Large Impact Parameters Research Articles

Excitation of atoms and molecules by highly relativistic ions

We study the cross section for inelastic collisions of atoms and small molecules under the influence of highly relativistic charged ions as they occur in storage rings and accelerators. Starting from fully time-resolved calculations of the electronic dynamics, we study a set of complementing approximations, a sudden approximation for the extremely fast collision at low impact parameter combined with time-dependent perturbation theory for the weak and slow collisions at large impact parameters. This leads eventually to a simple, yet reliable, estimate in terms of the ion-hydrogen cross section and the variance of the dipole moment for the actual system. We discuss, in particular, the systems H, He, C, N, O, Ne, ${\mathrm{H}}_{2}$, and ${\mathrm{N}}_{2}$.

Anisotropic proton emission after fragmentation of H2O by multiply charged ions

Ion-induced fragmentation of H2O molecules was investigated experimentally by 3He2+ impact as a function of the energy in the range from 1 to 5 keV, as well as a function of the charge state of 20 keV 20Neq+ projectiles (q = 3 and 7). The fragments were detected in the angular range from 25° to 135° with respect to the incident beam direction. Particular emphasis is given to protons originating from collisions at large impact parameters involving a Coulomb explosion mechanism. Absolute cross sections dσ/dΩ, differential in the emission angle, are found to be anisotropic. Protons are preferentially emitted at angles near 90°, with cross sections being ∼50% larger than those at forward and backward angles. Possible mechanisms causing anisotropic emission of protons from fragmenting H2O are discussed.

Vibrational mode and collision energy effects on reaction of H2CO+ with CO2

The effects of collision energy (Ecol) and five different modes of H2CO+ vibration on the title reaction have been studied over the center-of-mass Ecol range from 0.1 to 3.2 eV, including measurements of product ion recoil velocity distributions. Electronic structure and Rice-Ramsperger-Kassel-Marcus calculations were used to examine properties of various complexes and transition states that might be important along the reaction coordinate. Two product channels are observed, corresponding to Hydrogen Transfer (HT) and Proton Transfer (PT). Both channels are endothermic with similar onset energies of approximately 0.9 eV; however, HT dominates over the entire Ecol range and accounts for 70-85% of the total reaction cross section. Both HT and PT occur by direct mechanisms over the entire Ecol range, and have similar dependence on reactant vibrational and collision energy. Despite these similarities, and the fact that the two channels are nearly isoenergetic and differ only in which product moiety carries the charge, their dynamics appear quite different. PT occurs primarily in large impact parameter stripping collisions, where most of the available energy is partitioned to product recoil. HT, in contrast, results in internally hot products with little recoil energy and a more forward-backward symmetric product velocity distribution. Vibration is found to affect the reaction differently in different collision energy regimes. The appearance thresholds are found to depend only on total energy, i.e., all modes of vibration are equivalent to Ecol. With increasing Ecol, vibrational energy becomes increasingly effective, relative to Ecol, at driving reaction. For HT, this transition occurs just above threshold, while for PT it begins at roughly twice the threshold energy.

Shapiro effect as a possible cause of the low-frequency pulsar timing noise in globular clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated (infrared) noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. Currently available pulsar timing methods allow the statistical parameters of this noise to be reliably measured by decomposing the PAT residual function into orthogonal Fourier harmonics. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved spacetime of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Extremely important (from an astrophysical point of view) information about the structure of the globular cluster core, which is inaccessible to study by other observational methods, could be obtained by analyzing the spectral parameters of the low-frequency noise caused by the Shapiro effect and attributable to the random passages of stars near the line of sight to the pulsar. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the σz statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n = −1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n = −1.5.

Signatures of TeV scale gravity in cosmic rays

In TeV scale unification models, gravity propagates in 4 + δ dimensions while gauge and matter fields are confined to a four dimensional brane, with gravity becoming strong at the TeV scale. For a such scenario, we study strong gravitational interactions in a effective Schwarzschild geometry. Two distinct regimes appear. For large impact parameters, the ratio ρ ∼ ( R s / r 0 ) 1 + δ , (with R s the Schwarzschild radius and r 0 the closest approach to the black hole), is small and the deflection angle χ is proportional to ρ (this is like Rutherford-type scattering). For small impact parameters, the deflection angle χ develops a logarithmic singularity and becomes infinite for ρ = ρ crit = 2 / ( 3 + δ ) . This singularity is reflected into a strong enhancement of the backward scattering (like a glory-type effect). We suggest as distinctive signature of black hole formation in particle collisions at TeV energies, the observation of backward scattering events and their associated diffractive effects.

