Dependence of the scattering length for hydrogen atoms on effective mass

The possibility that the non-adiabatic correction to the scattering length of a pair of hydrogen atoms interacting via the ground state molecular potential, X¹Σ_g ⁺, of H₂ could be made by replacing the mass of each nucleus by a different effective mass is explored. The Born-Oppenheimer potential with adiabatic, relativistic and radiative corrections is used in calculations of the scattering lengths and the mass-dependent shifts of the rotationless vibrational levels with fixed and varying effective masses. The shifts are compared with established values and it is demonstrated that the semi-classical formula for the scattering length accounts well for the effect of changing the mass. A perturbing potential that is equivalent to a change in mass is derived and it is compared to a published local non-adiabatic potential.     

Three-dimensional vibration analysis of a torus with circular cross section

The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, theta) at each circular cross section and the circumferential coordinate phi around the ring, is developed. Each of the displacement components u(r), v(theta), and w(phi) in the r, theta, and phi directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the theta and phi directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem.     

A biosynthetic proposal for ring formation in the antitumor agent halichomycin. Asymmetric synthesis of the AB-carbon backbone of halichomycin

[reaction: see text] A biosynthetic proposal for ring formation in the antitumor agent halichomycin is presented in which macrocyclization of the putative prehalichomycin intermediate 1 is the first step. Compound 2 then undergoes dehydration to the alpha-keto N-acylimine 3 followed by tandem nucleophilic addition of the C(16)-hydroxyl to form the hemimacrolactam. A stereospecific Michael ring closure and enol protonation complete C-ring assembly. So far, synthetic efforts toward 1 have resulted in 8.     

A high statistics measurement of the Lambda(+)(c) lifetime

A high statistics measurement of the Lambda(+)(c) lifetime from the Fermilab fixed-target FOCUS photoproduction experiment is presented. We describe the analysis technique with particular attention to the determination of the systematic uncertainty. The measured value of 204.6 +/- 3.4 (stat) +/- 2.5 (syst) fs from 8034 +/- 122 Lambda(+)(c)-->pK(-)pi(+) decays represents a significant improvement over the present world average.     

Phase measurement accuracy of feedback interferometers

Feedback interferometers are described with specific reference to potential applications in micro-machines. A theoretical analysis is developed to determine the linearity, stability, and noise performance of this type of interferometer. The theoretical analysis was tested using a prototype high-precision feedback interferometer which showed that, at a feedback loop gain which enabled the system to track 6 fringes, the linearity of the interferometer was better than λ/100 and single phase measurements could be made with an accuracy of λ/80.     

Laser spectroscopy of FeO: Rotational analysis of some subbands of the orange system

Extensive laser excitation spectra and rotationally resolved laser-induced fluorescence spectra have been recorded for the “orange system” of gaseous FeO in the wavelength regions 5790–6140 and 5580–5640 Å. Detailed rotational analyses have been performed for about $\text{20}\text{Ω}\text{′}$ substates lying between 16 350 and 18 550 cm^?1. These are found to comprise a very severely perturbed ⁵Δ_i excited electronic state with a bond length of about 1.69 Å (which is responsible for the parallel polarization of the electronic transition from the ⁵Δ_i ground electronic state) and a large number of “extra” $\text{Ω}$ substates with B′ values ranging from 0.38 to 0.50 cm^?1, which almost certainly belong to high vibrational levels of lower-lying electronic states. Evidence about the natures of the “extra” states is confusing, however, with the ⁵⁴FeO⁵⁶FeO isotope shifts apparently being in conflict with the patterns of vibrationally resolved laser-induced fluorescence. Every single $\text{Ω}$ substate that has been analyzed shows rotational perturbations of varying severity. The density and magnitude of the rotational perturbations are quite exceptional for a diatomic molecule, and result in a new type of totally chaotic diatomic spectrum. There is a remarkable similarity to the visible spectrum of NO₂: in NO₂ the complications arise from the high density of perturbing ground state vibrational levels; in FeO there is a correspondingly high density of perturbing electronic states at lower energy. The great complexity of the FeO spectrum arises because the states are in an awkward intermediate spin-coupling case which still resembles Hund's case (a) but shows strong tendencies toward Hund's case (c) coupling.     

Newton's method for nonlinear ordinary and partial differential equations

A unified approach is presented for proving the local, uniform and quadratic convergence of the approximate solutions and a-posteriori error bounds obtained by Newton's method for systems of nonlinear ordinary or partial differential equations satisfying an inverse-positive property. An important step is to show that, at each iteration, the linearized problem is inverse-positive. Many classes of problems are shown to satisfy this property. The convergence proofs depend crucially on an error bound derived previously by Rosen and the author for quasilinear elliptic, parabolic and hyperbolic problems.     

Predissociated rotational structure in the 2490-Å band of 15NO2

The rotational structure of the 000-000 band of the 2490-Å system of ¹⁵NO₂ ($\text{2}{}^2\text{B}{}_2\text{-}\text{X}\text{?}{}^2\text{A}{}_1$) has been analyzed from high dispersion grating spectrograph plates. The band is found to be slightly predissociated, exactly as in the ¹⁴NO₂ isotope, which suggests that it might be usable for laser separation of the isotopes of nitrogen; tables of the wavenumbers of the lines are given. The upper-state molecular constants are close to the values calculated by the isotope relations from those of ¹⁴NO₂.