Results of semiempirical, adiabatic hyperspherical calculations are presented for the photodetachment cross section of the process ${\mathrm{H}}^{\mathrm{-}}$ 2${\mathit{p}}^2$${(}^3$${\mathit{P}}^{\mathit{e}}$)+γ→H(n=2)+${\mathit{e}}^{\mathrm{-}}$ at photon energies in the range from threshold to 0.125 a.u. above. We find the detachment cross section to have a maximum value of 482 Mb at 25.7 meV above threshold, in good agreement with results of close-coupling calculations by Jacobs, Bhatia, and Temkin [Astrophys. J. 242, 1278 (1980)]. In contrast to the close-coupling results, however, we find that the detachment cross section rises by a factor of more than 400 from its threshold value to its maximum.

Recently a class of quantum-mechanical potentials was presented that is characterized by the fact that they are exactly solvable only when some of their parameters are fixed to a convenient value, so they were christened as conditionally exactly solvable potentials. Here we intend to expand this class by introducing examples in two dimensions. As a byproduct of our search, we found also another exactly solvable potential.

In this paper, we work out a most general and the simplest relationship between the energy eigenstates of a d-dimensional hydrogen atom and those of a D-dimensional harmonic oscillator in terms of the su(1,1) algebra.

The collapse and revival of spin is studied for a particle with a spin moving in a spherical harmonic oscillator potential with spin-orbit interaction. We have concentrated our study on the particular initial conditions that lead to the most transparent formulas and that can be treated analytically. A detailed comparison of the quantum evolution to the classical one is given.

The high-resolution corrections to the energy levels of rotating-vibrating diatomic molecules, arising due to the centrifugal distortion, are calculated using the extended Dunham approach and a deformational self-consistent numerical procedure. The proposed method applied to ${}_{}{}^7{}_{}{}^{}\mathrm{LiH}$ and ${}_{}{}^{115}{}_{}{}^{}\mathrm{InD}$, for which the Dunham potential is unable to fit the observed transitions satisfactorily reproduces the detected bands to within experimental errors, and ensures a good convergence of the Dunham function.

We present results obtained by the application of a semianalytical method to the ground and excited states associated with the Zeeman effect on a hydrogen atom. In this case, where the wave equation is not separable, we show that the method works very well for both weak and strong fields.

We investigate possible asymmetrical configurations of Coulombic three-body systems (${\mathit{A}}^{\mathit{n}\mathrm{-}}$+${\mathit{B}}^{\mathit{m}+}$+${\mathit{B}}^{\mathit{m}+}$), within Langmuir’s rigid-rotator model. The recently found effect by Poirier [Phys. Rev. A 40, 3498 (1989)] that in the two-electron atoms asymmetrical configurations appear possible for certain charge ratios n/m (in addition to symmetrical ones) has been generalized to constituents of arbitrary masses. Results for realistic cases of the charge ratios 1/2 and 2/3 are presented. It is found that these systems possess the same type of degrees of instabilities as those investigated by Poirier.

We examine the stability of classical two-electron systems with an electron moving along elliptic orbits on the Wannier ridge. Lyapunov exponents are evaluated analytically for circular orbits within the first-order perturbation theory. In the case of the helium atom, these results compare favorably with numerical values obtained by means of the monodromy matrix method.

The role of postcollisional and polarization-correlation effects in energy-sharing (e,2e) collisions is considered. Theoretical and experimental results are presented for the ionization of hydrogen in a symmetric coplanar geometry. A kinematical regime is identified where the triple-differential cross section is sensitive to three-body effects in both the incident and final channels.

We obtain a formula for the general N-dimensional optical theorem in quantum mechanics, generalizing the standard result for three dimensions. It is obtained by an application of the method of steepest descents. The formula holds for arbitrary (anisotropic, nonlocal) short-range potentials.

We present convergent close-coupling calculations of low-energy unpolarized electrons scattering elastically on sodium atoms in a polarized or unpolarized 3P state. We find that the polarization of the target has little effect on the calculated differential cross sections. The agreement with available experiment is only fair, though convergence in the multichannel expansion is readily achieved. Detailed analysis of recoil-type experiments from laser-excited atoms, in terms of the state multipole language, is presented. Mechanisms for extraction of data other than differential cross sections from recoil-type experiments are suggested.

We perform a simple model calculation of electron resonance scattering. The process takes place in a powerful laser field with frequency components ω and 2ω. By changing the relative phase cphi of the two components, the strength of the scattering resonances can be controlled.

A classical study is performed of the ionization of hydrogen Rydberg atoms by circularly polarized microwaves. It is shown that the electron survival probability may decay algebraically for long microwave pulses. The character of the decay is sensitive to the initial atomic state as well as to the assumed shape of the microwave pulse.

The role of collisional cross relaxation in saturated laser amplification is considered by using a simple strong-collisional model. Expressions for the particle-state density distribution and gain are derived for a four-level system. These are reduced to a simple analytic form, subject to an approximation of wide applicability. The role of collisions in changing an inhomogeneous-broadened line to homogeneous, with a change from rebroadening to narrowing on saturation, is demonstrated. The results are shown to be consistent with the existing limited experimental data.

We have measured the nonlinear refractive index ${\mathit{n}}_2$ and two-photon absorption coefficient β in GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As multiple-quantum-well waveguides in the band tail region about 45 meV below the n=1 heavy hole exciton absorption line. At 883 nm we find that β=1.9×${10}^{\mathrm{-}8}$ cm ${\mathrm{W}}^{\mathrm{-}1}$ and that ${\mathit{n}}_2$≊-1×${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^2$ ${\mathrm{W}}^{\mathrm{-}1}$. The linear loss coefficient is measured to be 6.3 ${\mathrm{cm}}^{\mathrm{-}1}$ at the same wavelength. Based on these values, we estimate that up to 4.5 dB pulsed squeezing is possible.

The completeness relation of the eigenstates of the operator ${\mathit{a}}^{\mathit{k}}$, k=2,3,4,..., a being the annihilation operator of the radiation field, is discussed. Through a modification of the normalization factor of the eigenstate of ${\mathit{a}}^{\mathit{k}}$, proposed by several authors including Sun, Wang, and Wang [Phys. Rev. A 44, 3369 (1991)], the correct completeness relation is proposed.

In connection with a paper by Kálmán [Phys. Rev. A 39, 2428 (1989)], we present an independent analysis of the behavior of the matrix element of r and p, relevant for the ground-state photoelectric cross section in hydrogen, evaluated in the Born approximation. This analysis, performed in momentum space, proves once again that, in the plane-wave approximation, the result obtained in momentum gauge is the correct one in the lowest order in αZ (α being the fine-structure constant, Z the atomic number).

It is argued that, contrary to the statement of Cionga and Florescu [preceding Comment, Phys. Rev. A 50, 4422 (1994)], in the plane-wave approximation there is no difference between the results obtained for the S matrix element of x-ray absorption in the length and radiation gauges.