Effect of gas pressure and pulse length on the isotopically selective multiphoton dissociation of CF3Cl under CO2 laser pulses

The multiphoton dissociation of CF₃Cl induced by TEA-CO₂ laser pulses has been studied in a focused beam geometry. TheR(10) [00°1–02°0] ( ) laser line was used, so as to dissociate preferentially the minor isotopic component¹³CF₃Cl. The isotopic selectivityS and the dissociation probability per pulse ω were measured in the pressure range between 0.25 and 8 Torr. With short laser pulses (90 ns FWHM),S is found to increase slightly with gas pressure up to 2 Torr, and ω, to increase almost linearly over the whole pressure range studied. A schematic model is proposed which satisfactorily explains these results if the transition rates across the energy level spectrum of the CF₃Cl molecules are assumed to increase with gas pressure.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

Problems with the ζ-function method

The -function method for evaluating effective actions is applied to an operator containing a potential localized on two parallel planes. This operator is characterized by a continuous spectrum and broken translation invariance. In this case, the -method leads to a divergent volume factor independent of the physical parameters. In a suitable regularization scheme, only the next to leading order term reproduces a physically interesting result.     

Linear optical properties of frequency doubling polymers

Measurements of linear optical properties of methylmethacrylate copolymers with non-linear optical 4-alkoxy-4-alkylsulfone stilbene side-chains are presented. From there two methods for phase matching are discussed; one aiming to equalize the refractive indices of the fundamental and the second harmnic wave, the other to suppress the destructive character of the interference. The matter of photo stability of frequency doubling polymers is also discussed.     

Laser-induced electron emission from an Au surface irradiated by single picosecond pulses at λ=2.94 μm. The intermediate region between multiphoton and tunneling effects

The photoinduced electron emission from the surface of a solid gold target irradiated by single picosecond pulses of an erbium laser is investigated. The applied laser intensity (5–120 GW/cm²) corresponds to the intermediate interaction region between the pure multiphoton and tunnel effects, where the decisive Keldysh-parameter, , is in the range 1<<12=n ₀. In the light intensity region which is free of surface heating (I _L<80 GW/cm²), the slope of the measured logarithmic intensity dependence of the photocurrent decreases from the n ₀=12 perturbative value down to n 5. Therefore the experiment shows that the Keldysh-type theories, which have recently been proved to describe correctly the ionization of atoms, are also valid to a certain extent in the case of the photoeffect in metals.     

A contribution to shape theory for the ising model at low temperature

Summary We consider low temperature limits of Gibbs states of the ferromagnetic nearest-neighbour Ising Hamiltonian in the positive orthant of the lattice ^d ,d=1, 2,..., under a negative boundary condition and a small positive external fieldh that decreases linearly with the temperatureT. It is shown that positive and negative spins are separated by a staircase-shaped random boundary. Its explicit distribution is computed in the case that the ratio =h/T exceeds some positive ₀. For < ₀, our results do not rule out infinite negative areas.     

Shock fluctuations in asymmetric simple exclusion

Summary The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities < to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (=0) we prove, in the scale t^1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle.     

The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is