Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the M_k (k = ξ, αβ, γ, m) X‐ray production cross sections for ₆₆Dy have been measured at incident photon energies across its L_j (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of L_j subshell vacancies as the tunable incident energy ionizes progressively different ₆₆Dy L_j subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the L_j (j = 1–3) subshell to the M_i (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the M_αβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.     

Preconcentration method on modified silica fiber for chromium speciation

A new method involving pre-concentration on modified silica fiber is described for the speciation of chromium(III) [Cr(III)] and chromium(VI) [Cr(VI)] in aqueous media. This method is based on the different chelating behavior of Cr(III) and Cr(VI) with morpholine-4-carbodithioate (MDTC). Both complexes are extracted on silica fiber modified by sol-gel technology by using 3-aminopropyltriethoxysilane (APS) as a precursor. All extracted samples are directly injected into an high-performance liquid chromatography injector for the simultaneous determination of Cr(III) and Cr(VI). Cr(VI) forms two different complexes, and Cr(III) forms a single complex with MDTC. Therefore, the concentration of Cr(VI) is determined directly from the peak area obtained at 5.4 min; whereas, the assay of Cr(III) is based on subtracting the peak area of Cr(VI) from the total peak area obtained at 4.3 min. Under the optimized conditions, the limits of detection for Cr(III) and Cr(VI) are found to be 0.7 ng/mL and 0.2 ng/mL, respectively.     

Monitoring of trace levels of p-dioxan in high purity benzene feedstock by capillary gas chromatography

Summary A procedure has been standarized for the determination of p-dioxan (1,4-dioxan) in benzene feedstock in the range of 1 to 100 ppm by capillary GC. The GC conditions such as oven temperature, length of the column etc were optimized to achieve better resolution of p-dioxan from hydrocarbons. The standard addition method of quantitation, was used to determine the amount of p-dioxan and was found to give better results than those obtained by external standardization. Prior to analysis the identity of the p-dioxan peak was established by GC-MS. The proposed method has been applied for the monitoring of p-dioxan in high purity benzene feedstock produced by the Udex extraction process in the refinery. The data were used for optimization of plant conditions for the production of high purity benzene feedstock. By using this method, the p-dioxan content down to 0.5 ppm can be determined in the benzene feedstock.     

Central limit theorem for perturbed empirical distribution functions evaluated at a random point

Let be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n from a (smooth) distribution function F. Sufficient conditions are given for the central limit theorem to hold for the target statistic where {U_n} is a sequence of U-statistics.     

Quantum entanglement in an oscillating macroscopic mirror

In this paper, we revisit the problem of quantum entanglement in an oscillating macroscopic mirror previously studied by Marshall et al. consisting of a modified Michelson interferometer where one of the mirrors is free to oscillate about its center of mass. A photon incident upon the oscillating mirror becomes entangled with the mirror, driving the mirror into a superposition of quantum states. Once the photon and mirror decouple, the mirror returns to its initial state. The purpose of our investigations was to optimize the parameter regime, taking into consideration the current state of technology and the demands imposed by the need to maintain a stable environment in the presence of thermal noise. Optimization should not demand ultra-low temperatures and this is reflected in our results. Our results also show that if the separation between states is maintained at 10^-14 m, the mirror size is reduced, making it easier to induce superposition in the mirror. The critical nature of mirror reflectivity and its connection to cavity decay rate was also revealed by our investigations. The results obtained through our investigations could be useful in quantum error correction, where decoherence negatively affects the results of computations performed by quantum computers. Finally, we note that we are only concerned with an isolated system, where no losses to the external environment occur and any decoherence that occurs within the system remains internal to the system; that is, any mention of decoherence refers specifically to recoverable decoherence.     

Electron energy losses from thin silver films

A simple dielectric theory of electron energy losses in a thin metal overlayer is extended to include multiple losses. This theory is then compared with recent experimental data by Backes and Ibach. These comparisons reveal several inadequacies in the basic model, especially with regard to the shape and parameter dependence of the quasi-elastic peak.     

Analytical calculation of fusion barriers and cross-sections for spin-saturated colliding nuclei

We present an analytical formula for calculating the fusion barriers and fusion cross-sections. This is based on Skyrme energy density formalism and the Proximity force theorem. Comparisons with experimental data are also presented.     

On the rate of convergence in the central limit theorem for signed rank statistics

The problem of the rate of convergence of the cumulative distribution function of the one-sample rank order statistics S_N⁺ to the limiting normal one is studied for the case when the underlying observations are independent but not necessarily identically distributed. The results obtained are then used to derive a strong law and functional form of a central limit theorem for S_N⁺     

A sharpening of the remainder term in the higher-dimensional central limit theorem for multilinear rank statistics

A new approach to the asymptotic normality of the multivariate linear rank statistics is provided along with the Berry-Esséen and the Prohorov distance estimates for the remainder term in the convergence to normality.