Rotational variation of predissociation linewidths for the Schumann-Runge bands of molecular oxygen

Predissociation linewidths are presented as a function of rotation for the (3-0)-(14-0) Schumann- Runge bands of molecular oxygen. While there may be a slight tendency overall for the linewidths to increase with rotation, it is shown that previous assumptions of linewidths constant with rotation are generally valid within the experimental error for the range of rotation studied, N_n ? 21. There is no evidence for the sudden increase in linewidth with rotation reported elsewhere.     

Experimentally determined oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen—I. The (6-0)–(14-0) bands

Experimental oscillator strengths and predissociated linewidths have been measured at room temperature for the (6-0)–(14-0) Schumann-Runge bands of molecular oxygen using the Adelaide 6 m vacuum u.v. monochromator operated at a resolution of about 0.06 Å. Photoelectric detectors were used to measure the u.v. absorption at two different gas pressures for 138 groups of rotational lines distributed throughout the (6-0)–(14-0) bands and the resulting data were interpreted using an equivalent width type of analysis. Experimental measurements of the variation with N″ of the oscillator strengths within each band have been obtained for the first time. Measured oscillator strengths are found to be somwhat higher in general than previously reported values with a slightly faster decrease as N″ increases than is predicted theoretically. The mean predissociated linewidths obtained for each band show a smooth variation with v′, agreeing well with other results for v′=12?14 and lying between previously reported experimental and theoretical values for v′=6?9. The present work provides results which can be used to construct highly accurate synthetic absorption profiles for studies of the atmospheric absorption of u.v. radiation by the Schumann-Runge bands.     

Tunneling and transport problems for a quantum mechanical Brownian particle

The Kanai model of a quantum mechanical Brownian particle is used to examine the effect of interactions between particles and their environment. Random forces cause the thermalization of the particle. Reflection of a particle from a step barrier is analyzed. The problem of tunneling of the Brownian particle through a rectangular barrier is solved. Finally, a solution for a Brownian particle in a box is presented.     

Connection between the KdV equation and the two-dimensional Ising model

We construct the one-parameter family of solutions to d²w/dzsu2 = zw + 2w³ that tend to zero for z → +∞ by specializing an equation previously solved in connection with the two-dimensional Ising model. These solutions are intimately related to the KdV equation.     

Networks, dynamics, and modularity

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymptotically stable linear dynamics. Numerical experiments demonstrate that linear stability benefits from the presence of a hierarchy of modules and that this architecture improves the robustness of network stability to random perturbations in network structure. This work illustrates an approach to network science which is simultaneously structural and dynamical in nature.     

Bethe's Equation Is Incomplete for the XXZ Model at Roots of Unity

We demonstrate for the six vertex and XXZ model parameterized by = –(q+q^-1)/2±1 that when q^2N=1 for integer N2 the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl₂ loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl₂ loop algebra can be used to complete this specification.     

Comment on a recent conjectured solution of the three-dimensional Ising model

In a recent paper published in Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87 (2007) p.5309], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here, we disprove the conjecture and point out the flaws in the arguments leading to the conjectured expressions.     

Solvent-mediated charge redistribution in photodissociation of IBr(-) and IBr(-)(CO2)

A combined experimental and theoretical investigation of photodissociation dynamics of IBr(-) and IBr(-)(CO(2)) on the B ((2)Σ(1/2)(+)) excited electronic state is presented. Time-resolved photoelectron spectroscopy reveals that in bare IBr(-) prompt dissociation forms exclusively I? + Br(-). Compared to earlier dissociation studies of IBr(-) excited to the A' ((2)Π(1∕2)) state, the signal rise is delayed by 200 ± 20 fs. In the case of IBr(-)(CO(2)), the product distribution shows the existence of a second major (～40%) dissociation pathway, Br? + I(-). In contrast to the primary product channel, the signal rise associated with this pathway shows only a 50 ± 20 fs delay. The altered product branching ratio indicates that the presence of one solvent-like CO(2) molecule dramatically affects the electronic structure of the dissociating IBr(-). We explore the origins of this phenomenon with classical trajectories, quantum wave packet studies, and MR-SO-CISD calculations of the six lowest-energy electronic states of IBr(-) and 36 lowest-energy states of IBr. We find that the CO(2) molecule provides sufficient solvation energy to bring the initially excited state close in energy to a lower-lying state. The splitting between these states and the time at which the crossing takes place depend on the location of the solvating CO(2) molecule.     

Photoelectron spectroscopy of HC4N-

We report the 364-nm photoelectron spectrum of HC(4)N(-). We observe electron photodetachment from the bent X(2)A" state of HC(4)N(-) to both the near-linear X(3)A" and the bent ? (1)A' states of neutral HC(4)N. We observe an extended, unresolved vibrational progression corresponding to X(3)A" ← X(2)A" photodetachment, and we measure the electron affinity (EA) of the X(3)A" state of HC(4)N to be 2.05(8) eV. Photodetachment to the bent ? (1)A' state results in a single intense origin peak at a binding energy of 2.809(4) eV, from which we determine the singlet-triplet splitting (ΔE(ST)) of HC(4)N: 0.76(8) eV. For comparison and to aid in the interpretation of the HC(4)N(-) spectrum, we also report the 364-nm photoelectron spectra of HCCN(-) and DCCN(-). Improved signal-to-noise over the previous HCCN(-) and DCCN(-) photoelectron spectra allows for a more precise determination of the EAs and ΔE(ST)s of HCCN and DCCN. The EAs of HCCN and DCCN are measured to be 2.001(15) eV and 1.998(15) eV, respectively; ΔE(ST)(HCCN) is 0.510(15) eV and ΔE(ST)(DCCN) is 0.508(15) eV. These results are discussed in the context of other organic carbene chains.