285 research outputs found
Quantum dynamics of the Li+HF-->H+LiF reaction at ultralow temperatures
Quantum mechanical calculations are reported for the
Li+HF(v=0,1,j=0)-->H+LiF(v',j') bimolecular scattering process at low and
ultralow temperatures. Calculations have been performed for zero total angular
momentum using a recent high accuracy potential energy surface for the X 2A'
electronic ground state. For Li+HF(v=0,j=0), the reaction is dominated by
resonances due to the decay of metastable states of the Li...F-H van der Waals
complex. Assignment of these resonances has been carried out by calculating the
eigenenergies of the quasibound states. We also find that while chemical
reactivity is greatly enhanced by vibrational excitation the resonances get
mostly washed out in the reaction of vibrationally excited HF with Li atoms. In
addition, we find that at low energies, the reaction is significantly
suppressed due to the formation of rather deeply bound van der Waals complexes
and the less efficient tunneling of the relatively heavy fluorine atom.Comment: 24 pages, 8 figures, 1 table, submitted to J. Chem. Phy
Dimension dependence of correlation energies in twoâelectron atoms
Correlation energies (CEs) for twoâelectron atom ground states have been computed as a function of the dimensionality of space D. The classical limit Dââ and hyperquantum limit Dâ1 are qualitatively different and especially easy to solve. In hydrogenic units, the CE for any twoâelectron atom is found to be roughly 35% smaller than the realâworld value in the Dââ limit, and about 70% larger in the Dâ1 limit. Between the limits the CE varies almost linearly in 1/D. Accurate approximations to real CEs may therefore be obtained by linear interpolation or extrapolation from the much more easily evaluated dimensional limits. We give two explicit procedures, each of which yields CEs accurate to about 1%; this is comparable to the best available configuration interaction calculations. Steps toward the generalization of these procedures to larger atoms are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70213/2/JCPSA6-86-6-3512-1.pd
Dimensional expansions for twoâelectron atoms
Approximate expansions in inverse powers of the dimensionality of space D are obtained for the groundâstate energies of twoâelectron atoms. The method involves fitting polynomials in δ=1/D to accurate eigenvalues of the generalized Dâdimensional SchrĂśdinger equation. To the maximum order obtainable from the data, about δ7, the power series for nuclear charges Z=2, 3, and 6 all diverge at D=3. Asymptotic summation yields an energy for the Z=2 atom 1% in excess of the true value at D=3. However, expansions with a shifted origin, i.e., expansions in (δâδ0), show improved convergence. Of particular interest is the case δ0=1, because the expansion coefficients can in principle be calculated by perturbation theory applied to the oneâdimensional atom. Series in powers of (δâ1) appear to converge rapidly. Also the series in (δâ1) can be evaluated even for the hydride ion, with Z=1. For helium, this series is quite comparable to the more familiar expansion in powers of Îť=1/Z, with errors in the partial sums decreasing by roughly an order of magnitude per term. Thus, for Z=2 the first four terms of the expansion in (δâ1) yield an energy within 0.02% of the true value at D=3. Similar results are found in an analogous treatment of accurate eigenvalues for the HartreeâFock approximation. This provides a rapidly convergent dimensional expansion for the correlation energy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70931/2/JCPSA6-86-4-2114-1.pd
On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem
Group theoretic and graphical techniques are used to derive the N-body wave
function for a system of identical bosons with general interactions through
first-order in a perturbation approach. This method is based on the maximal
symmetry present at lowest order in a perturbation series in inverse spatial
dimensions. The symmetric structure at lowest order has a point group
isomorphic with the S_N group, the symmetric group of N particles, and the
resulting perturbation expansion of the Hamiltonian is order-by-order invariant
under the permutations of the S_N group. This invariance under S_N imposes
severe symmetry requirements on the tensor blocks needed at each order in the
perturbation series. We show here that these blocks can be decomposed into a
basis of binary tensors invariant under S_N. This basis is small (25 terms at
first order in the wave function), independent of N, and is derived using
graphical techniques. This checks the N^6 scaling of these terms at first order
by effectively separating the N scaling problem away from the rest of the
physics. The transformation of each binary tensor to the final normal
coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N
for arbitrary N. This has been accomplished using the group theory of the
