The leading term in the Neumann expansion of $\frac{1}{r_{12}}$ is $\frac{1}{r_{>}}$, where $r_{>}$ signifies the greater of $r_1$ and $r_2$. Defining the monopole Hamiltonian (also called the radial-limit Hamiltonian) as the two-electron Hamiltonian with the replacement $\frac{1}{r_{12}}\to \frac{1}{r_{>}}$, the author presents asymptotic forms of the eigenfunction of this operator. The bound-bound, bound-free, and free-free cases are treated. "Asymptotic" means here that $r_1\to \infty$, $r_2\to \infty$, but $\frac{r_1}{r_2}$ is not restricted.

Effective rate coefficients for dielectronic recombination of Fe-ix, -x, and -xi ions at electron densities in the range of 3 × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and electron temperatures up to 220 eV, were deduced from the time histories of emission lines in a small $\theta$-pinch plasma. The iron impurity in the hydrogen plasma was introduced by a laser puffing method. The intensities of lines from these ionization stages were measured as functions of time and interpreted by means of a time-dependent corona ionization-recombination model. A one-dimensional computer code, which takes into account the radial variations of $T_e$ and $n_e$, was used for the simulation of time histories. The effective rate coefficients were found to be equal to or smaller than currently accepted theoretical values for low-density plasmas.

Single electron-capture cross sections have been measured for boron ions ${\mathrm{B}}^{q+}$ with initial charges $q=2, 3, \mathrm{and} 4$ incident on an atomic hydrogen target. The cross sections ${\sigma }_{21}$ and ${\sigma }_{43}$ are large and show little dependence on the ion energy for the range studied, $6q$ to $23q$ keV. The cross section ${\sigma }_{32}$ increases with increasing energy in this same range. Also reported is a survey of single electron-capture cross sections for ions of carbon ($2\le q\le 4$), nitrogen ($2\le q\le 5$), and oxygen ($2\le q\le 5$) at the single energies $8q$ keV also incident on atomic hydrogen.

We have formulated Schwinger's variational principle for electron-ion collisions using the Coulomb Green's function. The theory is applied to a screened Coulomb potential to obtain analytic distorted waves, phase shifts, and quantum defects for energies near the ionization threshold of an ion with charge $z=1\mathrm{}$.

$K$-shell ionization cross sections of Al and Cu for proton impact have been measured over the projectile-energy range 0.5-40 MeV, and the results are compared with calculations of plane-wave Born approximation (PWBA) and binary-encounter approximation (BEA). In the PWBA calculation, contributions from close and distant collisions are separately estimated by an approximate calculation. It is found that the distant collisions make a predominant contribution in the high-projectile-energy region and the experimental results are in better agreement with the PWBA than the BEA, which takes into account only the close collision.

The experiments described in this paper probe the simultaneous effects of gravity, inertia, and quantum mechanics on the motion of the neutron. Using a neutron interferometer of the type developed by Bonse and Hart for x rays, we have observed quantum-mechanical interference phenomena induced by the gravitational field of the Earth and by the Earth's rotation relative to the fixed stars. The importance of these experiments with regard to the role of the principle of equivalence in quantum mechanics is discussed.

The cross section of the pair production in germanium at 1064 keV, only 42 keV above threshold, has been measured with the use of a Ge(Li) detector. The obtained cross section is 0.182 mb/atom and has a large deviation from the theoretical value by Øverbø, Mork, and Olsen. The present result suggests that the screening effect of atomic electrons has a large contribution to the pair-production cross section near threshold.

We present a new perturbation treatment of electron scattering. It is based on determining a primitive wave function which is nonsymmetric with respect to electron exchange. The theory is developed specifically for elastic scattering from atomic hydrogen but appears generalizable to many-electron atoms and to inelastic processes as well. From the first-order wave function, which can be made square-integrable, one obtains the phase shifts through third order. Calculations with a crude spherical-well initial approximation are carried out for illustrative purposes.

