Inelastic Rate Research Articles

Rotationally inelastic collisions of H2+ ions with He buffer gas: Computing cross sections and rates.

We present quantum calculations for the inelastic collisions between H2+ molecules, in rotationally excited internal states, and He atoms. This work is motivated by the possibility of experiments in which the molecular ions are stored and translationally cooled in an ion trap and a He buffer gas is added for deactivation of the internal rotational population, in particular at low (cryogenic) translational temperatures. We carry out an accurate representation of the forces at play from an ab initio description of the relevant potential energy surface, with the molecular ion in its ground vibrational state, and obtain the cross sections for state-changing rotationally inelastic collisions by solving the coupled channel quantum scattering equations. The presence of hyperfine and fine structure effects in both ortho- and para-H2+ molecules is investigated and compared to the results where such a contribution is disregarded. An analysis of possible propensity rules that may predict the relative probabilities of inelastic events involving rotational state-changing is also carried out, together with the corresponding elastic cross sections from several initial rotational states. Temperature-dependent rotationally inelastic rates are then computed and discussed in terms of relative state-changing collisional efficiency under trap conditions. The results provide the essential input data for modeling different aspects of the experimental setups which can finally produce internally cold molecular ions interacting with a buffer gas.

Quantum dynamics study on the binding of a positron to vibrationally excited states of hydrogen cyanide molecule

We present computational results of vibrationally enhanced positron annihilation in the e++HCN/DCN collisions within a local complex potential model. Vibrationally elastic and inelastic cross sections and effective annihilation rates were calculated by solving a time-dependent complex-potential Schrödinger equation under the ab initio potential energy surface for the positron attached HCN molecule, [HCN; e+], with multi-component configuration interaction level (Kita and Tachikawa, 2014). We discuss the effect of vibrational excitation on the positron affinities from the obtained vibrational resonance features.

Lindblad equation for the inelastic loss of ultracold atoms

The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.

Light-assisted collisions in ultracold Tm atoms

We studied light assisted collisions of Tm atoms in a magneto optical trap (MOT) for the first time, working on a weak cooling transition at 530.7 nm $(4f^{13}(^2F^0)6s^2,J=7/2,F=4$ to $4f^{12}(^3H_6)5d_{5/2}6s^2,J=9/2,F=5)$. We observed a strong influence from radiation trapping and light assisted collisions on the dynamics of this trap. We carefully separated these two contributions and measured the binary loss rate constant at different laser powers and detuning frequencies near the cooling transition. Analyzing losses from the MOT, we found the light assisted inelastic binary loss rate constant to reach values of up to $\beta=10^{-9}$ cm$^3$/s and gave the upper bound on a branching ratio $k<0.8\times 10^{-6}$ for the 530.7 nm transition.

Inelastic cross sections and rate coefficients for collisions between CO and H2

A five-dimensional coupled states (5D-CS) approximation is used to compute cross sections and rate coefficients for CO+H2 collisions. The 5D-CS calculations are benchmarked against accurate six-dimensional close-coupling (6D-CC) calculations for transitions between low-lying rovibrational states. Good agreement between the two formulations is found for collision energies greater than 10cm−1. The 5D-CS approximation is then used to compute two separate databases which include highly excited states of CO that are beyond the practical limitations of the 6D-CC method. The first database assumes an internally frozen H2 molecule and allows rovibrational transitions for v ≤ 5 and j ≤ 30, where v and j are the vibrational and rotational quantum numbers of the initial state of the CO molecule. The second database allows H2 rotational transitions for initial CO states with v ≤ 5 and j ≤ 10. The two databases are in good agreement with each other for transitions that are common to both basis sets. Together they provide data for astrophysical models which were previously unavailable.

Inelastic rate coefficients for collisions of C6H−with H2and He

The recent detection of anions in the interstellar medium has shown that they exist in a variety of astrophysical environments – circumstellar envelopes, cold dense molecular clouds and star-forming regions. Both radiative and collisional processes contribute to molecular excitation and de-excitation in these regions so that the ‘local thermodynamic equilibrium’ approximation, where collisions cause the gas to behave thermally, is not generally valid. Therefore, along with radiative coefficients, collisional excitation rate coefficients are needed to accurately model the anionic emission from these environments. We focus on the calculation of state-to-state rate coefficients of the C6H− molecule in its ground vibrational state in collisions with para-H2, ortho-H2 and He using new potential energy surfaces. Dynamical calculations for the pure rotational excitation of C6H− were performed for the first 11 rotational levels (up to j1 = 10) using the close-coupling method, while the coupled-states approximation was used to extend the H2 rate coefficients to j1 = 30, where j1 is the angular momentum quantum number of C6H−. State-to-state rate coefficients were obtained for temperatures ranging from 2 to 100 K. The rate coefficients for H2 collisions for Δj1 = −1 transitions are of the order of 10−10 cm3 s−1, a factor of 2 to 3 greater than those of He. Propensity rules are discussed. The collisional excitation rate coefficients produced here impact astrophysical modelling since they are required for obtaining accurate C6H− level populations and line emission for regions that contain anions.

