Recoil Velocity Distributions Research Articles

Multi-mass velocity map imaging study of the 805 nm strong field ionization of CF3I.

Multi-mass velocity map imaging studies of charged fragments formed by near infrared strong field ionization together with covariance map image analysis offer a new window through which to explore the dissociation dynamics of several different highly charged parent cations, simultaneously - as demonstrated here for the case of CF3IZ+ cations with charges Z ranging from 1 to at least 5. Previous reports that dissociative ionization of CF3I+ cations yields CF3+, I+ and CF2I+ fragment ions are confirmed, and some of the CF3+ fragments are deduced to undergo secondary loss of one or more neutral F atoms. Covariance map imaging confirms the dominance of CF3+ + I+ products in the photodissociation of CF3I2+ cations and, again, that some of the primary CF3+ photofragments can shed one or more F atoms. Rival charge symmetric dissociation pathways to CF2I+ + F+ and to IF+ + CF2+ products and charge asymmetric dissociations to CF3 + I2+ and CF2I2+ + F products are all also identified. The findings for parent cations with Z ≥ 3 are wholly new. In all cases, the fragment recoil velocity distributions imply dissociation dynamics in which coulombic repulsive forces play a dominant role. The major photoproducts following dissociation of CF3I3+ ions are CF3+ and I2+, with lesser contributions from the rival CF2I2+ + F+ and CF32+ + I+ channels. The CF32+ fragment ion images measured at higher incident intensities show a faster velocity sub-group consistent with their formation in tandem with I2+ fragments, from photodissociation of CF3I4+ parent ions. The measured velocity distributions of the I3+ fragment ions contain features attributable to CF3I5+ photodissociation to CF32+ + I3+ and the images of fragments with mass to charge (m/z) ratio ∼31 show formation of I4+ products that must originate from parent ions with yet higher Z.

Ultraviolet photodissociation of gas-phase transition metal complexes: dicarbonylcyclopentadienyliodoiron(II)

The ultraviolet photodissociation of the prototypical organometallic half-sandwich compound dicarbonylcyclopentadienyliodoiron(II) [η 5-CpFe(CO)2I] has been studied in the gas phase across the wavelength range 260 ≤ λ ≤ 310 nm using multi-mass velocity-map ion imaging with photoproducts detected using both resonance enhanced multiphoton and vacuum ultraviolet (λ = 118.2 nm) single photon ionisation methods. Ion images recorded for the atomic iodine and the cyclopentadienyl photoproducts reveal fast, anisotropic components to their recoil velocity distributions. The experimental work is supported by multi-reference (spin–orbit averaged) electronic structure calculations that suffice to illustrate the high electronic state density in such transition metal complexes and provide insights into the rival fragmentation dynamics. The ground state parent molecule has singlet spin multiplicity, but the product energy disposal measured following Fe–Cp bond fission shows the involvement of nominally spin-forbidden transitions. The Fe–I and Fe–Cp bond fissions should both be viewed as homolytic and occurring on excited state potentials that are dissociative in the relevant ligand elimination coordinate.

Photofragment Translational Spectroscopy Studies of H Atom Loss Following Ultraviolet Photoexcitation of Methimazole in the Gas Phase.

The ultraviolet (UV) photodissociation of gas-phase methimazole has been investigated by H Rydberg atom photofragment translational spectroscopy methods at many wavelengths in the range of 222.5-275 nm and by complementary electronic structure calculations. Methimazole is shown to exist predominantly as the thione tautomer, 1-methyl-2(3 H)-imidazolinethione, rather than the commonly given thiol form, 2-mercapto-1-methylimidazole. The UV absorption spectrum of methimazole is dominated by the S4 ← S0 transition of the thione tautomer, which involves electron promotion from an a' (p y) orbital localized on the sulfur atom to a σ* orbital localized around the N-H bond. Two H atom formation pathways are identified following UV photoexcitation. One, involving prompt, excited-state N-H bond fission, yields vibrationally cold but rotationally excited methimazolyl (Myl) radicals in their first excited (Ã) electronic state. The second yields H atoms with an isotropic recoil velocity distribution peaking at low kinetic energies but extending to the energetic limit allowed by energy conservation given a ground-state dissociation energy D0(Myl-H) ∼24 000 cm-1. These latter H atoms are attributed to the unimolecular decay of highly vibrationally excited S0 parent molecules. The companion electronic structure calculations provide rationales for both fragmentation pathways and the accompanying product energy disposals and highlight similarities and differences between the UV photochemistry of methimazole and that of other azoles (e.g., imidazole) and with molecules like thiourea and thiouracil that contain similar N-C═S motifs.

