Explicit scattering solutions of the one-dimensional Schrödinger equation are given. A one-parameter family of the potentials considered here causes the same scattering at all energies. The previously published explicit examples of nonuniqueness in the one-dimensional inverse quantum problem are special cases of the potentials given here.

The quantum hydrodynamics of an incompressible inviscid fluid in $R^2$ or $R^3$ is described by means of representations of the group of volume-preserving diffeomorphisms. In $R^2$ we obtain the surprising result that within the framework of the Euler equations point vortices cannot be consistently quantized, and the encouraging outcome that vortex filaments can be. We also discuss analogs of such configurations in $R^3$.

By our making use of the Monte Carlo renormalization-group method, it is shown that the deconfining phase transition of the (2+1)-dimensional $Z\left(2\right)\mathrm{}$ lattice gauge theory at finite temperature is governed by the same fixed point and critical indices as the two-dimensional Ising model, thus proving that both theories belong to the same universality class.

A unique and appealing chiral-color theory is presented. It involves five fermion families, four light neutrinos, and several more exotic states. The Glashow-Iliopoulos-Maiani mechanism is preserved and the theory is embedded in the unifying group ${\mathrm{}\left[\mathrm{S}\mathrm{U}\right(4\mathrm{}\left)\right]}^6$.

We present evidence for the exclusive reaction $e^{+}{e}^{-}\to {D_s}^{\pm }{D_s}^{*\mp }$, observed with the Mark III detector at the SLAC storage ring SPEAR. The ${D_s}^{\pm }$ is reconstructed in the $\phi {\pi }^{\pm }$ decay mode, while the ${D_s}^{*\mp }$ is detected as a narrow peak in the recoil-mass distribution. The mass of the ${D_s}^{*}$ is found to be 2109.3±2.1±3.1 MeV/${\mathit{c}}^2$, yielding a ${D_s}^{*}-D_s$ mass difference of 137.9±2.1±4.3 MeV/${\mathit{c}}^2$. The width of the ${D_s}^{*}$ is <22 MeV/${\mathit{c}}^2$ at the 90%-confidence level. The observed signal corresponds to $\sigma (e^{+}{e}^{-}\to {D_s}^{+}{D_s}^{*-}+{D_s}^{-}{D_s}^{*+})B({D_s}^{+}\to \phi {\pi }^{+})=30\mathrm{}\pm 6\pm 11$ pb at $\sqrt{s}=4.14\mathrm{}$ GeV.

With the basic concepts of the constituent-quark model formulated in the light-cone Fock approach we present a relativistic model of the pion and $\rho$-meson valence-quark structure. We point out that a nonstatic relativistic spin wave function and small transverse size of the valence configuration are essential to reproduce the basic features of the Chernyak-Zhitnitsky amplitudes for the $\pi$ and $\rho$ as they are obtained from QCD sum-rule techniques.

We consider baryons in a two-flavor Nambu-Jona-Lasinio-type model for self-interacting quarks in the large-$N$ limit using mean-field-theory techniques. We show that for slowly varying mean fields, all baryon properties are exactly those obtained from collective-coordinate quantization of the soliton in a nonlinear $\sigma$ model of mesons. We also indicate how the higher Fermi couplings can stabilize the soliton.

A superdeformed band ($\beta \approx 0.4-0.5$) was found in ${}_{}{}^{135}{}_{}{}^{}\mathrm{Nd}$, the first one in an odd-mass nucleus. It consists of thirteen transitions with an average moment of inertia ${\mathcal{I}}^{\mathrm{}\left(2\right)\mathrm{}}\approx 59{\hslash }^2$ Me${\mathrm{V}}^{-1\mathrm{}}$, and gathers at its bottom ∼10% of the reaction events leading to ${}_{}{}^{135}{}_{}{}^{}\mathrm{Nd}$. Of the three known superdeformed bands, it is the most strongly populated and the one observed to the lowest spins, and it is the first in which the transitions depopulating the band have been seen. It has a moment of inertia very similar to that of the superdeformed band in ${}_{}{}^{132}{}_{}{}^{}\mathrm{Ce}$. The less-deformed part of the decay scheme of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Nd}$ is also given.

We have studied the correlations among energies of three $\gamma$-rays emitted by high-spin nuclear states. The correlation features (ridges and dip) in coincidence with two $\gamma$ rays of a given energy are found to be the same, within our statistics, as those in coincidence with a single $\gamma$ ray of that energy. We believe that this implies that the full $\gamma$-ray spectrum is a mixture of some essentially undamped rotational cascades and some rather strongly damped ones.

