitation functions of the y→a’ and x→a’ bands have similar shapes below about 50 eV with a peak near 32 eV, and are approximately proportional to 1/E at high energies. We have measured the emission cross section of the $o_3$ ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$→a ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$(0,0) band as a function of electron energy. The excitation function of the $o_3$→a(0,0) band has a broader shape than the excitation functions of the y→w, y→a’, and x→a’ bands. We have calculated Franck-Condon factors for the y→w, y→a’, and x→a’ band systems and compare them with the experimental emission cross sections of these band systems. The apparent electron-impact-excitation cross sections of the vibrational levels of the x and y electronic states are estimated.

High-resolution ionization efficiency curves using electron impact (58–59 eV) on helium are presented. Two previously unknown structures are clearly seen in the spectra at 58.415±0.005 and 58.48±0.02 eV in addition to the large (${\mathrm{He}}^{\mathrm{*}}$${)}^{\mathrm{-}}$2s2${\mathrm{p}}^2$${(}^2$D) negative-ion resonance. The line-shape parameters for the ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ state obtained by fitting the data to theoretical line profiles are $E_R$=58.283±0.003 eV, Γ=59±4 meV, and Q=-0.70±0.04. The two new structures are tentatively assigned to the (${\mathrm{He}}^{\mathrm{*}}$${)}^{\mathrm{-}}$2${\mathrm{p}}^3$ electron configuration.

Two-photon absorption cross sections of ground-state xenon atoms to the 2$p_5$(J=0), 2$p_6$(J=2), and 2$p_9$(J=2) states in the 5$p^5$6p configuration and photoionization cross sections at 193 and 248 nm from the 2$p_5$ and 2$p_6$ states have been determined and are compared with previous experimental and theoretical values where such exist. Fluorescence depletion spectroscopy as a method for determining excited-state photoionization cross sections is described and discussed and shown to have many attractive features. Based on our cross-section measurements, we calculate that (2+1)-photon photoionization in Xe with a laser intensity of 30 MW/${\mathrm{cm}}^2$ during 25 ns at 249.6 nm, using the 2$p_5$(J=0) state as an intermediate state, can produce a fractional ionization of 10%.

Cross sections for the process in which photoionization of an atom is accompanied by excitation of an electron from an occupied orbital to an unoccupied orbital are calculated in lowest order in perturbation theory. The calculation is carried out in a local-effective-potential model for the atom that permits the summation over the intermediate states by using the Green’s function for ordinary differential equations. It is assumed that the coupling scheme for the final ionic state is that the two holes couple to a state of definite $L_{12}$ and $S_{12}$ that then combines with the particle state to give a state of definite L and S. Expressions for the total cross section and asymmetry parameter are given for closed-shell atoms. Calculated results for Ne photoionization are compared with experimental results.

We evaluate the exact propagator for a system of n-coupled harmonic oscillators with time-dependent coupling constants $k_{\mathrm{ij}}$(t). .AE

There have been very few measurements of electron-loss cross sections for high-energy (>1-MeV) negative and neutral hydrogen projectiles interacting with gas targets. Previous approaches to the estimation of these cross sections have been based mainly on semiempirical fits aimed at tying the existing low-energy data to theoretical high-energy Born approximation values. Such target-dependent approaches are reliable only for targets for which a sufficient amount of experimental data exist. The more general approach presented here is based on the free-collision model and uses global properties of the momentum-domain atomic form factor to calculate electron-loss cross sections. The results are simple functions of E and Z, with a small number of target-independent parameters. For each single-electron-loss cross section, ${\sigma }_{\mathrm{-}1}$,0 and ${\sigma }_0$,1, fits to available data are presented.

The electron-impact ionization cross section is calculated in the distorted-wave approximation for the Ne-like ions ${\mathrm{Ar}}^{8+}$, ${\mathrm{Ti}}^{12+}$, ${\mathrm{Fe}}^{16+}$, ${\mathrm{Zn}}^{20+}$, and ${\mathrm{Se}}^{24+}$. For ionization from the 2$p^6$ ground state, the contributions from inner-shell excitation followed by autoionization are negligible. However, when these ions are initially in the 2$p^5$3s excited configuration, contributions arising from the inner-shell excitations 2$p^5$3s→2$p^4$3snl and 2$p^5$3s→2s2$p^5$3snl are large. The overall branching ratio for autoionization of the 2$p^4$3snl and 2s2$p^5$3snl levels increases when the atomic-structure calculations are extended beyond the single-configuration approximation to include the configuration interaction. The resulting correlation enhancement of the excited-state ionization cross section is found to increase as a function of Z. For ${\mathrm{Se}}^{24+}$ the correlation enhancement of the total ionization cross section is found to be 42%.