Localization in inelastic rate dependent shearing deformations

Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions.

Ab initio potential energy surfaces describing the interaction of CH(X2Π) with H2

We have determined four-dimensional ab initio quasi-diabatic potential energy surfaces describing the interaction of CH(X2Π) with H2, under the assumption of fixed CH and H2 internuclear separations. These calculations employed the multi-reference configuration interaction method [MRCISD+Q(Davidson)]. The computed points were fit to an analytical form suitable for time-independent quantum scattering calculations of rotationally inelastic cross sections and rate constants.

Hot-Electron Dynamics and Thermalization in Small Metallic Nanoparticles

The important role played by hot electrons in photocatalysis and light harvesting has attracted great interest in their dynamics and mechanisms of generation. Here, we theoretically study the temporal evolution of optically excited conduction electrons in small plasmon-supporting gold and silver nanoparticles. We describe the electron dynamics through a master equation incorporating transition rates for optical excitations and electron–electron collisions that are calculated using the screened interaction within an independent-electron picture. Upon optical excitation of the particle by a light pulse, a nonthermal electron distribution is produced, which takes 10s fs to thermalize at an elevated electron temperature due to electron–electron collisions and eventually relaxes back to ambient temperature via coupling to phonons and thermal diffusion. Phonons and diffusion are introduced through a phenomenological inelastic attenuation rate. We find the temporal evolution of the electron energy distribution t...

Estimating Price and Income Elasticities of Trade in Services in Nigeria

The study estimated the elasticity of trade in services to real exchange rates and income in Nigeria. Adopting the imperfect substitutes model, the empirical findings revealed an inelastic real exchange rate and income elasticities in export and import of services functions in the long and short run. However, the value of income elasticity significantly exceeds the value of real exchange rate elasticity. The results for the long and short run coefficient estimates are broadly consistent across alternative estimators with some exceptions. While the real exchange rate have a significant future impact on export of services, domestic income was found to be the major driver of future import of services in Nigeria. There is a need to formulate and implement government policies that can enhance the tradability of services in Nigeria and abroad.

Energy relaxation rate and its mesoscopic fluctuations in quantum dots

We analyze the applicability of the Fermi-golden-rule description of quasiparticle relaxation in a closed diffusive quantum dot with electron–electron interaction. Assuming that single-particle levels are already resolved but the initial stage of quasiparticle disintegration can still be described by a simple exponential decay, we calculate the average inelastic energy relaxation rate of single-particle excitations and its mesoscopic fluctuations. The smallness of mesoscopic fluctuations can then be used as a criterion for the validity of the Fermi-golden-rule description. Technically, we implement the real-space Keldysh diagram technique, handling correlations in the quasi-discrete spectrum non-perturbatively by means of the non-linear supersymmetric sigma model. The unitary symmetry class is considered for simplicity. Our approach is complementary to the lattice-model analysis of Fock space: though we are not able to describe many-body localization, we derive the exact lowest-order expression for mesoscopic fluctuations of the relaxation rate, making no assumptions on the matrix elements of the interaction. It is shown that for the quasiparticle with the energy ε on top of the thermal state with the temperature T, fluctuations of its energy width become large and the Fermi-golden-rule description breaks down at max{ε,T}∼Δg, where Δ is the mean level spacing in the quantum dot, and g is its dimensionless conductance.

Present-day oxidative subsidence of organic soils and mitigation in the Sacramento-San Joaquin Delta, California, USA.

Subsidence of organic soils in the Sacramento-San Joaquin Delta threatens sustainability of the California (USA) water supply system and agriculture. Land-surface elevation data were collected to assess present-day subsidence rates and evaluate rice as a land use for subsidence mitigation. To depict Delta-wide present-day rates of subsidence, the previously developed SUBCALC model was refined and calibrated using recent data for CO2 emissions and land-surface elevation changes measured at extensometers. Land-surface elevation change data were evaluated relative to indirect estimates of subsidence and accretion using carbon and nitrogen flux data for rice cultivation. Extensometer and leveling data demonstrate seasonal variations in land-surface elevations associated with groundwater-level fluctuations and inelastic subsidence rates of 0.5–0.8 cm yr–1. Calibration of the SUBCALC model indicated accuracy of ±0.10 cm yr–1 where depth to groundwater, soil organic matter content and temperature are known. Regional estimates of subsidence range from <0.3 to >1.8 cm yr–1. The primary uncertainty is the distribution of soil organic matter content which results in spatial averaging in the mapping of subsidence rates. Analysis of leveling and extensometer data in rice fields resulted in an estimated accretion rate of 0.02–0.8 cm yr–1. These values generally agreed with indirect estimates based on carbon fluxes and nitrogen mineralization, thus preliminarily demonstrating that rice will stop or greatly reduce subsidence. Areas below elevations of –2 m are candidate areas for implementation of mitigation measures such as rice because there is active subsidence occurring at rates greater than 0.4 cm yr–1.

