A solution in closed analytic form is obtained for the motion of a charged harmonic oscillator in a variable magnetic field. The time-dependent Schrödinger wave equation is solved in both Cartesian and polar coordinates. The canonical density matrix is calculated via the quasicoherent states.

This paper reports the first quadratic, nondifferential, and self-consistent solution to a Thomas-Fermi-Dirac(TFD)-type equation for many-electron atoms. The essential feature in the Euler-Lagrange equation is the inclusion of a ‘‘first-gradient’’ correction to the TF kinetic energy, which leads to chemical binding in molecules and solids. The calculations are easier to perform than other TFD-type calculations, while the radial density and energy obtained compare very well with similar calculations.

The parity-nonconserving (PNC) electric dipole matrix elements ($A_{\mathrm{el}\left(\mathrm{PNC}\right)\mathrm{})}$ for Cs (6$s_{1/2}$→7$s_{1/2}$) and Tl (6$p_{1/2}$→7$p_{1/2}$) are calculated. In each case the active valence electron is assumed to move in the potential of a Hartree-Fock core augmented by a semiempirical core-polarization potential. Also included are the modifications to the core potential created by PNC effects within the core. The results we obtain are in good agreement with other calculations and measurements.

A distinction between sharp and diffuse interlopers is parametrized by quantum-defect analysis. Increasing level density at the approach to an ionization threshold drives all interlopers into the diffuse class. The relevance of this behavior to the quasi-Landau states in the spectra of excitations in a magnetic field is indicated.

This paper extends earlier calculations [M. Yamanoi and J. H. Eberly, Phys. Rev. A 34, 1609 (1986)] of hole burning using continuous excitation to the finite excitation time used in experiments on Pr:${\mathrm{LaF}}_3$. Both Gaussian-Markov (GM) and random-telegraph (RT) dephasing models are studied. For the GM model, a new feature is the appearance of nutation structure near the center of the hole for a 400-μsec excitation time. In contrast for RT, a similar, although much weaker, structure appears in the wings of the hole. It is noted that for finite excitation times, a detuning as well as the usual intensity dependence of the dephasing time appears.

A generalized complex Lorenz system is derived for toroidal plasmas. The 26-dimensional set is found to have far-reaching similarities with the complex Lorenz system including unmodified asymptotic conservation relations and limit-cycle frequency. The complex Lorenz system is also found to dominate close to the stability boundary. An asymptotic analytical solution including 11 modes has been obtained which gives a good approximation of the full system in weakly unstable cases. For higher values of the Prandtl number the limit cycle is found to bifurcate to doubly periodic or chaotic motion.

Their absorption spectrum of both single crystals and powdered samples of acetanilide (a model system for proteins) has been studied in the amide i region, where a narrow band has been identified as a highly trapped soliton state. The powder-sample spectra have been decomposed using four Lorentzian bands. A strong temperature dependence has been found for the intensity of two of the subbands, which also show a complementary behavior. Polarization studies performed on thin crystals have shown that the subbands have the same polarization. Low-temperature spectra of partially deuterated samples show the presence of the subbands at the same absorption frequencies found using the fitting procedure in the spectra of nondeuterated samples. The soliton model currently proposed to explain the origin of the anomalous amide i component at 1650 ${\mathrm{cm}}^{\mathrm{-}1}$ still holds, but some modification of the model is required to account for the new features revealed by this study.

A classical model of a neutron as a current loop is examined. The importance of the mechanical structure (which was overlooked by Boyer) for the dynamical equations is elaborated. It is shown that the current loop has the same behavior in an external static electric field as was obtained for the neutron by Aharonov and Casher from the Dirac equation.

We report sub-Doppler laser spectroscopy of atomic oxygen. The atom is detected as a trace in a noble-gas radio-frequency discharge by means of optogalvanic effect. The fine structure of the $2p^{3}3p{}_{}{}^5{}_{}{}^{}P_{1,2,3}^{}{}_{}{}^{}\to 2p^3\left(4\mathrm{}{S}^0\right)4d{}_{}{}^5{}_{}{}^{}D_{4,3,2,1,0}^{}{}_{}{}^{}$ transitions is fully resolved and preliminary values for the upper level splittings are: ${\Delta }_{4,3}=1382\mathrm{}\left(20\right)\mathrm{}$ MHz, ${\Delta }_{3,2}=1594\mathrm{}\left(20\right)\mathrm{}$ MHZ, ${\Delta }_{2,1}=1360\mathrm{}\left(20\right)\mathrm{}$ MHz, and ${\Delta }_{1,0}=735\mathrm{}\left(20\right)\mathrm{}$ MHz. The best values so far derived from conventional spectroscopy are one order of magnitude less accurate and in marginal agreement with our data.

The behavior of excitable systems periodically stimulated by pulses is investigated. The non-self-oscillating regime is studied in the simplest realistic model. The global bifurcation structure is similar in several aspects to the one corresponding to driven oscillators. It includes phase locking, quasiperiodicity, period doubling, and chaos. The unexpected persistence of this structure is explained by analytical arguments and its scaling properties are numerically determined.