Exit-channel recoil resonances by imaging the photodissociation of single quantum-state-selected OCS molecules

In a recent letter [Phys. Rev. Lett. 118, 253001 (2017)] we have described how studies of the recoil velocity distribution in the photodissociation of OCS in the energy interval 42 600--42 900 ${\mathrm{cm}}^{\ensuremath{-}1}$ revealed an unexpected behavior: the recoil velocity distribution of only the lowest-kinetic-energy photofragments exhibited rapid, resonantlike variations with energy and caused complete inversion of the recoil direction. Periodic orbit analysis and quantum nonadiabatic calculations unveiled the existence of a resonance state localized at large bending angles towards the exit of the dissociation channel. In this article, we present an extensive theoretical study and we show how the fingerprints of these resonances are identified by the analysis of the nonadiabatic transitions and the stereodynamics of photofragments trajectories. Additionally, the experimental study is extended to a second photolysis energy region, 43 300--43 650 ${\mathrm{cm}}^{\ensuremath{-}1}$, where a similar rapid variation of the recoil direction is detected. The energy separation between this second resonance region and the one previously reported is $\ensuremath{\sim}800\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is twice the calculated period of the localized resonant state, offering a second point of convergence between the experiment and the theory.

Integral cross section measurements and product recoil velocity distributions of Xe(2+) + N2 hyperthermal charge-transfer collisions.

Charge exchange from doubly charged rare gas cations to simple diatomics proceeds with a large cross section and results in populations of many vibrational and electronic product states. The charge exchange between Xe(2+) and N2, in particular, is known to create N2 (+) in both the A and B electronic states. In this work, we present integral charge exchange cross section measurements of the Xe(2+) + N2 reaction as well as axial recoil velocity distributions of the Xe(+) and N2 (+) product ions for collision energies between 0.3 and 100 eV in the center-of-mass (COM) frame. Total charge-exchange cross sections decrease from 70 Å(2) to about 40 Å(2) with increasing collision energy through this range. Analysis of the axial velocity distributions indicates that a Xe(2+) - N2 complex exists at low collision energies but is absent by 17.6 eV COM. Analysis of the axial velocity distributions reveals evidence for complexes with lifetimes comparable to the rotational period at low collision energies. The velocity distributions are consistent with quasi-resonant single charge transfer at high collision energies.

A statistical method to search for recoiling supermassive black holes in active galactic nuclei

We propose an observational test for gravitationally recoiling supermassive black holes (BHs) in active galactic nuclei, based on a correlation between the velocities of BHs relative to their host galaxies, |\Delta v|, and their obscuring dust column densities, \Sigma_{dust} (both measured along the line of sight). We use toy models for the distribution of recoil velocities, BH trajectories, and the geometry of obscuring dust tori in galactic centres, to simulate 2.5x10^5 random observations of recoiling quasars. BHs with recoil velocities comparable to the escape velocity from the galactic centre remain bound to the nucleus, and do not fully settle back to the centre of the torus due to dynamical friction in a typical quasar lifetime. We find that |\Delta v| and \Sigma_ {dust} for these BHs are positively correlated. For obscured (\Sigma_{dust}>0) and for partially obscured (0<\Sigma_{dust}<~2.3 g/m^2) quasars with |\Delta v|>=45 km/s, the sample correlation coefficient between log10(|\Delta v|) and \Sigma_{dust} is r_{45} = 0.28+/-0.02 and r_{45} = 0.13+/-0.02, respectively. Allowing for random +/-100 km/s errors in |\Delta v| unrelated to the recoil dilutes the correlation for the partially obscured quasars to r_{45} = 0.026+/-0.004 measured between |\Delta v| and \Sigma_{dust}. A random sample of >~3,500 obscured quasars with |\Delta v|>=45 km/s would allow rejection of the no-correlation hypothesis with 3 sigma significance 95% of the time. Finally, we find that the fraction of obscured quasars, F_{obs}(|\Delta v|), decreases with |\Delta v| from F_{obs}(<10 km/s)>~0.8 to F_{obs}(>10^3 km/s)<~0.4. This predicted trend can be compared to the observed fraction of type II quasars, and can further test combinations of recoil, trajectory, and dust torus models.

