A 2-MeV beam of ${\mathrm{H}}_2^{+}$ molecular ions was excited by 193-nm photons from an ArF laser. The ${\mathrm{H}}^{+}$ photofragments were energy analyzed by an electrostatic analyzer, and the potential energy released in the ${\mathrm{H}}_2^{+}$ rest frame was determined. The released energy corresponds to absorption from low-lying vibrational levels of the $1s{\sigma }_g$ ground state to the $2p{\sigma }_u$ state of ${\mathrm{H}}_2^{+}$.

The repulsion between positively charged projectiles and the nucleus of target atoms gives rise to a Coulomb-deflection factor that reduces the inner-shell-ionization cross sections calculated for straight-line particle trajectories. In the monopole approximation to the repulsion, this factor depends on the function $G_0\mathrm{}\left(x\right)={\left[x\frac{d{K}_{\mathrm{ix}}\mathrm{}\left(y\right)\mathrm{}}{\mathrm{dy}{|}_{y=x}}\right]}^2$, where $K_{\mathrm{ix}}$ is the Bessel function of imaginary order. Through identities between Bessel functions of complex order and argument we have, in this addendum to an earlier paper [W. Brandt and G. Lapicki, Phys. Rev. A 20, 465 (1979)], reduced the evaluation of $G_0\mathrm{}\left(x\right)\mathrm{}$ to computed functions. Values of $G_0\mathrm{}\left(x\right)\mathrm{}$ and its integrals as they appear in the theory of $K$- and $L$-shell ionizations are tabulated. The monopole approximation is compared with results based on the standard approximation $G\left(x\right)=1\mathrm{}$ which describes the experimental data.

Results of a previous work on the nonlinear scattering by electrostatic waves in a laser-produced plasma are reconsidered and corrected.

We have measured the photoionization of atomic potassium in the vicinity of the minimum in the cross section. We have bypassed the problem of molecular photoionization, which may have distorted previous results, using a simple, generally applicable, time-of-flight technique. The results are now in qualitative agreement with theoretical predictions.

A new method for accurately measuring relative oscillator strengths is presented. The method is based on measurements of the frequencies at which a nonlinear-optical sum-mixing process is phase matched. By applying this technique to Ca I, the relative strengths of the $4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-4\mathrm{snp}{}_{}{}^1{}_{}{}^{}P_1^0{}_{}{}^{}$ transitions for $n=10-13\mathrm{}$ are measured to an accuracy of ±2%, more than six times better than previous measurements.

A successful two-photon spectroscopy experiment using combined C${\mathrm{O}}_2$ and diode lasers operating in the 10-μm region is reported. Beams from the two lasers were passed in nearly opposite directions through a sample cell while the intensity of the transmitted diode laser beam was monitored as a function of its frequency. Doppler-free two-photon absorption signals were observed for the rovibrational transitions of N${\mathrm{H}}_3$, $T(v_2,J,K)=(2^{-},7,7)\leftarrow (0^{-},7,7) \mathrm{and} (2^{-},1,1)\leftarrow (0^{-},1,1)$.

A method of statistically characterizing an area-preserving, doubly periodic mapping is presented. This method allows one to calculate the characteristic functions, and the joint probabilities of the mapping.

The existence of corrections, due to annihilation, to the usual expressions for the energy levels and decay rates of the $m=0\mathrm{}$ triplet and singlet states of positronium in a magnetic field are noted. The corrections cause the value of the hyperfine interval $\nu$, as obtained from wellknown resonance experiments, to increase by 1.8 standard deviations of the current experimental error to $\nu =203\mathrm{}387.5\left(1\right)\mathrm{}$ MHz where $\nu \left(\mathrm{theor}\right)=203\mathrm{}400\left(10\right)\mathrm{}$ MHz. This shift could be observable in the near future when calculations of $\nu$ to order ${\alpha }^2$ are completed.

The electron excitation cross section of the metastable $1s_5$ level of neon is measured by a new technique that involves laser excitation of the metastables to a fluorescing level. A method for obtaining an absolute calibration of the cross section is given. The value of the direct cross section is 16×${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ at 20 eV energy of the incident electrons.

