On the semiclassical approach to cold atomic collisions

We extend the semiclassical description of two-state atomic collisions to low energies for which the impact parameter treatment fails. The problem reduces to solving a system of first-order differential equations with coefficients whose semiclassical asymptotes experience the Stokes phenomenon in the complex coordinate plane. Primitive semiclassical and uniform Airy approximations are discussed.

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.

Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

The 0.5M(J) transiting exoplanet WASP-13b

We report the discovery of WASP-13b, a low-mass M-p = 0.46(-0.05)(+0.06) M-J transiting exoplanet with an orbital period of 4.35298 +/- 0.00004 days. The transit has a depth of 9 mmag, and although our follow-up photometry does not allow us to constrain the impact parameter well (0 <b <0.46), with radius in the range R-p similar to 1.06-1.21 R-J the location of WASP-13b in the mass-radius plane is nevertheless consistent with H/He-dominated, irradiated, low core mass and core-free theoretical models. The G1V host star is similar to the Sun in mass (M-* = 1.03(-0.09)(+0.11) M-circle dot) and metallicity ([M/H] = 0.0 +/- 0.2), but is possibly older (8.5(-4.9)(+5.5) Gyr).

WASP-34b: a near-grazing transiting sub-Jupiter-mass exoplanet in a hierarchical triple system

We report the discovery of WASP-34b, a sub-Jupiter-mass exoplanet transiting its 10.4-magnitude solar-type host star (1SWASP J110135.89-235138.4; TYC 6636-540-1) every 4.3177 days in a slightly eccentric orbit (e = 0.038±0.012). We find a planetary mass of 0.59±0.01 MJup and radius of 1.22-0.08+0.11 RJup. There is a linear trend in the radial velocities of 55±4 m s-1 y-1 indicating the presence of a long-period third body in the system with a mass ?0.45 MJup at a distance of ?1.2 AU from the host star. This third-body is either a low-mass star, a white dwarf, or another planet. The transit depth ((RP/Rstar)2 = 0.0126) and high impact parameter (b = 0.90) suggest that this could be the first known transiting exoplanet expected to undergo grazing transits, but with a confidence of only 80%. Radial velocity and photometric data are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/526/A130

Independent Discovery of the Transiting Exoplanet HAT-P-14b

We present SuperWASP observations of HAT-P-14b, a hot Jupiter discovered by Torres et al. The planet was found independently by the SuperWASP team and named WASP-27b after follow-up observations had secured the discovery, but prior to the publication by Torres et al. Our analysis of HAT-P-14/WASP-27 is in good agreement with the values found by Torres et al. and we provide additional evidence against astronomical false positives. Due to the brightness of the host star, V-mag = 10, HAT-P-14b is an attractive candidate for further characterization observations. The planet has a high impact parameter and the primary transit is close to grazing. This could readily reveal small deviations in the orbital parameters indicating the presence of a third body in the system, which may be causing the small but significant orbital eccentricity. Our results suggest that the planet may undergo a grazing secondary eclipse. However, even a non-detection would tightly constrain the system parameters.

WASP-23b: a transiting hot Jupiter around a K dwarf and its Rossiter-McLaughlin effect

We report the discovery of a new transiting planet in the southern hemisphere. It was found by the WASP-south transit survey and confirmed photometrically and spectroscopically by the 1.2 m Swiss Euler telescope, LCOGT 2m Faulkes South Telescope, the 60 cm TRAPPIST telescope, and the ESO 3.6 m telescope. The orbital period of the planet is 2.94 days. We find that it is a gas giant with a mass of 0.88 ± 0.10 MJ and an estimated radius of 0.96 ± 0.05 RJ. We obtained spectra during transit with the HARPS spectrograph and detect the Rossiter-McLaughlin effect despite its small amplitude. Because of the low signal-to-noise ratio of the effect and a small impact parameter, we cannot place a strong constraint on the projected spin-orbit angle. We find two conflicting values for the stellar rotation. We find, via spectral line broadening, that v sin I = 2.2 ± 0.3 km s-1, while applying another method, based on the activity level using the index log R'_HK, gives an equatorial rotation velocity of only v = 1.35 ± 0.20 km s-1. Using these as priors in our analysis, the planet might be either misaligned or aligned. This result raises doubts about the use of such priors. There is evidence of neither eccentricity nor any radial velocity drift with time. Using WASP-South photometric observations confirmed with LCOGT Faulkes South Telescope, the 60 cm TRAPPIST telescope, the CORALIE spectrograph and the camera from the Swiss 1.2 m Euler Telescope placed at La Silla, Chile, as well as with the HARPS spectrograph, mounted on the ESO 3.6 m, also at La Silla, under proposal 084.C-0185. The data is publicly available at the CDS Strasbourg and on demand to the main author.RV data is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/531/A24Appendix is available in electronic form at http://www.aanda.org