Predicting the effect of angular momentum on the dissociation dynamics of highly rotationally excited radical intermediates.

We present a model which accurately predicts the net speed distributions of products resulting from the unimolecular decomposition of rotationally excited radicals. The radicals are produced photolytically from a halogenated precursor under collision-free conditions so they are not in a thermal distribution of rotational states. The accuracy relies on the radical dissociating with negligible energetic barrier beyond the endoergicity. We test the model predictions using previous velocity map imaging and crossed laser-molecular beam scattering experiments that photolytically generated rotationally excited CD2CD2OH and C3H6OH radicals from brominated precursors; some of those radicals then undergo further dissociation to CD2CD2 + OH and C3H6 + OH, respectively. We model the rotational trajectories of these radicals, with high vibrational and rotational energy, first near their equilibrium geometry, and then by projecting each point during the rotation to the transition state (continuing the rotational dynamics at that geometry). This allows us to accurately predict the recoil velocity imparted in the subsequent dissociation of the radical by calculating the tangential velocities of the CD2CD2/C3H6 and OH fragments at the transition state. The model also gives a prediction for the distribution of angles between the dissociation fragments' velocity vectors and the initial radical's velocity vector. These results are used to generate fits to the previously measured time-of-flight distributions of the dissociation fragments; the fits are excellent. The results demonstrate the importance of considering the precession of the angular velocity vector for a rotating radical. We also show that if the initial angular momentum of the rotating radical lies nearly parallel to a principal axis, the very narrow range of tangential velocities predicted by this model must be convoluted with a J = 0 recoil velocity distribution to achieve a good result. The model relies on measuring the kinetic energy release when the halogenated precursor is photodissociated via a repulsive excited state but does not include any adjustable parameters. Even when different conformers of the photolytic precursor are populated, weighting the prediction by a thermal conformer population gives an accurate prediction for the relative velocity vectors of the fragments from the highly rotationally excited radical intermediates.

The Cl + O3 reaction: a detailed QCT simulation of molecular beam experiments.

We have studied in detail the dynamics of the Cl + O3 reaction in the 1-56 kcal mol(-1) collision energy range using quasi-classical trajectory (QCT) calculations on a recent potential energy surface (PES) [J. F. Castillo et al., Phys. Chem. Chem. Phys., 2011, 13, 8537]. The main goal of this work has been to assess the accuracy of the PES and the reliability of the QCT method by comparison with the existing crossed molecular beam results [J. Zhang and Y. T. Lee J. Phys. Chem. A, 1997, 101, 6485]. For this purpose, we have developed a methodology that allows us to determine the experimental observables in crossed molecular beam experiments (integral and differential cross sections, recoil velocity distributions, scattering angle-recoil velocity polar maps, etc.) as continuous functions of the collision energy. Using these distributions, raw experimental data in the laboratory frame (angular distributions and time-of-flight spectra) have been simulated from first principles with the sole information on the instrumental parameters and taking into account the energy spread. A general good agreement with the experimental data has been found, thereby demonstrating the adequacy of the QCT method and the quality of the PES to describe the dynamics of this reaction at the level of resolution of the existing crossed beam experiments. Some features which are apparent in the differential cross sections have also been analysed in terms of the dynamics of the reaction and its evolution with the collision energy.