Hylleraas method variational calculations with up to 458 expansion terms are reported for the n ${}_{}{}^1{}_{}{}^{}D$, n ${}_{}{}^3{}_{}{}^{}D$ terms and for the n ${}_{}{}^1{}_{}{}^{}F$, n ${}_{}{}^3{}_{}{}^{}F$ terms (n=4–8) of neutral helium. Convergence arguments are presented to obtain new estimates of the exact nonrelativistic energies of these terms. The reliability of the estimates ranges from 3×${10}^{\mathrm{-}10}$ a.u. in the worst case to ${10}^{\mathrm{-}11}$ a.u. in the best case. The nonrelativistic singlet and triplet energies are combined with previously calculated values for relativistic and other small energy contributions to evaluate the total ionization energies for the n D and n F levels. Comparisons of the n ${}_{}{}^1{}_{}{}^{}D$ and n ${}_{}{}^3{}_{}{}^{}D$ energies with other calculations and available data yield improved values for relativistic contributions. The calculated relativistic n F ionization energies agree with values based on core-polarization theoretical n G and n H energies within deviations of 3 MHz (5×${10}^{\mathrm{-}11}$ a.u.) for n=5 to 1 MHz (1.5×${10}^{\mathrm{-}11}$ a.u.) for n=7,8. The calculated n F fine-structure separations generally agree with experiment for n=5–8 within uncertainties of the order of 1 to 0.1 MHz. Predicted values given for the 4 F fine-structure separations and the $4^1$F ionization energy are probably accurate within a few MHz.

The nonadiabatic rovibronic energy levels for all species of hydrogenlike molecules of the form [(xμy)z2e], where x,y,z=p,d,t, have been calculated. Employing an isotopic scaling method for the nonadiabatic corrections, an accuracy of 0.05 meV was achieved.

Employing the supersymmetric quantum-mechanical transformations recently developed by Baye, we obtain a class of exactly soluble one-dimensional quantum-mechanical problems that are phase equivalent to the Coulomb problem but have one less bound state.

For rotational-vibrational states of the ionized hydrogen molecule ${\mathrm{H}}_2^{+}$, the Schrödinger equation is solved in the framework of the shifted 1/N expansion with the effective potential derived by means of the Born-Oppenheimer approximation. We also show that rotational-vibrational eigenstates obtained via the shifted 1/N expansion are in agreement to some extent with those of the Morse potential.

We derive a formula for the relativistic decay rates in atoms in a formulation of quantum electrodynamics based upon the electron’s self-energy. Relativistic Coulomb wave functions are used, the full spin calculation is carried out, and the dipole approximation is not employed. The formula has the correct nonrelativistic limit and is used for calculating the decay rates in hydrogen and muonium for the transitions 2P→1$S_{1/2}$ and 2$S_{1/2}$→1$S_{1/2}$. The results for hydrogen are Γ(2P→${1S}_{1/2}$)=6.2649×${10}^8$ ${\mathrm{s}}^{\mathrm{-}1}$ and Γ(${2S}_{1/2}$→${1S}_{1/2}$)=2.4946×${10}^{-6}$. Our result for the 2P→1S transition rate is in perfect agreement with the best nonrelativistic calculations as well as with the results obtained from the best known radiative decay lifetime measurements. As for the hydrogen 2$S_{1/2}$→1$S_{1/2}$ decay rate, the result obtained here is also in good agreement with the best known magnetic dipole calculations. For muonium we get Γ(2P→${1S}_{1/2}$)=6.2382×${10}^8$ ${\mathrm{s}}^{\mathrm{-}1}$ and Γ(${2S}_{1/2}$→${1S}_{1/2}$)=2.3997×${10}^{-6}$ ${\mathrm{s}}^{\mathrm{-}1}$.

We have computed the excitation probabilities of the ${\mathrm{T}}_2$ molecules in the crystal surrounding the β-decaying tritium. The influence of this effect on the neutrino mass determination has been studied. For a neutrino mass of the order of a few eV the effect has been shown to be very important. Its importance decreases, however, with increasing neutrino mass. In addition we consider the influence of the high-energy portion (E>164 eV) of the probability distribution on the neutrino mass.

Hermitian tilted so(4,2) operators are constructed, acting on the bound states of the Coulomb problem, and are shown to have simple time dependence in the Heisenberg picture. The periodic time dependence of the corresponding classical variables can be regarded as a consequence of their simple geometrical interpretation and their simple expressions in terms of action-angle variables. Corresponding results are indicated for unbound states.

The rotating displaced oscillator problem has been treated by the shifted 1/N expansion method. Next, the Hamiltonian for this problem is framed in supersymmetric form for certain values of the parameter. Exact eigenvalues and eigenfunctions are obtained. The eigenvalues obtained from the shifted 1/N expansion method are compared with those obtained by numerical methods and supersymmetric exact values, and are found to be in satisfactory agreement both at low and high values of the coupling parameter.

With the use of formulas given by the author for the expansion of Slater-type orbitals (STO’s) in terms of STO’s at a new origin [I.I. Guseinov, Phys. Rev. A 31, 2851 (1985)], one- and two-electron multicenter integrals of $r^{\mu \mathrm{-}1}$$e^{\mathrm{-}\kappa r}$$S_{\nu \sigma }$(θ,cphi) for q=R and $r^{\mu \mathrm{-}1}$$e^{\mathrm{-}\kappa r}$$Y_{\nu \sigma }$(θ,cphi) for q=C are expressed in terms of the overlap integrals. The analytical formulas used for the evaluation of these integrals have recently been established by the author [I.I. Guseinov, J. Mol. Sci. (China), 5 (2) (1987)]. The relationships obtained are valid for general values of the STO parameters and for μ≥-(ν+1) and κ≥0.

We present a uniform semiclassical analysis of the radial coupling A(r)(d/dr) in the adiabatic basis. Various approximations are tested for solving the perturbative form of the probability integrals. Our model is applied to the excitation transfer He${(}^1$S)+${\mathrm{Ne}}^2$+${(}^1$D)→He${(}^1$S)+${\mathrm{Ne}}^{2+}$${(}^1$S). The results we obtain are in good agreement among themselves and provide an alternative model in the adiabatic frame to complete the current Landau-Zener-Stückelberg–like calculations. The dominating role of the turning points in such curve-crossing problems is also demonstrated.