Theoretical investigation of electron transfer and detachment processes in low energy H− + Li and Li− + H collisions

The charge exchange and collisional detachment processes in H− + Li and Li− + H collisions have been studied by using the quantal molecular orbital close-coupling (QMOCC) method in the energy ranges of about 0.12–1000 eV u−1 and 0.1 meV–1000 eV, respectively, and the inelastic collision cross sections and rate coefficients have been computed and presented. It is found that the electron transfer process in the H− + Li and Li− + H collisions is due to the Demkov coupling between the 12Σ+ and 22Σ+ states at internuclear distances of about 15a0. The collisional electron detachment in the considered collision system is due to the excitation of the remaining six states, which are all unstable against autodetachment. These states are populated through a series of Landau–Zener couplings of the 22Σ+ state with upper 2Σ+ states and by the rotational 2Σ+–2Π couplings at small internuclear distances. The cross sections for electron transfer in H− + Li and Li− + H collisions in the energy range of 10–1000 eV u−1 attain values in the range of 10−16–10−15 cm2 (reaching their maximum values of about 5 × 10−15 cm2 at 500–600 eV u−1), while the values of the corresponding electron detachment cross sections in this energy range attain generally smaller values.

Inverstigation on loading of the Dimple optical trap based on a magnetically levitated large-volume crossed optical dipole trap

Optical trapping techniques and the ability to tune the atomic interactions both have made the unprecedented progress in the quantum gas research field. The major advantage of the optical trap is that the atoms are likely to be trapped at various sub-levels of the electronic ground state and the interaction strength can be controlled by Feshbach resonance. Optical trapping methods in combination with magnetic tuning of the scattering properties directly lead to the experimental achievements of Bose-Einstein condensation (BEC) of Cesium, which at first failed by using magnetic trapping approaches due to the large inelastic collision rate. The rapid loss of cesium atoms due to the inelastic two-body collisions greatly suppresses the efficient evaporative cooling to obtain a condensate. For optical production of cesium atomic BEC, it is necessary to prepare a large number of Cs atoms at specified state in an optical trap for condensation, especially for an efficient forced evaporation cooling. In this paper, we demonstrate our research on enhancing the loading rate of the atoms by using a dimple trap combined with a large-volume optical dipole trap (reservoir trap). In our work, the cold cesium atoms are prepared by a three-dimensional degenerated Raman sideband cooling, and then loaded into a large-volume crossed dipole trap by using the magnetic levitation technique. Effective load of the dimple optical trap is realized by superposing the small-volume dimple trap on the center of the largevolume optical trap. The theoretical analyses are performed for the magnetically levitated large-volume crossed dipole trap in variable magnetic field gradients and uniform bias fields. Optimal experimental values are acquired accordingly. The combined potential curve of the dimple trap, which is superimposed on the magnetically levitated large-volume dipole trap, is also given. The loading of precooled atoms from Raman sideband cooling into the magnetically levitated large-volume optical trap is measured in variable magnetic field gradients and uniform bias fields. Different loading results of the dimple trap are investigated, including direct loading after Raman sideband cooling, the large-volume optical trap and the magnetically levitated large-volume dipole trap without anti-trapping potential. Comparatively, the atomic number density is enhanced by a factor of ~15 by loading the atomic sample from the magnetically levitated large-volume dipole trap into the dimple optical trap. The experimental results lay a sound basis for the further cooling and densifying the atomic cloud through the evaporating cooling stage. This method can be used to obtain more cold atoms or a large number of Bose-Einstein condensation atoms for atomic species with large atom mass.