Effects of Translational and Vibrational Excitation on the Reaction of HOD+ with C2H2 and C2D2: Mode- and Bond-Specific Effects in Exoergic Proton Transfer

Reactions of mode-selectively excited HOD(+) with C2H2 and C2D2 were studied over the center-of-mass collision energy (Ecol) range from 0.15 to 2.9 eV. HOD(+) was prepared in each of its fundamental vibrational states: ground state (000), bend (010), OD stretch (100), and the OH stretch (001). Charge transfer is the dominant reaction at all energies, although it is inhibited by increasing Ecol, and is accompanied by hydrogen exchange. The total charge transfer cross section is similar for C2H2 and C2D2, however, the tendency toward charge transfer with hydrogen exchange (CTHE) is significantly greater for C2D2 compared to C2H2. Charge transfer shows no significant effects of HOD(+) vibrational excitation, however, CTHE is significantly enhanced by vibration at Ecol < 0.62 eV. Both H(+) and D(+) transfer reactions (HT, and DT, respectively) are observed for both C2H2 and C2D2, with little dependence on collision energy, but with mode- and bond-specific enhancements from excitation of the OH and OD stretches. Recoil velocity measurements show that all channels are direct, except perhaps at the lowest collision energies. Mode-specific effects on the recoil velocity distributions are also observed, revealing how vibrational excitation affects reaction at different collision impact parameters.

Fragmentation dynamics of the ethyl bromide and ethyl iodide cations: a velocity-map imaging study

The photodissociation dynamics of ethyl bromide and ethyl iodide cations (C2H5Br(+) and C2H5I(+)) have been studied. Ethyl halide cations were formed through vacuum ultraviolet (VUV) photoionization of the respective neutral parent molecules at 118.2 nm, and were photolysed at a number of ultraviolet (UV) photolysis wavelengths, including 355 nm and wavelengths in the range from 236 to 266 nm. Time-of-flight mass spectra and velocity-map images have been acquired for all fragment ions and for ground (Br) and spin-orbit excited (Br*) bromine atom products, allowing multiple fragmentation pathways to be investigated. The experimental studies are complemented by spin-orbit resolved ab initio calculations of cuts through the potential energy surfaces (along the RC-Br/I stretch coordinate) for the ground and first few excited states of the respective cations. Analysis of the velocity-map images indicates that photoexcited C2H5Br(+) cations undergo prompt C-Br bond fission to form predominantly C2H5(+) + Br* products with a near-limiting 'parallel' recoil velocity distribution. The observed C2H3(+) + H2 + Br product channel is thought to arise via unimolecular decay of highly internally excited C2H5(+) products formed following radiationless transfer from the initial excited state populated by photon absorption. Broadly similar behaviour is observed in the case of C2H5I(+), along with an additional energetically accessible C-I bond fission channel to form C2H5 + I(+) products. HX (X = Br, I) elimination from the highly internally excited C2H5X(+) cation is deemed the most probable route to forming the C2H4(+) fragment ions observed from both cations. Finally, both ethyl halide cations also show evidence of a minor C-C bond fission process to form CH2X(+) + CH3 products.

Cooperative Mechanics of Multi-Motor Axonal Transport Revealed by Novel Nanomanipulation in Live Neurons

Despite remarkable advances in characterizing molecular motors and microtubular transport in vitro, our understanding of intracellular cargo transport is rudimentary. The intracellular mechanochemical properties and cooperative mechanics of multiple motors, sharing load and coordinating cargo direction, are fundamental in this regard. To elucidate these, we developed two novel approaches for manipulating the transport of axonal endosomes, loaded with nanoprobes (<100nm) by receptor-mediated endocytosis, in microfluidic DRG cultures.Firstly, we show that by culturing neurons in a novel microfluidic-magnetic device, with axons aligned along high magnetic gradient zones, we can exert pN forces on axonal endosomes carrying magnetic nanoparticles (MNP∼100nm). TIRF imaging of axonal MNP-endosome transport under external load reveals that mechanical means alone can transiently reverse endosome directionality. This suggests that mechanical force balance between kinesins and dyneins is critical for the regulation of endosome direction.Secondly, we show that laser-absorption by a gold nanoparticle (GNP∼80nm) in the endosome, stochastically results in the endosome being elastically tethered in axon (mechanism will be discussed). Motors driving the tethered endosome gradually come to a stall (like beads held by an optical trap) before detaching from the microtubule. The instantaneous recoil velocity of the endosome following lead-motor(s) detachment is proportional to the multi-motor stall force. We captured the recoil velocity distribution of dynein-driven retrograde and kinesin-driven anterograde endosomes using darkfield imaging at <2ms time, <5nm spatial resolutions. The peak structure of these distributions reflects discrete multi-motor stall forces and the peak-separation represents single-motor detachment velocity. Surprisingly, we find the single-motor detachment velocity for dynein comparable to that for kinesin suggesting comparable single-motor stall forces in this case. Further high-resolution motion analyses and stochastic modeling of GNP-endosome trajectories reveal several key signatures of cooperative mechanics, multi-motor force profiles and detachment kinetics.