The $\alpha$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ resonating-group-method calculation which fits well the spectroscopic data of the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ levels is shown to fit well also the scattering cross section up to high energy. The equivalent local potential derived from the resonating-group method is found to be very similar to the optical potential of Michel et al. Thus it is concluded that a significant part of the energy dependence of the real part of the $\alpha$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ optical potential is due to the internucleus antisymmetrization.

Neutral sodium atoms have been continuously loaded into a 0.1-K-deep superconducting magnetic trap with laser light used to slow and stop them. At least 1 × ${10}^9$ atoms were trapped with a decay time of 2½ min. The fluorescence of the trapped atoms was studied as a function of time; possible loss mechanisms from the trap are discussed.

We report the first measurements of elastic scattering of spin-polarized electrons from spin-polarized Na atoms as a function of scattering angle. The incident energy is 54.4 eV, and the angular range is 20° - 135°. Data are presented as an exchange asymmetry and a spin-orbit asymmetry. Each asymmetry has a magnitude of 3% to 4%, indicating that both the exchange and spin-orbit interactions must be taken into account to predict our experimental results.

Quantum phase interference is shown to occur in sodium Rydberg states ($n=26-31\mathrm{}$) when they are exposed to weak rf electric fields during the first few volts per centimeter of an increasing electric-field ramp. The effect is observed as an oscillation of intensity in a component of the selective-field-ionization signal as a function of applied frequency in the range 250-990 MHz. The phenomenon is explained in terms of dressed states, and the frequencies of the peaks are modeled in good agreement with experiment.

Successive transitions from Hopf bifurcation to Shilnikov chaos and eventually to regular spiking are observed in a laser with feedback on increase of a control parameter. Each one of these regimes is due to the dominant attraction of one at a time among three coexisting unstable fixed points. Hence, each situation has a global behavior sufficiently described by attribution of the major part of the return time to a single fixed point.

We consider a nonlinear, passive optical system contained in an appropriate cavity, and driven by a coherent, plane-wave, stationary beam. Under suitable conditions, diffraction gives rise to an instability which leads to the emergence of a stationary spatial dissipative structure in the transverse profile of the transmitted beam.

The results of an experimental and numerical investigation into a new mechanism for the onset of time dependence in Taylor-Couette flow are presented. The interaction between a symmetry-breaking bifurcation and a fold point gives rise to Hopf bifurcation. The resulting time-dependent flows may be either periodic or irregular.

The use of radio frequency waves in the ion cyclotron range of frequencies is shown to stabilize ballooning modes in tokamaks when the frequency and spatial wave structure are appropriately chosen. The physics of rf stabilization may provide access to high-$\beta$ tokamak operation in the second stability regime and may also be useful in the suppression of edge-localized modes in present experiments. Estimates of the required power in the ion cyclotron range of frequencies are given for two examples of rf stabilization.

It is observed that the extraordinary mode near the second harmonic effectively couples to electrons at largely down-shifted frequencies. From measurements of soft-x-ray radiation and third-harmonic electron-cyclotron emission, selective heating of electrons with an energy satisfying the relativistic cyclotron resonance condition is deduced. It is demonstrated that the selective electron-cyclotron heating of 70 kW produces a 65-kA/sec rampup of the lower-hybrid-driven plasma current.

Synchrotron x-ray diffraction results of phospholipid monolayers at an air/water interface are reported and compared with fluorescence microscopic observations of the fluid-gel lipid phase transition. The pressure-induced transition to an orientationally ordered phase occurs at a pressure ${\pi }_c$ which is by more than 15 mN/m below a pressure ${\pi }_s$ where a transition to a positionally ordered phase occurs. Hence there exists an intermediate phase with long-range orientational and short-range positional order.

We have used synchrotron radiation to study organic monolayers on water ("Langmuir films"). At high monolayer pressures, lead stearate [Pb${\left({\mathrm{C}}_{17}{\mathrm{H}}_{35}\mathrm{C}\mathrm{O}\mathrm{O}\right)}_2$] shows a powder peak at 1.60 ${\mathrm{\AA }}^{-1\mathrm{}}$, implying an area per unit cell of 17.8 ${\mathrm{\AA }}^2$ if the lattice is triangular. The correlation length is about 250 Å. Lignoceric acid (${\mathrm{C}}_{23}$${\mathrm{H}}_{47}$COOH) shows a similar peak even though no heavy ions are attached. When the pressure is reduced, the peak in lead stearate does not observably move or broaden; below the "knee" in the isotherm, however, the peak height decreases slowly with increasing area, implying a first-order melting transition.