A time-independent Hamiltonian formulation of relativistic atomic structure and scattering problems is developed in which virtual-pair creation and annihilation effects are explicitly included. The method is discussed in the context of a specific problem—the scattering of a positron by a system consisting of two electrons bound to a nucleus of charge Z. This provides the basis for a consistent treatment of spontaneous positron production that can occur when Z exceeds a critical value $Z_{\mathrm{cr}\mathrm{\approxeq }173}$. For Z not too much greater than $Z_{\mathrm{cr}}$ the two-electron atom is stable and represents the (doubly charged) vacuum state. In the approach adopted here the one-electron state, which is unstable against spontaneous pair creation, is viewed as a resonance in the scattering of the positron by the two-electron target atom. The lifetime of the unstable state is determined, in the usual way, from a knowledge of the width of the resonance. The formal resonance theory required to carry out this analysis is developed here with the aid of an effective-potential description of the scattering problem of the type familiar from standard treatments of resonant processes in nonrelativistic atomic and nuclear reaction theories.

Absolute cross sections for simultaneous ionization and excitation by electron impact of some Ne ii(2$p^4$3p), Ar ii(3${\mathrm{p}}^4$4p), and Kr ii(4$p^4$5p) levels from the atomic ground state have been measured with the optical method. Dependence of the emission cross sections on electron energy was studied between threshold and 1000 eV. The measured maximum cross sections for level excitation at the maximum are in the range (19.0–4.7)×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$ for Ne ii, (97.4–B71.7)×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$ for Ar ii, and (98.7–69.2)×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$ for Kr ii.

We present a schematic study of muon-pair production with capture of the negative muon into the $1s_{\frac{1}{2}}$ ground state in relativistic heavy-ion collisions. The muon pairs are generated by a time-dependent, screened electromagnetic field. Our numerical calculations are carried out on a three-dimensional lattice with 20-30 mesh points in each direction, utilizing the $B$-spline collocation method. Numerical convergence has been demonstrated using a Lorentz-boosted screened Coulomb potential. For the system ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ at collider energies of 0.2, 1.0 and 2.0 GeV/nucleon, we obtain probabilities for dimuon production with capture between 1.0 × ${10}^{-3\mathrm{}}$ and 7.0 × ${10}^{-2\mathrm{}}$ at grazing impact parameters. This may indicate that the electromagnetic lepton-pair production is strongly nonperturbative.

Cross sections for charge-transfer reactions of ground-state ${\mathrm{C}}^{+}$${(}^2$P) and metastable-state ${\mathrm{C}}^{+}$${(}^4$P) ions with ${\mathrm{H}}_2$ have been measured in the 10- to 500-eV kinetic energy range. Ground-state reaction cross sections range from 0.3 to 0.5×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^2$, and the corresponding values for metastable state ${\mathrm{C}}^{+}$${(}^4$P) ions vary from 20 to 12×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^2$. Both sets of cross-section values smoothly extrapolate to previously measured data at higher energies.

Differential cross sections for the electron-impact excitation of the first ten electronic states of ${\mathrm{N}}_2$ have been determined at five incident energies ranging from 15 to 50 eV. These differential cross sections were obtained for the scattering range 10°–90° by analyzing electron-energy-loss spectra in ${\mathrm{N}}_2$ at a number of fixed scattering angles within that range. The present study represents a comprehensive remeasurement of the earlier work of Cartwright and co-workers [Phys. Rev. A 16, 1013 (1977)] and was undertaken with a view to resolving certain anomalies which have been reported in the literature when the earlier cross-section set has been applied to model calculations of swarm parameters.

The line ratios of the intercombination line x (1s2p ${}_{}{}^3{}_{}{}^{}\mathrm{P}_2^{}{}_{}{}^{}$→1${\mathrm{s}}^2$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$), the dielectronic and inner-shell satellite line t [1s2p${(}^3$P)2s ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$→1${\mathrm{s}}^2$2${\mathrm{s}}^2$${\mathrm{S}}_{1/2}$], and the n≥3 dielectronic satellite lines (1s2pnl→1$s^2$nl) to the resonance line w (1s2p ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$→1${\mathrm{s}}^2$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$) in the spectrum of heliumlike nickel are measured with a high-resolution x-ray crystal spectrometer on the JET tokamak. The central electron temperatures for which the spectra are taken range from about one-third to twice the threshold energy for the line excitation. The measurements are compared with predictions from a model taking into account the spatial emission profiles of the different ionization stages of nickel calculated from the radial profiles of JET plasma parameters. The rate coefficients for the formation of excited states are taken from a single, self-consistent source of calculations of dielectronic and radiative recombination and electron-impact excitation. The rate coefficients for the calculation of the ionization balance are critically reviewed. Good agreement is found for the ratios t/w and (n≥3)/w, but for x/w significant disagreement is found. Possible causes for this disagreement are discussed. In particular, charge-exchange processes, which are omitted from the model, are found not to be plausible contributors. It is concluded that the present coronal equilibrium model correctly describes the ionization balance, the radiative and dielectronic recombination, and the electron-impact excitation of electric dipole transitions, but that there is a problem with the excitation of nondipole transitions.