Vibrationally enhanced charge transfer and mode/bond-specific H+ and D+ transfer in the reaction of HOD+ with N2O

The reaction of HOD(+) with N2O was studied over the collision energy (E(col)) range from 0.20 eV to 2.88 eV, for HOD(+) in its ground state and in each of its fundamental vibrational states: bend (010), OD stretch (100), and OH stretch (001). The dominant reaction at low E(col) is H(+) and D(+) transfer, but charge transfer becomes dominant for E(col) > 0.5 eV. Increasing E(col) enhances charge transfer only in the threshold region (E(col) < 1 eV), but all modes of HOD(+) vibrational excitation enhance this channel over the entire energy range, by up to a factor of three. For reaction of ground state HOD(+), the H(+) and D(+) transfer channels have similar cross sections, enhanced by increasing collision energy for E(col) < 0.3 eV, but suppressed by E(col) at higher energies. OD stretch excitation enhances D(+) transfer by over a factor of 2, but has little effect on H(+) transfer, except at low E(col) where a modest enhancement is observed. Excitation of the OH stretch enhances H(+) transfer by up to a factor of 2.5, but actually suppresses D(+) transfer over most of the E(col) range. Excitation of the bend mode results in ~60% enhancement of both H(+) and D(+) transfer at low E(col) but has little effect at higher energies. Recoil velocity distributions at high E(col) are strongly backscattered in the center-of-mass frame, indicating direct reaction dominated by large impact parameter collisions. At low E(col) the distributions are compatible with mediation by a short-lived collision complex. Ab initio calculations find several complexes that may be important in this context, and RRKM calculations predict lifetimes and decay branching that is consistent with observations. The recoil velocity distributions show that HOD(+) vibrational excitation enhances reactivity in all collisions at low E(col), while for high E(col) with enhancement comes entirely from the subset of collisions that generate strongly back-scattered product ions.

Polarization‐ and time‐resolved DFWM spectroscopy of the A 2Σ+− X 2Π (0,0) band transitions of nascent OH radicals generated by 266 nm laser photolysis of H2O2

The potential of a non‐linear spectroscopic technique – degenerate four‐wave mixing (DFWM) spectroscopy – for photo‐dissociation studies is investigated. By applying a carefully considered control of the input beam polarizations, the technique is used to measure the line shapes of specific rovibrational transitions in the A 2Σ+ − X 2Π (0,0) band of nascent OH radicals upon pulsed photo‐dissociation of H2O2. The photofragmentation is performed by linearly polarized radiation at 266 nm, and DFWM spectra are observed at various time delays. In contrast to linear spectroscopic methods, isotropic and anisotropic components of the non‐linear susceptibility tensor are separately accessible by using appropriate polarization geometries. In particular, four‐wave mixing signals can be generated that are exclusively due to the occurrence of the transient anisotropy of the recoil velocity and angular momentum vector distributions of the fragments emerging from the dissociation reaction. The observed line shapes in isotropic and anisotropic DFWM spectra are governed by the Doppler effect and vectorial correlations between the parent H2O2 molecule's transition dipole moment, the OH fragments’ recoil velocity and angular momentum, as well as by the processes of collision‐induced rotational and translational relaxation. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Effects of Collisional and Vibrational Velocity on Proton and Deuteron Transfer in the Reaction of HOD+ with CO

