Two-photon decays of hadronic molecules

In many calculations of the two--photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force. In the leading order one gets the well-known point-like limit answer. We estimate, in a self-consistent and gauge invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small. The role of possible short-ranged operators and of the width of the scalars remains to be investigated.Comment: LaTeX2e, 26 pages, new figure and additional appendix added, version to appear in Phys.Rev.

Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model

We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson model). The special emphasis is on the probability of the anomalously localized states (ALS) with $|\psi|^{2}$ much larger than the inverse typical localization length $\ell_{0}$. Using the solution to the generating function $\Phi_{an}(u,\phi)$ found recently in our works we find the ALS probability distribution $P(|\psi|^{2})$ at $|\psi|^{2}\ell_{0} >> 1$. As an auxiliary preliminary step we found the asymptotic form of the generating function $\Phi_{an}(u,\phi)$ at $u >> 1$ which can be used to compute other statistical properties at the center-of-band anomaly. We show that at moderately large values of $|\psi|^{2}\ell_{0}$, the probability of ALS at E=0 is smaller than at energies away from the anomaly. However, at very large values of $|\psi|^{2}\ell_{0}$, the tendency is inverted: it is exponentially easier to create a very strongly localized state at E=0 than at energies away from the anomaly. We also found the leading term in the behavior of $P(|\psi|^{2})$ at small $|\psi|^{2}<< \ell_{0}^{-1}$ and show that it is consistent with the exponential localization corresponding to the Lyapunov exponent found earlier by Kappus and Wegner and Derrida and Gardner.Comment: 25 pages, 9 figure

Universal statistics of wave functions in chaotic and disordered systems

We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of Lorentzian distribution.Comment: 6 Europhys pages, 2 Ps figures, new version to appear in Europhys. Let

Mass splittings of nuclear isotopes in chiral soliton approach

The differences of the masses of nuclear isotopes with atomic numbers between \~10 and ~30 can be described within the chiral soliton approach in satisfactory agreement with data. Rescaling of the model is necessary for this purpose - decrease of the Skyrme constant by about 30%, providing the "nuclear variant" of the model. The asymmetric term in Weizsaecker-Bethe- Bacher mass formula for nuclei can be obtained as the isospin dependent quantum correction to the nucleus energy. Some predictions for the binding energies of neutron rich nuclides are made in this way, from, e.g. Be-16 and B-19 to Ne-31 and Na-32. Neutron rich nuclides with high values of isospin are unstable relative to strong interactions. The SK4 (Skyrme) variant of the model, as well as SK6 variant (6-th order term in chiral derivatives in the lagrangian as solitons stabilizer) are considered, and the rational map approximation is used to describe multiskyrmions.Comment: 16 pages, 10 tables, 2 figures. Figures are added and few misprints are removed. Submitted to Phys. Atom. Nucl. (Yad. Fiz.

Guided random walk calculation of energies and <\sq {r^2} > values of the 1Σg^1\Sigma_g state of H_2 in a magnetic field

Energies and spatial observables for the $^1\Sigma_g$ state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random walk Feynman-Kac algorithm. We demonstrate that the accuracy of the results and the simplicity of the method may prove it a viable alternative to large basis set expansions for small molecules in applied fields.Comment: 10 pages, no figure

Kaon Energies in Dense Matter

We discuss the role of kaon-nucleon and nucleon-nucleon correlations in kaon condensation in dense matter. Correlations raise the threshold density for kaon condensation, possibly to densities higher than those encountered in stable neutron stars.Comment: RevTeX, 11 pages, 2 PostScript figures; manuscript also available, in PostScript form, at http://www.nordita.dk/locinfo/preprints.htm

Variation of the hopping exponent in disordered silicon MOSFETs

We observe a complex change in the hopping exponent value from 1/2 to 1/3 as a function of disorder strength and electron density in a sodium-doped silicon MOSFET. The disorder was varied by applying a gate voltage and thermally drifting the ions to different positions in the oxide. The same gate was then used at low temperature to modify the carrier concentration. Magnetoconductivity measurements are compatible with a change in transport mechanisms when either the disorder or the electron density is modified suggesting a possible transition from a Mott insulator to an Anderson insulator in these systems.Comment: 6 pages, 5 figure

Determining the influence and effects of manufacturing variables on sulfur dioxide cells

A survey of the Li/SO2 manufacturing community was conducted to determine where variability exists in processing. The upper and lower limits of these processing variables might, by themselves or by interacting with other variables, influence safety, performance, and reliability. A number of important variables were identified and a comprehensive design experiment is being proposed to make the proper determinations