Screening effects on elastic electron–atom collisions in partially ionized hydrogen plasmas

The non-ideal collective and plasma screening effects on elastic electron–atom collisions are investigated in partially ionized hydrogen plasmas using the first-order eikonal method. The effective pseudopotential model, taking into account the screening and collective effects, is applied to describe the interaction potential in non-ideal plasmas. Semiclassical trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase and cross section as functions of the impact parameter, the non-ideality plasma parameter, the Debye length, and the collision energy. The results show that the collective and screening effects enhance the differential eikonal cross section for small impact parameters, but suppress the cross section for large impact parameters. It is also found that the non-ideal collective effects enhance the total eikonal cross section.

Oscillations of rotating bodies: a self-adjoint formalism applied to dynamic tides and tidal capture

Abstract We consider the excitation of the inertial modes of a uniformly rotating fully convective body due to a close encounter with another object. This could lead to a tidal capture or orbital circularization depending on whether the initial orbit is unbound or highly eccentric. We develop a general self-adjoint formalism for the response problem and thus solve it taking into account the inertial modes with m= 2 for a full polytrope with n= 1.5. We are accordingly able to show in this case that the excitation of inertial modes dominates the response for large impact parameters and thus cannot be neglected in calculations of tidal energy and angular momentum exchange or orbital circularization from large eccentricity.

Droplet Collisions Using A Level Set Method:Comparisons Between Simulation AndExperiments

Level Set methods are based on defining a continuous function where the zero level curve is the interface. That function is initialized as the signed distance to the interface in the computation field. Solving a convection equation allows one to follow the interface displacements in a given velocity field. One advantage is its ability to represent topological changes and geometrical information on the interface, such as the normal vector or curvature, which are obtained through a level set function gradient. To avoid the spreading and stretching of a level set, a re-distancing algorithm is applied to ensure that the function remains the signed distance to the interface. The Level Set method is coupled with the projection method for the direct numerical simulation of the incompressible Navier-Stokes equations. Spatial derivatives are estimated with the 2nd order central scheme, but convective terms are approximated by the 5th order WENO scheme discretization in order to get a robust behavior of the solution. Temporal derivatives are approximated with the Adams Bashforth scheme. The linear system deduced from the Poisson equation is solved with a multigrid algorithm for preconditioning the conjugate gradient method. To handle interface discontinuities the ghost fluid method is used. Numerical codes have been developed for 2D, 2Daxi and 3D geometries, with MPI parallelization. The results are presented for head-on droplets collisions in a coalescence regime and a reflexive regime with 2D axi-symmetric code, and for off-center droplets collision code in a separation regime for a large impact parameter with 3D code. Simulations provide realistic and various droplet collision behaviors and they correspond to experimental observations.

H2andN2ionization and dissociative ionization byC−andO−ions at intermediate velocities: Direct and electron loss channels

Cross sections for single ionization and dissociative ionization of molecular targets under the impact of atomic anions were measured. Three systems were investigated, a ${\mathrm{H}}_{2}$ target with ${\mathrm{C}}^{\ensuremath{-}}$ and ${\mathrm{O}}^{\ensuremath{-}}$ projectiles, and a ${\mathrm{N}}_{2}$ target with ${\mathrm{O}}^{\ensuremath{-}}$ projectiles. The velocity range was 1.07--2.14 a.u. Recoil ions originated from the target (${\mathrm{H}}_{2}^{+},{\mathrm{H}}^{+},{\mathrm{N}}_{2}^{+},{\mathrm{N}}^{+}$, and ${\mathrm{N}}^{2+}$) were measured in coincidence with projectiles in several final charge states ($q=\ensuremath{-}1$, 0, $+1$, and $+2$). These states, negative, neutral, and positive, respectively, correspond to direct, single, and multiple electron loss channels. Target ionization is mostly due to the projectile single electron loss and direct processes, while target fragmentation is dominated by the projectile double electron loss. These results point to both target ionization and projectile direct or single electron loss processes being dominated by large impact parameters, while fragmentation and multiple electron loss are associated to small impact parameters.