Reaction of HOD(+) with CO was studied over the collision energy (E(col)) range between 0.18 and 2.87 eV, for HOD(+) in its ground state and with one quantum in each of its vibrational modes: (001)--predominantly OH stretch; (010)--bend, and (100)--predominately OD stretch. In addition to integral cross sections, product recoil velocity distributions were also measured for each initial condition. The dominant reactions are near-thermoneutral proton and deuteron transfer, generating HCO(+) and DCO(+) product ions by a predominantly direct mechanism. The HCO(+) and DCO(+) channels occur with a combined efficiency of 76% for ground state HOD(+) at our lowest E(col), increasing to 94% for E(col) around 0.33 eV, then falling at high E(col) to ~40%. The HCO(+) and DCO(+) channels have a complicated dependence on the HOD(+) vibrational state. Excitation of the OH or OD stretch modes enhances H(+) or D(+) transfer, respectively, and inhibits D(+) or H(+) transfer. Bend excitation preferentially enhances H(+) transfer, with no effect on D(+) transfer. There is no coupling of energy initially in any HOD(+) vibrational mode to recoil velocity of either of the product ions, even at low E(col) where vibrational excitation doubles or triples the energy available to products. The results suggest that transfer of H or D atoms is enhanced if the atom in question has a high vibrational velocity, and that this effect offsets what is otherwise a general inhibition of reactivity by added energy. HOCO(+) + D and DOCO(+) + H products are also observed, but as minor channels despite being barrierless and exoergic. These channels appear to be complex mediated at low E(col), essentially vanish at intermediate E(col), then reappear with a direct reaction mechanism at high E(col).

H+ versus D+ transfer from HOD+ to N2: Mode- and bond-selective effects

Reactions of HOD(+) with N(2) have been studied for HOD(+) in its ground state and with one quantum of excitation in each of its vibrational modes: (001)--predominately OH stretch, 0.396 eV, (010)--bend, 0.153 eV, and (100)--predominately OD stretch, 0.293 eV. Integral cross sections and product recoil velocities were recorded for collision energies from threshold to 4 eV. The cross sections for both H(+) and D(+) transfer rise slowly from threshold with increasing collision energy; however, all three vibrational modes enhance reaction much more strongly than equivalent amounts of collision energy and the enhancements remain large even at high collision energy, where the vibration contributes less than 10% of the total energy. Excitation of the OH stretch enhances H(+) transfer by a factor of ∼5, but the effect on D(+) transfer is only slightly larger than that from an equivalent increase in collision energy, and smaller than the effect from the much lower energy bend excitation. Similarly, OD stretch excitation strongly enhances D(+) transfer, but has essentially no effect beyond that of the additional energy on H(+) transfer. The effects of the two stretch vibrations are consistent with the expectation that stretching the bond that is broken in the reaction puts momentum in the correct coordinate to drive the system into the exit channel. From this perspective it is quite surprising that bend excitation also results in large (factor of 2) enhancements of both H(+) and D(+) transfer channels, such that its effect on the total cross section at collision energies below ∼2 eV is comparable to those from the two stretch modes, even though the bend excitation energy is much smaller. For collision energies above ∼2 eV, the vibrational effects become approximately proportional to the vibrational energy, though still much larger than the effects of equivalent addition of collision energy. Measurements of the product recoil velocity distributions show that reaction is direct at all collision energies, with roughly half the products in a sharp peak corresponding to stripping dynamics and half with a broad and approximately isotropic recoil velocity distribution. Despite the large effects of vibrational excitation on reactivity, the effects on recoil dynamics are small, indicating that vibrational excitation does not cause qualitative changes in the reaction mechanism or in the distribution of reactive impact parameters.

