A systematic analysis is presented of the possible elementary processes which determine the fate of negative pions stopped in hydrogen-containing samples with use of a phenomenological description in comparison with the available experimental information on pion capture by hydrogen in gas mixtures.

It is noted that the results of Horváth's preceding Comment do not invalidate the conclusions of Jackson and collaborators. It has already been shown that there is a connection between the parameters of the two models.

The linear relationship between the mean number of multiply ionized outer-shell electrons and the centroid energy of the corresponding Auger spectra, established experimentally, is discussed. The origin of this trend can be explained by the equidistant energies of the satellite line groups in the Auger spectra.

Lo and Shimony have proposed a molecular test of local hidden-variables theories, which should eliminate a loophole arising in all tests dealing with photons. It is pointed out that the proposed correction for accidental coincidences invalidates the test. Conditions for the reliability of the experiment are stated.

Several criticisms by Santos are answered. Objections are raised against a variant analysis which he proposed. Two cogent objections by Pritchard against Lo and Shimony are mentioned.

Table II of the paper of J. Testa and G. A. Held [Phys. Rev. A 28, 3085 (1983)] on the cubic map has been corrected. A new equation is demonstrated to calculate the valid numbers of periodic orbits of the cubic map in agreement with the work of O. Chavoya and co-worders on the same map.

We have built a parametric motion transducer that is a prototype for a "back-action-evasion" measuring device. Our tests demonstrate that it has the expected phase sensitivity in its fundamental mechanical-to-electrical coupling when appropriately pumped. Another test verifies the anticipated frequency and loss dependence of the coupling. A third test verifies that the absolute magnitude of coupling is reasonably close to model predictions.

We report the best variational energies obtained to date of the bound states of muonic molecules containing nucleons of unit charge, or isotopes of hydrogen. Hylleraas wave functions are used to describe the three-particle systems, and the convergence of the energies is carefully studied; as many as 440 terms have been included in some cases. These results are compared with the best previous values.

Preliminary results are reported for the dielectronic recombination cross sections of ${\mathrm{Mg}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{O}}^{5+}$, and ${\mathrm{Cl}}^{6+}$. The method is based on multichannel quantum-defect theory. The results are compared with experiments and other theoretical calculations. The peak cross sections for the multiply charged ions are within a factor of 2 agreement with the available data; these and other discrepancies are discussed.

The existence of the theoretically predicted $2s 2p^2{}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{}$ metastable ${\mathrm{Be}}^{-}$ ion has been confirmed by experiment. The autodetachment decay rates at several decay times after formation show the presence of more than one substate, with the lifetime of the longest component exceeding 100 μs.

The present Rapid Communication makes two points. (1) The exact matrix elements for the transitions between two hydrogenic states accompanied by the emission or absorption of one photon has been calculated in closed form without resorting to multiple expansions. Thus, retardation is taken into account exactly. (2) In addition to using these exact matrix elements to calculate transition probabilities, one can make estimates of the contribution to second-order processes of these matrix elements. In particular, it can be shown that the total contribution of bound-state matrix elements to the electromagnetic shift of the ground state is finite without renormalization.

A direct numerical simulation of kinetic aggregation is presented in which the probability of sticking depends on the size of the clusters. It is found that the fractal dimension of the largest cluster is different depending on whether the gelation phenomenon occurs or not. In the case of Brownian diffusion, the model of Witten and Sander is recovered when gelation occurs, while the alternative model of "clustering of clusters" is recovered when gelation does not occur. Another model (with long-range forces) is also considered.

We report the observation of an instability in a flexoelectric nematic domain due to a linear coupling with an external dc electric field. We use a hybrid aligned nematic cell with two antiparallel flexopolarized domains. Above a certain threshold, the field induces a twist instability in domains with the flexopolarization opposed to the field. The threshold field in methoxybenzylidenebutylaniline is in reasonable agreement with a calculation which also includes the effect of the dielectric anisotropy.

The systematic admixture of high angular momentum into the low-lying states of atoms constitutes a class of correlated electron motion resulting from a single physicomathematical mechanism. In the region of configuration space where the mean-square distance of electrons from the nucleus ($R^2=\Sigma {i=1\mathrm{}}^N\frac{r_i^2}{N}$) is less than its expectation value, the atomic shell structure is strongly perturbed. In the limit $R\to 0$ high angular momentum becomes more favorable energetically and the shell structure approaches that of a Fermi gas. Results include a list of configurations which mix strongly with ground states of atoms from beryllium to argon.

The two-photon decay mode of hydrogenic atoms from an arbitrary state ($n_1$, $l_1$, $m_1$) to an arbitrary state ($n_2$, $l_2$, $m_2$) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions $n_{1}s\to n_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the $2s$ metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\tau }=8.2284\mathrm{}$ ${\sec }^{-1\mathrm{}}$, agrees with Klarsfeld. For transitions of $n_{1}s\to 1s$ and $n_{1}d\to 1s (n_1\ge 3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the $n_{1}d\to 1s$ transitions is shown to be significantly different from the $n_{1}s\to 1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.

A quantum-mechanical linear-response formalism is used to calculate the frequency shift and lifetime of an excited atom near an arbitrary flat interface. The results depend on the frequency-dependent atom and field susceptibilities, and in the vicinity of an interface can be expressed in terms of the appropriate Fresnel reflection coefficients; the contributions from surface excitations are easily identified. As examples, we consider an atom above a metal and a dielectric waveguide.

By expressing the Fermi-Dirac functions $F_{\alpha }\mathrm{}\left(z\right)\mathrm{}$ as a contour integral, we can, after some manipulations, apply the theorem of residues to obtain several high-precision functional series expansions which represent these functions in wide regions of the complex $z$ plane, and which analytically continue the well-known power series expansions valid for $\left|z\right| <1\mathrm{}$. We also evaluate the respective Fermi-Dirac functions $F_{\alpha }\mathrm{}\left(z\right)\mathrm{}$ to an accuracy of nine decimal places for $\alpha =\frac{1}{2}, \frac{3}{2}, \mathrm{and} \frac{5}{2}$ and positive real $z$ (the parameter $\alpha$ commonly found in the literature corresponds to $\alpha -1\mathrm{}$ in our notation). In particular for $\alpha =\frac{3}{2} \mathrm{and} \frac{5}{2}$ (both cases of great interest for applications) elementary functions are found, which represent a very good approximation to the respective $F_{\alpha }\mathrm{}\left(z\right)\mathrm{}$ functions in wide intervals of the $z$ variable.

Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength $B$. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to $L_z{B}^{\frac{1}{3}}$). For small values of this parameter there is an "elliptical regime" in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values of the parameter there is a "helical regime" in which the electron circles rapidly around a magnetic field line and bounces slowly back and forth along the field. Between these two regimes there is an irregular regime, with "chaotic" orbits and a "transition regime" in which the trajectories can be described in oblate spheroidal coordinates. Bound states persist even at energies above the escape energy, provided that the angular momentum (or field strength) is sufficiently large. With use of action-variable quantization, some formulas for semiclassical energy eigenvalues are given for regimes where the trajectories are regular.