The observation of two-photon excitation of selected $6p$ levels in krypton atoms using tunable ArF* laser radiation at 193 nm is reported. Using time-resolved detection of visible fluorescence lines in the vicinity of 430 nm arising from $6p-5s$ transitions, radiative lifetimes for the $6p{\left[\frac{1}{2}\right]}_0$ and $6p{\left[\frac{3}{2}\right]}_2$ states of 123 ± 5 and 115 ± 5 nsec, and collisional self-quenching rates of (4.1 ± 0.4) × ${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$/sec and (6.7 ± 0.7) × ${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$/sec, respectively, have been determined. By carefully measuring the visible fluorescence intensity as a function of incident laser intensity, the photoionization cross section of the $6p{\left[\frac{3}{2}\right]}_2$ state has been established as (3.2 ± 2.0) × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$.. The two-photon transition rates for both states have been theoretically calculated, and good agreement is found with measurements of the relative excitation rates for the two transitions.

Recent experimental investigations of atomic x rays in protonium have revived interest in the atomic cascade process. Following a calculation of Leon and Bethe, which includes chemical and Auger deexcitation, Stark mixing and annihilation, as well as radiative transitions, we investigate the dependence of the yields of $K$ and $L$ x rays on the target density, and on the hadronic shifts and widths of the $1s$ and $2p$ levels. Numerical results are also given for kaonic, pionic, and muonic hydrogen.

The exact solution of the Schrödinger equation for a chargeless particle with arbitrary spin and magnetic moment interacting with a helical magnetic field of general strength and period is derived. (A helical field has the property of being constant and homogeneous in a family of parallel planes but such that its direction rotates continuously as one proceeds to adjacent planes.) By exploiting the screw symmetry of this Hamiltonian, it is shown that the Schrödinger equation can be reduced to an algebraic eigenvalue equation for a matrix which is a Hermitian quadratic form in the spin matrices $J_x$, $J_y$, $J_z$. For particles of spin $j$ less than $\frac{5}{2}$, it is shown that the solution can be obtained in analytic form. For higher spins the exact analytic expressions are difficult to obtain, however, the solution can be given numerically by evaluating the roots of a polynomial of degree $2j+1$. The solutions in the spin-½ and spin-1 cases are discussed in detail. Several interesting physical aspects of these results emerge. For example, it is found that in spite of the periodicity of the Hamiltonian, the energy spectrum has no band structure. It is also found that the group velocities behave quite differently depending on the spin orientation of the states relative to the field. Other properties such as the spin behavior of the wave functions and the effective mass tensor are discussed. Finally, it is shown that these results, apart from some minor modifications, also hold for charged spin particles provided their momentum points in the direction perpendicular to the magnetic field.

A theoretical model of two-step resonant ionization which includes an autoionizing state is developed. The effects examined include interactions with a multimode laser and Zeeman and hyperfine multiplets. We approach this problem starting from first principles by treating the atom-radiation system as a unit. Theoretical analysis and numerical calculations of ionization probabilities are given. The intermode scattering is investigated in detail, and a simple physical interpretation of the dynamical effect is given. Comparisons of ionization probabilities for two-step processes with first-step excitations by single-mode or two-mode lasers are made. It is found that, if the mode spacing in a multimode-laser beam is less than the Doppler width of the atom, the multimode laser can more effectively produce ions than a single-mode laser does. This leads to the conclusion that the resonance effect is more important than the power-broadening effect. This is shown to be also true when Zeeman and hyperfine multiplets are included.

Procedures for computing molecular photoabsorption cross sections via finite expansions in sets of $L^2$ complex basis functions are discussed. Two recently proposed schemes for analytically continuing a matrix representation of the Born-Oppenheimer Hamiltonian are investigated. Both of these matrix analytic continuations are used to compute the parallel component of the photoionization cross section for ${\mathrm{H}}_2^{+}$. It is found that to obtain numerically stable results it is necessary to use complex-basis functions which are capable of describing cusps in the molecular wave function at complex values of the coordinates. The application of this technique to larger molecules is also discussed.