Reaction of C2H2+ (n·ν2, m·ν5) with NO2: Reaction on the singlet and triplet surfaces

Integral cross sections and product recoil velocity distributions were measured for reaction of C(2)H(2)(+) with NO(2), in which the C(2)H(2)(+) reactant was prepared in its ground state, and with mode-selective excitation in the cis-bend (2ν(5)) and CC stretch (n · ν(2), n = 1, 2). Because both reactants have one unpaired electron, collisions can occur with either singlet or triplet coupling of these unpaired electrons, and the contributions are separated based on distinct recoil dynamics. For singlet coupling, reaction efficiency is near unity, with significant branching to charge transfer (NO(2)(+)), O(-) transfer (NO(+)), and O transfer (C(2)H(2)O(+)) products. For triplet coupling, reaction efficiency varies between 13% and 19%, depending on collision energy. The only significant triplet channel is NO(+) + triplet ketene, generated predominantly by O(-) transfer, with a possible contribution from dissociative charge transfer at high collision energies. NO(2)(+) formation (charge transfer) can only occur on the singlet surface, and appears to be mediated by a weakly bound complex at low energies. O transfer (C(2)H(2)O(+)) also appears to be dominated by reaction on the singlet surface, but is quite inefficient, suggesting a bottleneck limiting coupling to this product from the singlet reaction coordinate. The dominant channel is O(-) transfer, producing NO(+), with roughly equal contributions from reaction on singlet and triplet surfaces. The effects of C(2)H(2)(+) vibration are modest, but mode specific. For all three product channels (i.e., charge, O(-), and O transfer), excitation of the CC stretch fundamental (ν(2)) has little effect, 2 · ν(2) excitation results in ∼50% reduction in reactivity, and excitation of the cis-bend overtone (2 · ν(5)) results in ∼50% enhancement. The fact that all channels have similar mode dependence suggests that the rate-limiting step, where vibrational excitation has its effect, is early on the reaction coordinate, and branching to the individual product channels occurs later.

A guided-ion beam study of the reactions of Xe+ and Xe2+ with NH3 at hyperthermal collision energies

We have measured the absolute cross sections for reactions of Xe(+) and Xe(2+) with NH(3) at collision energies in the range from near-thermal to ∼34 and ∼69 eV, respectively. For Xe(+), the cross section for charge transfer, the only exothermic channel, decreases from ∼200Å(2) below 0.1 eV to ∼12Å(2) at the highest energies studied. The production of NH(3) (+) is the only channel observed below 5 eV, above which a small amount of NH(2) (+) is also formed. In Xe(2+) reactions, the main products observed are NH(3) (+) and NH(2) (+). The charge transfer cross section decreases monotonically from ∼80 to ∼6Å(2) over the studied energy range. The NH(2) (+) cross section is similar to the charge transfer cross section at the lowest energies, and exhibits a second component above 0.4 eV, with a maximum of 65Å(2) at 0.7 eV, above which the cross section decreases to ∼30Å(2) at the highest energies studied. At energies above 10 eV, a small amount of NH(+) is also observed in Xe(2+) collisions. Product recoil velocity distributions were determined at selected collision energies, using guided-ion beam time-of-flight methods.

Remnant masses, spins and recoils from the merger of generic black hole binaries

We obtain empirical formulae for the final remnant black hole mass, spin, and recoil velocity from merging black hole binaries (BHBs) with arbitrary mass ratios and spins. Our formulae are based on the mass ratio and spin dependence of the post-Newtonian expressions for the instantaneous radiated energy, linear momentum, and angular momentum, as well as the ISCO binding energy and angular momentum. The relative weight between the different terms is fixed by amplitude parameters chosen through a least-squares fit of recently available fully nonlinear numerical simulations. These formulae can be used for statistical studies of N-body simulations of galaxy cores and clusters, and the cosmological growth of supermassive black holes. As an example, we use these formulae to obtain a universal spin magnitude distribution of merged black holes and recoil velocity distributions for dry and hot/cold wet mergers. We also revisit the long-term orbital precession and resonances and discuss how they affect spin distributions before the merging regime.