State-Selective Preparation of NO2+ and the Effects of NO2+ Vibrational Mode on Charge Transfer with NO

Two color resonance-enhanced multiphoton ionization (REMPI) scheme of NO(2) through the E (2)Sigma(u)(+) (3psigma) Rydberg state was used to prepare NO(2)(+) in its ground and (100), (010), (02(0)0), (02(2)0), and (001) vibrational states. Photoelectron spectroscopy was used to verify >96% state selection purity, in good agreement with results of Bell et al. for a similar REMPI scheme. The effects of NO(2)(+) vibrational excitation on charge transfer with NO have been studied over the center-of-mass collision energy (E(col)) range from 0.07 to 2.15 eV. Charge transfer is strongly suppressed by collision energy at E(col) < approximately 0.25 eV but is independent of E(col) at higher energies. Mode-specific vibrational effects are observed for both the integral and differential cross-sections. The NO(2)(+) bending vibration strongly enhances charge transfer, with enhancement proportional to the bending quantum number, and is not dependent on the bending angular momentum. The enhancement results from increased charge transfer probability in large impact parameter collisions that lead to small deflection angles. The symmetric stretch also enhances reaction at low collision energies, albeit less efficiently than the bend. The asymmetric stretch has virtually no effect, despite being the highest-energy mode. A model is proposed to account for both the collision energy and the vibrational state dependence.

Numerical simulation of binary liquid droplet collision

A numerical investigation of binary droplet collision has been conducted. The complete process of the collision of two liquid droplets is dynamically simulated by solving the incompressible Navier-Stokes equations coupled with the convective equation of the level set function that captures the interface between the liquid and the gas phases. The simulations cover four major regimes of binary collision: bouncing, coalescence, reflexive separation, and stretching separation. For water droplets in air, the numerical results are compared with the experiments by and Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] on collision consequences. For hydrocarbon (C14H30) droplets in nitrogen gas, the simulated results are compared in detail with the time-resolved photographic images of the collision processes obtained by Qian and Law [J. Fluid Mech. 331, 59 (1997)] in every collision regime. The present numerical results suggest that the mechanism of a bouncing collision is governed by the macroscopic dynamics. However, the fact that the present macroscopic numerical model is unable to capture the collision regime of coalescence after minor deformation supports the speculation that its mechanism is related to the microscopic dynamics. Furthermore, the transition from bouncing to coalescence collisions has been predicted and agrees well with the analytical model. The mechanism of satellite droplet formation for head-on collision and stretching separation collision is also studied based on the detailed time-resolved dynamic simulation results. It is then confirmed that end pinching is the main cause of satellite formation in head-on collisions whereas the capillary-wave instability becomes dominant in large impact parameter cases. In the case of an intermediate impact parameter, the effects of twisting and stretching due to the angular momentum and the inertia of the colliding droplets are significant for the satellite formation.

Application of a level set method for simulation of droplet collisions

A level set technique for interface tracking is presented, both for the continuum surface force formulation and the ghost fluid method approach. A projection method is used to solve incompressible Navier–Stokes equations that are coupled to a transport equation for the level set function, defined as the algebraic distance to interface. Results are presented for head-on droplet collisions in coalescence and reflexive regimes with a 2D axi-symmetric code, and for an off-center droplet collision in a separation regime for a large impact parameter with 3D code. Simulations provided realistic and various droplet collision behaviors and they correspond to experimental observations.

SIGNATURES OF TEV SCALE GRAVITY IN HIGH ENERGY COLLISIONS

In TeV scale unification models, gravity propagates in 4+δ dimensions while gauge and matter fields are confined to a four-dimensional brane, with gravity becoming strong at the TeV scale. For a such scenario, we study strong gravitational interactions in an effective Schwarzschild geometry. Two distinct regimes appear. For large impact parameters, the ratio ρ~(Rs/r0)1+δ, (with Rs the Schwarzschild radius and r0 the closest approach to the black hole), is small and the deflection angle χ is proportional to ρ (this is like Rutherford-type scattering). For small impact parameters, the deflection angle χ develops a logarithmic singularity and becomes infinite for ρ = ρ c = 2/(3+δ). This singularity is reflected into a strong enhancement of the backward scattering (like a glory-type effect). We suggest as distinctive signature of black hole formation in particle collisions at TeV energies, the observation of backward scattering events and their associated diffractive effects.

