An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Spitzer infrared spectrograph point source classification in the Small Magellanic Cloud

The Magellanic Clouds are uniquely placed to study the stellar contribution to dust emission. Individual stars can be resolved in these systems even in the mid-infrared, and they are close enough to allow detection of infrared excess caused by dust. We have searched the Spitzer Space Telescope data archive for all Infrared Spectrograph (IRS) staring-mode observations of the Small Magellanic Cloud (SMC) and found that 209 Infrared Array Camera (IRAC) point sources within the footprint of the Surveying the Agents of Galaxy Evolution in the Small Magellanic Cloud (SAGE-SMC) Spitzer Legacy programme were targeted, within a total of 311 staring-mode observations. We classify these point sources using a decision tree method of object classification, based on infrared spectral features, continuum and spectral energy distribution shape, bolometric luminosity, cluster membership and variability information. We find 58 asymptotic giant branch (AGB) stars, 51 young stellar objects, 4 post-AGB objects, 22 red supergiants, 27 stars (of which 23 are dusty OB stars), 24 planetary nebulae (PNe), 10 Wolf-Rayet stars, 3 H II regions, 3 R Coronae Borealis stars, 1 Blue Supergiant and 6 other objects, including 2 foreground AGB stars. We use these classifications to evaluate the success of photometric classification methods reported in the literature.

Swellable polymer films containing Au nanoparticles for point-of-care therapeutic drug monitoring using surface-enhanced Raman spectroscopy

Large (10 × 10 cm) sheets of surface-enhanced Raman spectroscopy (SERS) active polymer have been prepared by stabilising metal nanoparticle aggregates within dry hydroxyethylcellulose (HEC) films. In these films the aggregates are protected by the polymer matrix during storage but in use they are released when aqueous analyte droplets cause the films to swell to their gel form. The fact that these "Poly-SERS" films can be prepared in bulk but then cut to size and stored in air before use means that they provide a cost effective and convenient method for routine SERS analysis. Here we have tested both Ag and Au Poly-SERS films for use in point-of-care monitoring of therapeutic drugs, using phenytoin as the test compound. Phenytoin in water could readily be detected using Ag Poly-SERS films but dissolving the compound in phosphate buffered saline (PBS) to mimic body fluid samples caused loss of the drug signal due to competition for metal surface sites from Cl^- ions in the buffer solution. However, with Au Poly-SERS films there was no detectable interference from Cl^- and these materials allowed phenytoin to be detected at 1.8 mg L^-1, even in PBS. The target range of detection of phenytoin in therapeutic drug monitoring is 10-20 mg L^-1. With the Au Poly-SERS films, the absolute signal generated by a given concentration of phenytoin was lower for the films than for the parent colloid but the SERS signals were still high enough to be used for therapeutic monitoring, so the cost in sensitivity for moving from simple aqueous colloids to films is not so large that it outweighs the advantages which the films bring for practical applications, in particular their ease of use and long shelf life.