We have exposed a variety of Čerenkov radiators to relativistic Ne, Ar, and Fe ions at the Lawrence Berkeley Laboratory's Bevalac and have examined the charge dependence of the Čerenkov emission. Classically, and to first order in relativistic quantum theory, the dependence is $Z^2$, although certain higherorder corrections suggest a $Z^4$ dependence as well. Our experimental results are consistent with a pure $Z^2$ dependence and limits are placed on $Z^3$ and $Z^4$ higher-order contributions to Čerenkov emission, whose theoretical bases are briefly discussed. In addition to primary Čerenkov emission, we discuss light sources such as Čerenkov emission by secondary electrons, saturated radiator scintillation, and others which are confronted in most experimental configurations incorporating Čerenkov radiators.

An experimental study of pressure broadening and shifts on the 5882-Å line of NeI was conducted with a resolution of one part per billion by means of saturation spectroscopy with a zero-pressure reference line provided by a metastable-atomic-beam apparatus. A broadening of 11±2 MHz per Torr was found for Ne-Ne collisions and an upper limit of 500 kHz per Torr was found for the shift. The cross section for largeangle Ne*-Ne scattering was found to be 46±4 ${\mathrm{\AA }}^2$ from collisional cross-relaxation effects. A theory was developed to account for line-shape distortion effects in saturation spectroscopy with optically thick samples.

The authors report on optical Kerr effect measurements performed in the isotropic phase of the nematogen $p$-methoxy-benzoate-$p$-$n$-pentylbenzene. The optical Kerr constant is found to obey the well-known ${(T-T^{*})}^{-1\mathrm{}}$-type law near the isotropic-nematic transition temperature, but to deviate from it at higher temperatures. An argument is presented for the existence of a roughly temperature-independant mechanism involved in the response of isotropic phases of nematogens to an intense electric field. A possible microscopic interpretation is suggested.

The ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$-${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ spin-exchange cross section has been measured in ${\mathrm{N}}_2$ buffered cells as a function of the ${\mathrm{N}}_2$ density using an alkali vapor magnetometer technique. The strong dependence of the spin-exchange cross section on the ${\mathrm{N}}_2$ density indicates a significant role for the Rb-Xe van der Waals molecule in the spin-exchange process. Our data have allowed us to estimate the Rb-Xe molecular formation rate, which is in reasonable agreement with previous measurements. The extrapolated binary spin-exchange cross-section term is found to be ${\sigma }_{\mathrm{ex}}{\overline{V}}^2=1.5\mathrm{}\times {10}^{-10\mathrm{}}$ ${\mathrm{cm}}^4$ ${\sec }^{-2\mathrm{}}$.

The decay of the $4s4p{}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$ level in Krvii following beam-foil excitation has been simulated using theoretical initial-state populations and calculated transition probabilities. It was found that the decay curve was substantially influenced by cascading from higher levels and that such cascades dominate the decay in the region beyond three times the lifetime of the $4s4p{}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$ level. The simulation is in good agreement with an experimental decay curve at short decay times, but is unable to reproduce the long-time behavior of the experimental data. However, recent spectroscopic evidence indicates that line blending is responsible for this aspect. Complications due to core-excited states and other complex cascade mechanisms are discussed.

We present a formalism based on density-functional theory capable of describing polarization-type many-body effects influencing the photoresponse of small electronic systems. The self-consistent field approach we describe incorporates correlations into a local, effective single-particle potential which takes account of the time-dependent fields induced by an external radiation field. In this paper we present calculations of the static polarizabilities, total photoabsorption cross sections, and selected partial photoabsorption cross sections of the rare gases which yield results in good agreement with experiment. A study of the energy and spatial dependence of the local field leads to a clear physical picture of the dielectric properties of these systems.

The interaction of a resonant radiation field with two-level atoms (in the long-wavelength limit) is described by a Hamiltonian trilinear in the boson operators. It is shown that the dynamics of the system can be determined nearly exactly if either at least one of the three modes is strongly populated for all times or any two modes are separately strong in two complementary time domains. Explicit results are given in two important specific cases: (i) pumping of a ground-state atomic system by a coherent radiation field and (ii) coherent spontaneous emission. The results are compared with previously known approximate results. Our results are also applicable to certain parametric processes such as parametric amplification, frequency conversion, Raman and Brillouin scattering, etc., where an identical trilinear Hamiltonian is used to describe these processes.