Fragmentation of H 2O molecules following interaction with slow He 2+ ions

The energy distributions of fragments produced in He 2+ + H 2O collisions at projectile energies ranging from 1 keV up to 5 keV have been investigated experimentally as a function of the detection angle. Two groups of peaks are clearly visible. The first one, which extends up to ∼30 eV, corresponds to Coulomb explosion (CE) of the ionized target (H 2O) q+ following electron capture at relatively large impact parameters. At higher energies, a second group corresponds to fast fragments and scattered projectiles produced by quasi-binary collisions. In the analysis, particular attention was paid to these highly energetic ions. In this case, our absolute cross sections d σ/d Ω, differential in the observation angle, are smaller than those predicted by the Rutherford formula. Rather, our experimental values are in good agreement with absolute cross sections calculated using the ZBL potential that implies screening by the bound electrons.

Ultra-peripheral collisions of fully stripped gold ions at RHIC energies

In relativistic heavy-ion collisions, the strong Lorentz-contracted electromagnetic fields are capable of producing copious numbers of lepton pairs through the two-photon mechanism. The calculated cross section of electron–positron pair production at the Relativistic Heavy Ion Collider (RHIC) is about 33 000 barns and pair production can occur at large impact parameters. Here we calculate differential cross sections of pair production as a function of transverse momentum pT, rapidity, invariant mass and impact parameter.

PHYSICS OF ULTRA-PERIPHERAL NUCLEAR COLLISIONS

▪ Abstract Moving highly-charged ions carry strong electromagnetic fields that act as a beam of photons. In collisions at large impact parameters, hadronic interactions are not possible, and the ions interact through photon-ion and photon-photon collisions known as ultra-peripheral collisions (UPCs). Hadron colliders like the Relativistic Heavy Ion Collider (RHIC), the Tevatron, and the Large Hadron Collider (LHC) produce photonuclear and two-photon interactions at luminosities and energies beyond that accessible elsewhere; the LHC will reach a γp energy ten times that of the Hadron-Electron Ring Accelerator (HERA). Reactions as diverse as the production of anti-hydrogen, photoproduction of the ρ0, transmutation of lead into bismuth, and excitation of collective nuclear resonances have already been studied. At the LHC, UPCs can study many types of new physics processes.

Anisotropic screening effects on electron-ion bremsstrahlung process in an anisotropic plasma

The plasma screening and electric field effects on the low-energy electron-ion Coulomb bremsstrahlung process are investigated for both soft and hard photon radiation in an anisotropic plasma in the presence of an external electric field. The impact-parameter trajectory analysis is applied to the motion of the projectile electron in order to investigate the variation of the bremsstrahlung cross section as a function of the drift velocity, impact parameter, Debye length, and radiation photon energy. The results show that the bremsstrahlung radiation cross section decreases with increasing bremsstrahlung photon energy. The screening effect is more significant for the soft photon case. It is also found that the electric field effect enhances the bremsstrahlung cross section for soft photon radiation and large impact parameters and increases with increasing photon energy.

Experimental and theoretical studies of charge transfer and hydride transfer in the reactions of OD + and C 2H 4

We present a crossed beam and density functional theory (DFT) study of the dynamics of charge transfer and hydride transfer in collisions of OD + with C 2H 4 at relative collision energies between 19.3 and 102 kJ mol −1 (0.20–1.06 eV). Charge transfer to form C 2H 4 + is a direct process occurring through large impact parameters. A comparison of the internal energy distributions of reaction products with the photoelectron spectrum of C 2H 4 is consistent with a Franck–Condon picture for long distance electron transfer. Charge transfer with H/D rearrangement to form C 2H 3D + + OH does not occur, unlike the related system D 2O + + C 2H 4, in which comparable amounts of C 2H 4 + and C 2H 3D + are observed. This difference is accounted for by the significantly smaller proton affinity of OH relative to H 2O. Reactive processes are initiated by the formation of a protonated oxirane triplet diradical, which undergoes intersystem crossing to the singlet manifold. Formation of C 2H 3 + + HOD, nominally a hydride transfer reaction, is shown to occur at the lowest collision energy through transient singlet intermediates in which the timescale for rate-limiting hydrogen atom migration corresponds to a significant fraction of a rotational period. Formation of hydride transfer products is sufficiently exothermic (ΔH = −489 kJ mol −1) that a fraction of the C 2H 3 + products may be formed above the dissociation threshold to C 2H 2 +. Increasing collision energy results in enhanced yields of C 2H 2 + relative to C 2H 3 +, consistent with unimolecular decay of the most highly excited C 2H 3 + products. However, the very small translational energy releases at all collision energies also require significant vibrational excitation in the HOD products; the most probable internal excitation in HOD is approximately 60 kJ mol −1 at all collision energies.