The dynamics of nonstationary wave packets in model quantum-mechanical systems are studied for the properties of ergodicity and instability. The long-time-average Wigner phase-space distribution is calculated for each wave packet and analyzed for uniformity on a surface of section. A mild transition from nonergodic to ergodic behavior is observed with increasing energy. These results are compared to long-time averages of the wave-function probability density. The "stability" of each packet is also analyzed by several methods, including the "survival" of the initial state and a new measure of "separation" of similar wave packets. The relationships between the wave-packet ergodicity and instability and the corresponding classical dynamics are developed. Comparisons to other quantum-ergodic studies, and implications for intramolecular energy transfer and classical-ergodic studies are discussed.

By expressing the two-electron wave functions in hyperspherical coordinates ($R$,$\Omega$) in an adiabatic approximation $F_{\mu }\mathrm{}\left(R\right)\mathrm{}{\Phi }_{\mu }(R;\Omega )$, I describe a simple procedure for obtaining the channel functions ${\Phi }_{\mu }(R;\Omega )$ analytically. These analytical functions, ${\Phi }_{\mu }(R;\Omega )$ in the finite-$R$ region, are obtained by generalizing the known hydrogenic solutions in the asymptotic ($R\to \infty$) limit for each channel $\mu$ and are required to satisfy proper boundary conditions in the hyperangles $\Omega$ rigorously. It is shown that these analytical functions compare well with the channel functions obtained previously from numerical calculations and, in a straightforward manner, describe the + and - channels of doubly excited states. The implication of this result as a method of generalizing hyperspherical coordinates to many-electron problems is discussed.

The case of the quantum unidimensional motion of a point particle subject to a viscous force proportional to the square of the speed of the particle is treated. Once a suitable Lagrangian has been chosen, the canonical quantization procedure is applied leading to a Schrödinger equation for quadratic friction and an arbitrary potential. The cases of an exponentially decreasing potential plus a linearly increasing term is explicitly solved.

Correlated calculations using many-body perturbation theory and good basis sets for the dipole moment, polarizability, and hyperpolarizabilities of ${\mathrm{H}}_2$O are reported. The finite-field coupled Hartree-Fock (CHF) theory is used as a zeroth-order approximation, with electron correlation included via the linked-diagram theorem. Single-, double-, and quadruple-excitation contributions are included. It is found that correlation changes $\left|\beta \right(\omega =0\left)\right|$ by about 50% compared to the CHF result. Even larger changes are found among the components of $\overleftrightarrow{\gamma }$. The dependence of the $\overleftrightarrow{\beta }$ hyperpolarizability on geometric displacements is investigated, finding that $\overleftrightarrow{\beta }$ can be highly sensitive to slight changes in bond lenghts.

The energy and structure of molecules and ions formed by attaching quarks to light nuclei were computed in the self-consistent-field approximation. In spite of equilibrium shifts and increases in reaction half-lives caused by the expected low quark concentration, it seems quite possible that free quarks in undisturbed matter exist as electrically neutral molecules. However, if such molecules are split into fractionally charged fragments, these fragments will recombine only slowly on a laboratory time scale. This is of particular significance in assessing the validity of experiments designed to estimate the upper limit of free quark density in matter.

We point out how the presence of hyperfine structure can improve the coherent excitation and ionization of $J\to J-1\mathrm{}$ and $J\to J$ transitions. In the limit of Rabi frequency dominating hyperfine splitting one recovers previously noted rules.

We analyze the free-space propagation of matter waves with a view to placing an upper limit on the strength of possible nonlinear terms in the Schrödinger equation. Such additional terms of the form $\psi F\left({\left|\psi \right|}^2\right)$ were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity of the form $F=-\mathit{b}\ln {\left|\psi \right|}^2$, we find that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of $\mathit{b}$. Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allow us to deduce an upper limit for $\mathit{b}<3.3\mathrm{}\times {10}^{-15\mathrm{}}$ eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.

Configuration-interaction calculations have been carried out for the core-excited ${}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}$ bound states of neutral Li. The levels $1s2p {}_{}{}^3{}_{}{}^{}P 3d$, $1s2p {}_{}{}^3{}_{}{}^{}P 4d$ and $1s2p {}_{}{}^1{}_{}{}^{}P 3d$ are estimated to lie 524 235.5(3.0), 530 306.1(3.0), and 532 058.8(4.5) ${\mathrm{cm}}^{-1\mathrm{}}$ above the ground state, respectively. Using additional theoretical and experimental data for core-excited Li levels and calculated oscillator strengths, we have developed a consistent scheme for the decay of ${\mathrm{Li}}^{**}$ doublets which explains the main features of this spectrum. Two previously observed lines $\lambda =2846\mathrm{} \mathrm{and} 3661$ Å correspond to transitions between ${}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P$ bound states, in agreement with an earlier assignment. Three other lines $\lambda =2640, 3144, \mathrm{and} 4590$ Å result from bound states ${}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P$ decaying into ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ core-excited states which undergo rapid autoionization, in agreement with the prominent linewidths exhibited experimentally. Possible spin-forbidden electric-dipole transitions are discussed.