High-precision transit observations of the exoplanet WASP-13b with the RISE instrument

WASP-13b is a sub-Jupiter mass exoplanet orbiting a G1V type star with a period of 4.35 d.The current uncertainty in its impact parameter (0 < b < 0.46) results in poorly definedstellar and planetary radii. To better constrain the impact parameter, we have obtained highprecisiontransit observations with the rapid imager to search for exoplanets (RISE) instrumentmounted on 2.0-m Liverpool Telescope. We present four new transits which are fitted witha Markov chain Monte Carlo routine to derive accurate system parameters. We found anorbital inclination of 85. ◦ 2 ± 0. ◦ 3 resulting in stellar and planetary radii of 1.56 ± 0.04 Rand 1.39 ± 0.05RJup, respectively. This suggests that the host star has evolved off the mainsequence and is in the hydrogen-shell-burning phase.We also discuss how the limb darkeningaffects the derived system parameters.With a density of 0.17ρJ,WASP-13b joins the group oflow-density planets whose radii are too large to be explained by standard irradiation models.We derive a new ephemeris for the system, T0 = 245 5575.5136 ± 0.0016 (HJD) and P =4.353 011 ± 0.000 013 d. The planet equilibrium temperature (Tequ = 1500 K) and the brighthost star (V = 10.4mag) make it a good candidate for follow-up atmospheric studies.

An experimental investigation of dechanneling in copper single crystals

This investigation comprises a comparison of experimental and theoretical dechanneling of MeV protons in copper single crystals. Dechanneling results when an ion's transverse energy increases to the value where the ion can undergo small impact parameter collisions with individual atoms. Depth dependent dechanneling rates were determined as functions of lattice temperature, ion beam energy and crystal axis orientation. Ion beam energies were IMeV and 2MeV,temperatures ranged from 35 K to 280 K and the experiment was carried out along both the (lOa) and <110) axes. Experimental data took the form of aligned and random Rutherford backscattered energy spectra. Dechanneling rates were extracted from these spectra using a single scattering theory that took explicit account of the different stopping powers experienced by channeled and dechanneled ions and also included a correction factor to take into account multiple scattering effects along the ion's trajectory. The assumption of statistical equilibrium and small angle scattering of the channeled ions allows a description of dechanneling in terms of the solution of a diffusion like equation which contains a so called diffusion function. The diffusion function is shown to be related to the increase in average transverse energy. Theoretical treatments of increase in average transverse energy due to collisions of projectiles with channel electrons and thermal perturbations in the lattice potential are reviewed. Using the diffusion equation and the electron density in the channel centre as a fitting parameter dechanneling rates are extracted. Excellent agreement between theory and experiment has been demonstrated. Electron densities determined in the fitting procedure appear to be realistic. The surface parameters show themselves to be good indicators of the quality of the crystal.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Application of inclusive probability theory to heavy ion-atom collisions

Using the independent particle model as our basis we present a scheme to reduce the complexity and computational effort to calculate inclusive probabilities in many-electron collision system. As an example we present an application to K - K charge transfer in collisions of 2.6 MeV Ne{^9+} on Ne. We are able to give impact parameter-dependent probabilities for many-particle states which could lead to KLL-Auger electrons after collision and we compare with experimental values.

Inclusive probability calculations for the K-vacancy transfer in collisions of S{^15+} on Ar

Using the single-particle amplitudes from a 20-level coupled-channel calculation with ab initio relativistic self consistent LCAO-MO Dirac-Fock-Slater energy eigenvalues and matrix elements we calculate within the frame of the inclusive probability formalism impact-parameter-dependent K-hole transfer probabilities. As an example we show results for the heavy asymmetric collision system S{^15+} on Ar for impact energies from 4.7 to 16 MeV. The inclusive probability formalism which reinstates the many-particle aspect of the collision system permits a qualitative and quantitative agreement with the experiment which is not achieved by the single-particle picture.

Multiple vacancy inclusive probabilities for the scattering system 16 MeV S{^16+} on Ar

To evaluate single and double K-shell inclusive charge transfer probabilities in ion-atom collisions we solve the time-dependent Dirac equation. By expanding the timedependent wavefunction in a set of molecular basis states the time-dependent equation reduces to a set of coupled-channel equations. The energy eigenvalues and matrix elements are taken from self-consistent relativistic molecular many-electron Dirac-Fock-Slater calculations. We present many-electron inclusive probabilities for different final configurations as a function of impact parameter for single and double K-shell vacancy production in collisions of bare S on Ar.

Could saturation effects be visible in a future electron-ion collider?

We expect to observe parton saturation in a future electron-ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron-ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total. longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A and small Q(2), allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton Saturation. (C) 2008 Elsevier B.V. All rights reserved.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the derection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.