One singularly perturbed system of partial differential equations of the first order

Translated from Matematicheskie Zametki, Vol. 57, No. 3, pp. 338–349, March, 1995.     

Measurements of total and positronium-formation cross sections for the scattering of positrons by alkali atoms

We present a review of our recent measurements of total cross sections (Q _T's) for the scattering of positrons by Na, K, and Rb, and positronium-formation cross sections (Q _Ps's) for Na and K. For our total cross section measurements, a beam transmission technique has been used. For ourQ _Ps measurements, our approach involves setting upper and lower limits onQ _Ps using a combination of (1) measuring the transmission of the positron beam with the angular discrimination of the apparatus made as poor as possible, and (2) measuring the 511 keV annihilation gamma rays in coincidence produced by the decay of para-Ps formed in the scattering cell. Comparison with theoretical calculations shows that our measuredQ _T's andQ _Ps's for Na and K agree reasonably well with a close coupling approximation (CCA) calculation which takes into account the formation of Ps in then=1 andn=2 states. In the 3–10 eV energy range, this calculation predicts a peak in theQ _T's andQ _Ps's for K which also appears in our measurements. The absence of such a peak in our measuredQ _T's andQ _Ps's (preliminary) for Na in this energy range is also consistent with the same theory. Comparisons with five-state CCA calculations ofQ _T which do not take Ps-formation into account also show good agreement with our positron-Na, K, and RbQ _T measurements for energies above 20 eV, but show dramatic departures from our measurements below 10 eV for K and Rb.     

Muon spin resonance and repolarization in amorphous silicon monoxide (a-SiO)

Studies of the muonium fractions in the amorphous oxide a-SiO have been carried out by RF resonance at TRIUMF, Canada and LF repolarization techniques at RAL, U.K. The resonance measurements confirm the presence of the interstitial Mu centre in this intermediate oxide of silicon. Analysis of the data gathered at RAL, using a recently-developed fitting technique, reveals that the Mu^* state is present here as well, but with lower relative fractions than in a-Si. However, as in the latter material, but in contrast to c-Si, this bond-centre species appears to be stable up to room temperature.     

Specular reflectance of cold-rolled aluminum surfaces

The specular reflectance of cold-rolled aluminum surface is studied using a fiber optic system. An approximation for the determination of surface roughness is presented.     

Average and local magnetic moments on Fe atoms in microcrystalline and amorphous Fe100−xPx alloys

We have measured the concentration dependence of the average magnetic moment per Fe atom _Fe(x) in microcrystalline and amorphous Fe-P alloys obtained over a wide concentration range using electrochemical deposition. The model of local magnetic moments has been used to described _Fe(x). On the basis of this model the effects of phosphorus on the value _Fe are explained in terms of the parameters of the local environment of the Fe atom.     

Europium-151 Mössbauer spectroscopic and XANES investigation of europium-exchanged Y-zeolite

Eu³⁺ in ca. 10 wt% europium-exchanged Y-zeolite is partially reduced by treatment in hydrogen at 600°C to Eu²⁺. The reduction of Eu³⁺ is more readily achieved in Y-zeolite than in europium(III) oxide. The discrepancy in the extent of reduction as revealed by¹⁵¹Eu Mössbauer spectroscopy and near edge X-ray absorption fine structure (XANES) is associated with any difference in the recoil free fractions of Eu²⁺ and Eu³⁺ which may exist at 298 K and the enhanced sensitivity of the XANES to changes in the europium oxidation state.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

Monitoring of safety features,fissile material accumulation and concentration in nuclear reprocessing by active and passive neutron counting techniques

The application, the advantage and limits of neutron monitoring techniques, such as Hf-monitors, fissile material accumulation and concentration monitors are being discussed. The active neutron counting technique applied to emptied pulsed extraction columns containing Hf-sieve plates allows conclusive answers as to the position of the plates in the columns. Pu-accumulations on Hf-sieve plates in pulsed extraction columns can be estimated within a factor of two, whereby the detection limit is about equal to or less than 1 g Pu/plate. Fissile material concentration changes of 1.1 g/l can be detected in the case of²³⁵U in solution and of 0.4 Pu/l if a²³⁹Pu/²⁴⁰Pu ratio of 4 to 1 is assumed.