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.

Electron-ion scattering

Recent advances in the elucidation of electron-ion scattering phenomena is reviewed, with particular emphasis on the new generation of experiments where scattered electrons are analysed and detected, The sensitivity of measurements as a probe of collision dynamics, application to plasma studies, and future directions are considered.

Low-energy electron attachment to chloroform (CHCl3) molecules: A joint experimental and theoretical study

Results from a joint experimental and theoretical study of electron attachment to chloroform (CHCl3) molecules in the gas phase are reported. In an electron swarm study involving a pulsed Townsend technique with equal gas and electron temperatures, accurate attachment rate coefficients were determined over the temperature range 295-373 K; they show an Arrhenius-type rise with increasing temperature, corresponding to an activation energy of 0.11 (1) eV. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for Cl- formation from CHCl3 over the energy range 0.001-1.25 eV at the gas temperature T-G = 300 K was measured. It exhibits clear downward cusp structure at the threshold for excitation of one quantum of the vibrational symmetric deformation mode nu(3), indicating that this mode is active in the primary attachment process. With reference to our thermal attachment rate coefficient k(T = 300 K) = 3.9(2) x 10(-9) cm(3) s(-1), a new highly resolved absolute attachment cross section for T-G = 300 K was determined. This cross section is extended to higher energies by measurements, carried out with a pulsed electron beam apparatus which also provided new data for the distinctly weaker fragment anions HCl2- and CCl2-. The resulting total absolute cross section for anion formation is used to calculate the dependence of the attachment rate coefficient k(T-e;T-G) on electron temperature T-e over the range 50-15000 K at the fixed gas temperature T-G = 300 K. In addition, we report the dependence of the relative cross section for Cl- formation on gas temperature T-G = 310-435 K). For comparison with the experimental data, R-matrix calculations have been carried out for the dominant anion channel Cl-. The results recover the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level nu(3) and on the vibrational temperature. Our results are compared with those of previous electron beam and electron swarm experiments.

A low-energy core-collapse supernova without a hydrogen envelope

The final fate of massive stars depends on many factors. Theory suggests that some with initial masses greater than 25 to 30 solar masses end up as Wolf-Rayet stars, which are deficient in hydrogen in their outer layers because of mass loss through strong stellar winds. The most massive of these stars have cores which may form a black hole and theory predicts that the resulting explosion of some of them produces ejecta of low kinetic energy, a faint optical luminosity and a small mass fraction of radioactive nickel. An alternative origin for low-energy supernovae is the collapse of the oxygen-neon core of a star of 7-9 solar masses. No weak, hydrogen-deficient, core-collapse supernovae have hitherto been seen. Here we report that SN 2008ha is a faint hydrogen-poor supernova. We propose that other similar events have been observed but have been misclassified as peculiar thermonuclear supernovae (sometimes labelled SN 2002cx-like events). This discovery could link these faint supernovae to some long-duration gamma-ray bursts, because extremely faint, hydrogen-stripped core-collapse supernovae have been proposed to produce such long gamma-ray bursts, the afterglows of which do not show evidence of associated supernovae.

Low-energy excitations of a boson pair in a double-well trap

The states of a boson pair in a one-dimensional double-well potential are investigated. Properties of the ground and lowest excited states of this system are studied, including the two-particle wave function, momentum pair distribution, and entanglement. The effects of varying both the barrier height and the effective interaction strength are investigated.

Low-Energy Electron Attachment to the Dichlorodifluoromethane (CCl2F2) Molecule

Results from a joint experimental study of electron attachment to dichlorodifluoromethane (CCl2F2) molecules in the gas phase are reported. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for formation of the dominant anion Cl- wits measured over the energy range 0.001-1.8 eV at the gas temperature T-G = 300 K. It exhibits cusp structure at thresholds for vibrational excitation of the v(3)(a(1)) mode due to interaction with the attachment channels. With reference to the thermal attachment rate coefficient k(T-e;T-G = 300 K) = 2.2(8) x 10(-9) cm(-3) s(-1) (fitted average from several data), a new highly resolved absolute attachment cross section for TG = 300 K was determined. Partial cross sections for formation of the anions Cl-, Cl-2(-), F-, ClF-, and CCl2F- were measured over the range 0-12 eV, using three different electron beam experiments of medium energy resolution. The dependence of the attachment rate coefficient k(T-e;T-G = 300 K) on electron temperature T-e wits calculated over the range 50-15 000 K, based on a newly constructed total cross section for anion formation at T-G = 300 K. R-matrix Calculations for Cl- production have been carried out for comparison with the experimental data. The R-matrix results are in line with the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level v(3) and on the vibrational temperature. Furthermore, the cross section for I Vibrational excitation of the v(3) mode hits been computed.

Target Structure Induced Suppression of the Ionization Cross Section for Very Low Energy Antiproton-Hydrogen Collisions

Low energy antiprotons have been used previously to give benchmark data for theories of atomic collisions. Here we present measurements of the cross section for single, nondissociative ionization of molecular hydrogen for impact of antiprotons with kinetic energies in the range 2-11 keV, i.e., in the velocity interval of 0.3-0.65 a.u. We find a cross section which is proportional to the projectile velocity, which is quite unlike the behavior of corresponding atomic cross sections, and which has never previously been observed experimentally.