symmetric group. This achievement results in an analytic solution for the wave
function, exact through first order, that scales as N^0, effectively
circumventing intensive numerical work. This solution can be systematically
improved with further analytic work by going to yet higher orders in the
perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and
is under revie
Chemical Accelerator Studies of Isotope Effects on Collision Dynamics of IonâMolecule Reactions: Elaboration of a Model for Direct Reactions
This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/53/2/10.1063/1.1674042.Crossedâbeam studies on isotopic variants of the reaction Ar+â+âH2âArH+ are reported. Both velocity and angular distributions of the ionic product as a function of initial translational energy, down to 0.1 eV (center of mass), have been measured. At lowest energies there is a gain in the translational energy of the products over that of the reactants, but at higher energies there is increasing conversion of kinetic into internal energy. While this represents the most probable course of the reaction there is a fairly wide distribution about the median values. Results confirm that this reaction is predominantly direct at all energies and provide no evidence for intermediate persistent complex formation. They are also consistent with a model for direct reactions previously proposed. The data on reaction with HD permit further development of this mechanism. The reactants are mutually accelerated by their longârange attractive potential until hydrogen atom transfer occurs. The liberated H (or D) atom is reflected from the ArD+(ArH+ and the products separate, being decelerated in the process by the attractive potential acting between them. This âpolarizationâreflectionâ model yields a reasonable value for the radius at which transfer occurs, and it accounts quantitatively for the magnitudes of, and isotopic effects on, the median product velocities. It also predicts the significant back scattering observed at very low as well as very high energies. With appropriate modification for the attractive potentials involved the model can provide a simple representation of direct reactions in general
Two and three electrons in a quantum dot: 1/|J| - expansion
We consider systems of two and three electrons in a two-dimensional parabolic
quantum dot. A magnetic field is applied perpendicularly to the electron plane
of motion. We show that the energy levels corresponding to states with high
angular momentum, J, and a low number of vibrational quanta may be
systematically computed as power series in 1/|J|. These states are relevant in
the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure
Part of the D - dimensional Spiked harmonic oscillator spectra
The pseudoperturbative shifted - l expansion technique PSLET [5,20] is
generalized for states with arbitrary number of nodal zeros. Interdimensional
degeneracies, emerging from the isomorphism between angular momentum and
dimensionality of the central force Schrodinger equation, are used to construct
part of the D - dimensional spiked harmonic oscillator bound - states. PSLET
results are found to compare excellenly with those from direct numerical
integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge
Pulsed rotating supersonic source used with merged molecular beams
We describe a pulsed rotating supersonic beam source, evolved from an
ancestral device [M. Gupta and D. Herschbach, J. Phys. Chem. A 105, 1626
(2001)]. The beam emerges from a nozzle near the tip of a hollow rotor which
can be spun at high-speed to shift the molecular velocity distribution downward
or upward over a wide range. Here we consider mostly the slowing mode.
Introducing a pulsed gas inlet system, cryocooling, and a shutter gate
eliminated the main handicap of the original device, in which continuous gas
flow imposed high background pressure. The new version provides intense pulses,
of duration 0.1-0.6 ms (depending on rotor speed) and containing ~10^12
molecules at lab speeds as low as 35 m/s and ~ 10^15 molecules at 400 m/s.
Beams of any molecule available as a gas can be slowed (or speeded); e.g., we
have produced slow and fast beams of rare gases, O2, Cl2, NO2, NH3, and SF6.
For collision experiments, the ability to scan the beam speed by merely
adjusting the rotor is especially advantageous when using two merged beams. By
closely matching the beam speeds, very low relative collision energies can be
attained without making either beam very slow.Comment: 26 pages, 10 figure
Effect of atomic transfer on the decay of a Bose-Einstein condensate
We present a model describing the decay of a Bose-Einstein condensate, which
assumes the system to remain in thermal equilibrium during the decay. We show
that under this assumption transfer of atoms occurs from the condensate to the
thermal cloud enhancing the condensate decay rate
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