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Laser-induced breakdown spectroscopy (LIBS) is an established technique for material characterization applicable to a variety of problems in research, industry, environmental studies, and security. LIBS conducted with femtosecond laser pulses exhibits unique properties, arising from the characteristics of laser-matter interactions in this pulse width regime. The time evolution of the electric field of the pulse determines its interaction with sample materials. We present the design and performance of a femtosecond LIBS system developed to systematically optimize the technique for detection of uranium. Sample analysis can be performed in vacuum environment, and the spectral and temporal diagnostics are coupled through an adaptive feedback loop, which facilitates optimization of the signal-to-noise ratio by pulse shaping. Initial experimental results of LIBS on natural uranium are presented.

Three problems involving quasi-one-dimensional (1D) ideal gases are discussed. The simplest problem involves quantum particles localized within the 'groove', a quasi-1D region created by two adjacent, identical and parallel nanotubes. At low temperature (T), the transverse motion of the adsorbed gas, in the plane perpendicular to the axes of the tubes, is frozen out. Then, the low T heat capacity C(T) of N particles is that of a 1D classical gas: C(*)(T) = C(T)/(Nk(B)) --> 1/2. The dimensionless heat capacity C(*) increases when T ≥ 0.1T(x, y) (transverse excitation temperatures), asymptoting at C(*) = 2.5. The second problem involves a gas localized between two nearly parallel, co-planar nanotubes, with small divergence half-angle γ. In this case, too, the transverse motion does not contribute to C(T) at low T, leaving a problem of a gas of particles in a 1D harmonic potential (along the z axis, midway between the tubes). Setting ω(z) as the angular frequency of this motion, for T ≥ τ(z) ≡ ω(z)ħ/k(B), the behavior approaches that of a 2D classical gas, C(*) = 1; one might have expected instead C(*) = 1/2, as in the groove problem, since the limit γ ≡ 0 is 1D. For T << τ(z), the thermal behavior is exponentially activated, C(*) ∼ (τ(z)/T)(2)e(-τ(z)/T). At higher T (T ≈ ε(y)/k(B) ≡ τ(y) >> τ(z)), motion is excited in the y direction, perpendicular to the plane of nanotubes, resulting in thermal behavior (C(*) = 7/4) corresponding to a gas in 7/2 dimensions, while at very high T (T > ħω(x)/k(B) ≡ τ(x) >> τ(y)), the behavior becomes that of a D = 11/2 system. The third problem is that of a gas of particles, e.g. (4)He, confined in the interstitial region between four square parallel pores. The low T behavior found in this case is again surprising--that of a 5D gas.

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Van der Waals (VDW) forces arise from quantum mechanical fluctuations of local charge densities. Whereas computing VDW interactions between two atoms requires only 2-body interactions, by definition, computing interactions between macroscopic bodies required multi-body interactions, where the presence of a third atom affects how any two atoms interact, and a fourth atom affects the first three, and so on. Often, 3-body interactions have been found to be small, and 4-body and higher interactions are almost always neglected in calculating interactions between atoms. But is it possible that 4-body and higher order interactions can actually be more important than 3-body interactions, and indeed comparable to 2-body interactions? We explored the following question: how important is the sum of 4-body and higher order interactions? A set of problems involving finite and infinite chains was explored numerically and analytically, including a single chain, a pair of parallel, long chains and a two-dimensional array of long, parallel chains. The "coupled dipole method" was used, providing a type of "nanoscale Lifshitz theory" for calculations of nanoscale VDW interactions. Calculations were made for the static polarizability, as well as the VDW interaction between chains. This latter energy was compared with that found by summing 2-body interactions for the chains. It was found that when a "coupling constant" ν, which is the polarizability per unit volume of the material, is large, then the sum of 4-body and higher order interactions dominates both the 2-body and the 3-body interactions. In addition, it was found that for all geometries examined, a divergence of the polarizability and a dynamical energy instability occur simultaneously when ν reaches a limiting value ν max , giving a wellknown polarization catastrophe.