Computing rotational energy transfers of OD−/OH− in collisions with Rb: isotopic effects and inelastic rates at cold ion-trap conditions

We report close-coupling (CC) quantum dynamics calculations for collisional excitation/de-excitation of the lowest four rotational levels of OD− and of OH− interacting with Rb atoms in a cold ion trap. The calculations are carried out over a range of energies capable of yielding the corresponding rates for state-changing events over a rather broad interval of temperatures which cover those reached in earlier cold trap experiments. They involved sympathetic cooling of the molecular anion through a cloud of laser-cooled Rb atoms, an experiment which is currently being run again through a Heidelberg–Innsbruck collaboration. The significance of isotopic effects is analysed by comparing both systems and the range of temperatures examined in the calculations is extended up to 400 K, starting from a few mK. Both cross sections and rates are found to be markedly larger than in the case of OD−/OH− interacting the He atoms under the same conditions, and the isotopic effects are also seen to be rather significant at the energies examined in the present study. Such findings are discussed in the light of the observed trap losses of molecular anions.

Erratum: Corrigendum: Rotational state-changing cold collisions of hydroxyl ions with helium

Nature Physics 11, 467–470 (2015); published online 18 May 2015; corrected after print 1 October 2015. In the version of this Letter originally published the given rotational temperature of the trapped anions was obtained with an incorrect fit function, which also resulted in an overestimation of the measured inelastic rate coefficients.

The LHCb trigger and its upgrade

The current LHCb trigger system consists of a hardware level, which reduces the LHC inelastic collision rate of 30MHz, at which the entire detector is read out. In a second level, implemented in a farm of 20k parallel-processing CPUs, the event rate is reduced to about 5kHz. We review the performance of the LHCb trigger system during Run I of the LHC. Special attention is given to the use of multivariate analyses in the High Level Trigger. The major bottleneck for hadronic decays is the hardware trigger. LHCb plans a major upgrade of the detector and DAQ system in the LHC shutdown of 2018, enabling a purely software based trigger to process the full 30MHz of inelastic collisions delivered by the LHC. We demonstrate that the planned architecture will be able to meet this challenge.

Dynamics of ultracold dipolar particles in a confined geometry and tilted fields

We develop a collisional formalism adapted for the dynamics of ultracold dipolar particles in a confined geometry and in fields tilted relative to the confinement axis. Using tesseral harmonics instead of the usual spherical harmonics to expand the scattering wave function, we recover a good quantum number $\ensuremath{\xi}=\ifmmode\pm\else\textpm\fi{}1$ which is conserved during the collision. We derive the general expression of the dipole-dipole interaction in this convenient basis set as a function of the polar and azimuthal angles of the fields. We apply the formalism to the collision of fermionic and bosonic polar KRb molecules in a tilted electric field and in a one-dimensional optical lattice. The presence of a tilted field drastically changes the magnitude of the reactive and inelastic rates as well as the inelastic threshold properties at vanishing collision energies. Setting an appropriate strength of the confinement for the fermionic system, we show that the ultracold particles can even further reduce their kinetic energy by inelastic excitation to higher states of the confinement trap.

Elucidating the Crack Resistance of Alkali‐Activated Slag Mortars Using Coupled Fracture Tests and Image Correlation

The resistance of alkali silicate‐activated slag mortars to crack propagation is explored. With increasing SiO2‐to‐alkali oxide ratio (Ms) of the activating solution (between 1.0 and 2.0), the flexural strengths, fracture energies, and the strain energy release rates (crack resistance, GR) are noted to increase. The GR values, especially of the systems with Ms of 1.5 and 2.0, are higher than that of ordinary portland cement (OPC) mortar. In contrast, the fracture process zone (FPZ) was observed to be smaller for the alkali‐activated slag mortars, with higher localized strains. Similarly, the FPZs also shrink with increasing Ms. These responses are related to the differences in the reaction products in these systems. The fundamental differences in the fracture response of these binder systems are elucidated through tracking the FPZ development. The crack extension‐crack tip opening displacement relations and its relationship with the inelastic strain energy release rates are also used to bring out the differences between the binder systems.

Anisotropy induced Feshbach resonances in mixture of

We theoretically explore the scattering properties in collisions between in the ground state and fermionic in the metastable state. Unlike the role of the electronic spin degree of freedom in collisions of two alkali-metal atoms, the orbital degrees of freedom from the p electron of the metastable atoms, which induce not only mixings between different partial waves but also couplings between channels in different fine-structure manifolds, introduce the anisotropic interactions for producing broad-enough Feshbach resonances. Our closed-coupling calculation shows that this mechanism is similar to that in highly magnetic atoms, but the resonances also suffer from a large inelastic rate at the magnitude of to lower-lying fine-structure states or Zeeman sublevels, which will be an obstacle for associating ultracold polar molecules with both electron spin and electric dipole momentum. However, such a rich mixture of inelastic processes, and the experimental advantage of immunity from intraspecies inelastic collisions for metastable fermionic allow for precise investigations on the interspecies scattering properties for systems with excited-state atoms included.