Statistical studies of spinning black-hole binaries

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions ${\stackrel{\ensuremath{\rightarrow}}{S}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{S}}_{2}$ over the sphere and magnitudes $|{\stackrel{\ensuremath{\rightarrow}}{S}}_{1}/{m}_{1}^{2}|=|{\stackrel{\ensuremath{\rightarrow}}{S}}_{2}/{m}_{2}^{2}|=0.97$ for different mass ratios, where ${\stackrel{\ensuremath{\rightarrow}}{S}}_{i}$ and ${m}_{i}$ are the spin-angular momentum and mass of the $i$th black hole. Starting from a fiducial initial separation of ${R}_{i}=50M$, we perform 3.5-post-Newtonian-order evolutions down to a separation of ${R}_{f}=5M$, where $M={m}_{1}+{m}_{2}$, the total mass of the system. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, $\stackrel{\ensuremath{\rightarrow}}{L}$. We perform ${16}^{4}=65\text{ }536$ simulations for six mass ratios between $q=1$ and $q=1/16$ and compute the distribution of the angles $\stackrel{^}{\stackrel{\ensuremath{\rightarrow}}{L}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}}$ and $\stackrel{^}{\stackrel{\ensuremath{\rightarrow}}{L}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\stackrel{\ensuremath{\rightarrow}}{S}}$, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counteralignment of both scalar products. A post-Newtonian analysis shows that radiation-reaction-driven dissipative effects on the orbital angular momentum lead to this bias. To study the merger of black-hole binaries, we turn to full numerical techniques. In order to make use of the numerous simulations now available in the literature, we introduce empirical formulas to describe the final remnant black-hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. Our formulas are based on the post-Newtonian scaling, to model the plunge phase, with amplitude parameters chosen by a least-squares fit of recently available fully nonlinear numerical simulations, supplemented by inspiral losses from infinity to the innermost stable circular orbit. We then evaluate those formulas for randomly chosen directions of the individual spins and magnitudes as well as the binary's mass ratio. The number of evaluations has been chosen such that there are 10 configurations per each dimension of this parameter space, i.e. ${10}^{7}$. We found that the magnitude of the recoil velocity distribution decays exponentially as $P(v)\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}v/2500\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1})$ with mean velocity $⟨v⟩=630\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and standard deviation $\sqrt{⟨{v}^{2}⟩\ensuremath{-}⟨v{⟩}^{2}}=534\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, leading to a 23% probability of recoils larger than $1000\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, and a highly peaked angular distribution along the final orbital axis. The studies of the distribution of the final black-hole spin magnitude show a universal distribution highly peaked at ${S}_{f}/{m}_{f}^{2}=0.73$ and a 25\ifmmode^\circ\else\textdegree\fi{} misalignment with respect to the final orbital angular momentum, just prior to full merger of the holes. We also compute the statistical dependence of the magnitude of the recoil velocity with respect to the ejection angle. The spin and recoil velocity distributions are also displayed as a function of the mass ratio. Finally, we compute the effects of the observer orientation with respect to the recoil velocity vector to take into account the probabilities to measure a given redshifted (or blueshifted) radial velocity of accretion disks with respect to host galaxies.

Velocity map imaging studies of the photodissociation of H2O+ cations

The near-threshold photofragmentation dynamics of state-selected H2O+ cations have been investigated using velocity map ion imaging methods. The cations were prepared in the v = 0 level of the ground ( 2B1) electronic state, by 2 + 1 resonance enhanced multiphoton ionization via selected rotational levels of the H2O, 1B1, v = 0 state. Subsequent two photon excitation of the resulting H2O+ cations to 2B2 state levels lying above the lowest dissociation limit (i.e. at total energies in the range 46000–50600 cm−1) results in O–H bond fission and OH+ fragment ion formation. These fragments display isotropic recoil velocity distributions, which peak at low kinetic energy but extend to the highest speeds allowed by energy conservation. Ab initio calculations of key sections through the potential energy surfaces (PESs) for the ground and first few excited states of H2O+ suggest two possible mechanisms for the observed rotational and (when energetically allowed) vibrational excitation of the OH+ fragments. Both require initial non-adiabatic (vibronic coupling) from the photo-prepared state level to high levels of the 2A1 state, but involve different subsequent HO+−H bond fission mechanisms. One involves Renner–Teller coupling to the ground state PES, while the alternative requires spin-orbit induced coupling to the repulsive 4B1(4A″) state PES.