FARADAY ROTATION OBSERVATIONS OF MAGNETIC FIELDS IN GALAXY CLUSTERS

The presence of magnetic fields in the intracluster medium in clusters of galaxies has been revealed through several different observational techniques. These fields may be dynamically important in clusters as they will provide additional pressure support to the intracluster medium as well as inhibit transport mechanisms such as thermal conduction. Here, we review the current observational state of Faraday rotation measure studies of the cluster fields. The fields are generally found to be a few to 10 microG in non-cooling core clusters and ordered on scales of 10-20 kpc. Studies of sources at large impact parameters show that the magnetic fields extend from cluster cores to radii of at least 500 kpc. In central regions of cooling core systems the field strengths are often somewhat higher (10-40 microG) and appear to be ordered on smaller scales of a few to 10 kpc. We also review some of the recent work on interpreting Faraday rotation measure observations through theory and numerical simulations. These techniques allow us to build up a much more detailed view of the strength and topology of the fields.

Coulomb and nuclear breakup of a halo nucleus Be11

Breakup reactions of the one-neutron halo nucleus $^{11}\mathrm{Be}$ on lead and carbon targets at about $70\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\text{nucleon}$ have been investigated at RIKEN by measuring the momentum vectors of the incident $^{11}\mathrm{Be}$, outgoing $^{10}\mathrm{Be}$, and neutron in coincidence. The relative energy spectra as well as the angular distributions of the $^{10}\mathrm{Be}+n$ center of mass system (inelastic angular distributions) have been extracted both for Pb and C targets. For the breakup of $^{11}\mathrm{Be}$ on Pb, the selection of forward-scattering angles, corresponding to large impact parameters, is found to be effective to extract almost purely the first-order $E1$ Coulomb breakup component and to exclude the nuclear contribution and higher-order Coulomb breakup components. This angle-selected energy spectrum is thus used to deduce the spectroscopic factor for the $^{10}\mathrm{Be}({0}^{+})\ensuremath{\bigotimes}\ensuremath{\nu}2{s}_{1∕2}$ configuration in $^{11}\mathrm{Be}$ which is found to be $0.72\ifmmode\pm\else\textpm\fi{}\mathrm{0.04}$ with a $B(E1)$ strength up to ${E}_{\mathrm{x}}=4\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ of $1.05\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.2em}{0ex}}{e}^{2}\phantom{\rule{0.2em}{0ex}}{\mathrm{fm}}^{2}$. The energy weighted $E1$ strength up to ${E}_{\mathrm{x}}=4\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ explains $70%\ifmmode\pm\else\textpm\fi{}10%$ of the cluster sum rule, consistent with the obtained spectroscopic factor. The non-energy-weighted sum rule within the same energy range is used to extract the root-mean-square distance of the halo neutron to be $5.77(16)\phantom{\rule{0.3em}{0ex}}\mathrm{fm}$, consistent with previously known values. In the breakup with the carbon target, we have observed the excitations to the known unbound states in $^{11}\mathrm{Be}$ at ${E}_{\mathrm{x}}=1.78\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ and ${E}_{\mathrm{x}}=3.41\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. Angular distributions for these states show the diffraction pattern characteristic of $L=2$ transitions, resulting in a ${J}^{\ensuremath{\pi}}={(3∕2,5∕2)}^{+}$ assignment for these states. We finally find that even for the C target the $E1$ Coulomb direct breakup mechanism becomes dominant at very forward angles.