We have carried out configuration-interaction calculations for ${}_{}{}^4{}_{}{}^{}F_{}^{e,o}{}_{}{}^{}$ states of Li and ${\mathrm{Be}}^{+}$ and for the lowest ${}_{}{}^4{}_{}{}^{}D_{}^{e,o}{}_{}{}^{}$ states of ${\mathrm{Be}}^{+}$ in an effort to test the accuracy that can be achieved in transition-energy calculations by assuming transferability of relativistic, radiative, and mass-polarization corrections among similar electron cores. He and ${\mathrm{Li}}^{+}$ $2p4f{}_{}{}^{1,3}{}_{}{}^{}F$ states have also been considered. The nonrelativistic result for the Li $1s2p4f{}_{}{}^4{}_{}{}^{}F\to 1s2s4f{}_{}{}^4{}_{}{}^{}F_{}^o{}_{}{}^{}$ transition is ${\lambda }_{\mathrm{air}}=5474.3\mathrm{}\pm 0.4$ Å. Including relativistic, radiative, and mass-polarization corrections for the $1s2p{}_{}{}^3{}_{}{}^{}P$ and $1s2s{}_{}{}^3{}_{}{}^{}S$ ${\mathrm{Li}}^{+}$ cores we get $\lambda =5471.7\mathrm{}\pm 0.4$ Å, in excellent agreement with a $\lambda =5471.9\mathrm{}\pm 1.4$ Å recently observed in the beam-foil source. Stronger support for our basic assumption comes from three calculated (experimental) wavelengths $\lambda =3406.0\mathrm{}\pm 0.3(3405.6\pm 0.6), 4330.1\pm 0.5(4330.2\pm 0.5), \mathrm{and} 3510.8\pm 0.5(3510.8\pm 0.5)$ Å in the Be ${\mathrm{ii}}^{**}$ spectrum. Furthermore, three lines (the first two above and $\lambda =981\mathrm{}$ Å) have been reassigned and three new wavelengths are predicted for this spectrum. The $1s2s4f\pm 1s2p3d$ nature of the ${}_{}{}^4{}_{}{}^{}F_{}^o{}_{}{}^{}\mathrm{}\left(1\right)\mathrm{}$ and ${}_{}{}^4{}_{}{}^{}F_{}^o{}_{}{}^{}\mathrm{}\left(2\right)\mathrm{}$ states in ${\mathrm{Be}}^{+}$ is responsible for the uncommon situation that ${}_{}{}^4{}_{}{}^{}F_{}^o{}_{}{}^{}\mathrm{}\left(1\right)\mathrm{}$ is below $1s2s4d {}_{}{}^4{}_{}{}^{}D_{}^o{}_{}{}^{}\mathrm{}\left(2\right)\mathrm{}$, thus explaining the failure of some of the earlier assignments. The lowest ${\mathrm{Be}}^{+}$ $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ state is found 115.845±0.016 eV above the ${\mathrm{Be}}^{+}$ $1s^{2}2s$ ground state, in fair agreement with a recent experimental value of 115.7±0.1 eV. The He and ${\mathrm{Li}}^{+}$ $2p4f{}_{}{}^{1,3}{}_{}{}^{}F$ states decay to $1s4f{}_{}{}^{1,3}{}_{}{}^{}F$ states with wavelengths too close to the resonance transition $2p\to 1s$ of the corresponding one-electron system to be observed in beam-foil experiments. The ${\mathrm{Li}}^{+}$ $2p4f {}_{}{}^{1,3}{}_{}{}^{}F$ states, however, decay to $2p3d {}_{}{}^{1,3}{}_{}{}^{}D$ states with $\lambda =3825.4\mathrm{}\pm 0.1 \mathrm{and} 4352.2\pm 0.1$ Å, respectively, and they should be susceptible of experimental observation.

A proof by induction is given of the so-called contraction theorem for the evaluation of (anti)commutators of strings of Fermion creation and annihilation operators. This theorem bears some formal similarity to Wick's theorem but is essentially simpler and its applications do not lead to any disconnected diagrams. Examples of applications to configuration-interaction and coupled-cluster methods are presented.