Understanding
the dynamics of and kinetics of chemical reactions is a subject
of fundamental importance. Our work focuses on an increasingly
important topic that has until now received insufficient attention:
The need for rigorous methods and tools to interpret and understand
the results from large-scale computations and state-of-the-art
experiments. In atom-diatom collisions the partners are heavy
and, unlike in light particle scattering, a semiclassical analysis
is central for gaining full physical insight. Direct computation
of the semiclassical S-matrix elements is, however, difficult.
For this reason we apply semiclassical analysis, after the scattering
matrix has been calculated exactly with the help of one of the
high accuracy codes currently available. In particular, one
wishes to know
- Is the reaction mechanism direct, or are there long-lived
resonances present?
- If reactive cross sections show interference patterns,
what is their origin and physical nature?
These questions are best answered by means of the semiclassical
complex angular momentum (CAM) analysis we have developed
in the last decade. Its main applications are:
- CAM analysis of reactive differential cross sections.
A reactive collision can proceed via the direct or the resonance
mechanism. In the first case an atom is exchanged in a brief
encounter between the collision partnerswhose motion approximately
follows a (semi)classical trajectory.In the resonance case,
the atoms combine in a metastable riatomic complex which,
once formed, continues to rotate until breaking up into
products.Quantum mechanically, the two (or more, if different
types of complexes can be formed) possibilities must be
considered simultaniously and the inteference between them
can lead to structures in the angular distributions, one
example of which is given While the direct scattering can
be described in terms of primitive semiclassical (Ford-Wheeler)
amplitude, the formation of metastable complexes is best
expressed in terms of the (Regge) poles of the S-matrix
elementin the CAM plane. General description of the method
can b e found in [1],
while [2-4] give recent
examples of its application to reactions of current experimental
and theoretical interest.
- CAM analysis of reactive integral cross sections. Not
only reactive angular distributions but also integral cross-sections
are often affected by the the presence of long-lived complexes.
It was recently shown [5]
that the CAM approach is naturally suited for analysing
such resonance effects. A signature o a resonance may vary
from a smooth step in the short lifetime limit to a sharp
(Breit-Wigner) peak, or peaks if lifetime of a complex is
large. An example of of the power of CAM techniques is its
application to the F+H2 reaction [5]
which has revealed a new generic type of sinusoidal oscillations
produced by a CAM pole (Regge) trajectory with angular life
of order of one full rotation.
- Pade` reconstruction of a reactive scattering data..
Implementation of the theories described above require the
knowledge of analytical structure of the scattering matrix.
The standard codes compute the S-matrix elements at a discrete
set of integral physical values of the angular momentum from
which it must be analytically continued into the CAM plane.
To achieve this, we have developed an approach employing on
Pade` approximants of type II. General theory of Pade` approximants
is an important area of mathematics with applications in fields
ranging from quantum field theory to signal processing. Unlike
the Pade` approximants of type I (using as input the values
of derivative at a given point, rather than the values of
a function itself), approximants of type II are less well
studied. Among somewhat surprising features of such approximants
is that they often use available poles and zeroes to mark
an elliptic boundary, beyond which the approximation fails
catastrophically [5].
Discussion of other aspects of the Pade` reconstruction can
be found, for example, in [6].
[1]
D.Sokolovski and A.Z.Msezane, Semiclassical complex angular
momentum theory and Pade` reconstruction for resonances, rainbows
and reactive thresholds, Phys.Rev.A., 70, 032710 (2004)
[2]D.Sokolovski,
Glory and thresholds effects in H+D2 reactive angular scattering,Chem.Phys.Lett.,
370, 805-811, (2003).
[3]
D. Sokolovski ,S.K.Sen, V.Aquilanti, S. Cavalli and D. de
Fazio, Interacting resonances in the F+H2 reaction revisited:
Complex terms, Riemann surfaces and angular distributions,
J.Chem.Phys., 126, 0845305-1-11, (2007).
[4] D. Sokolovski, D. de Fazio, S. Cavalli and V.Aquilanti,
On the origin of the forward peak and backward oscialltions
in the F+H2 (v=0) -> HF(v`=2)+ H reaction, Phys.Chem.Chem.Phys,
9, 1-8, (2007).
[5]
D. Sokolovski, D. de Fazio, S. Cavalli and V.Aquilanti, Overlapping
resonances and Regge oscillations in the state-to-state integral
cross-sections of the F+H2 reaction, J.Chem.Phys., 126, 121101
1-4, (2007)
[6]
. D. Sokolovski and S.Sen, On the type II Pade` reconstruction
of a scattering matrix elemant, in the CCP6 booklet on Semiclassical
and other methods for understanding chemical reactions, ed.
By S.Sen. D.Sokolovski and J.N.L Connor (CCP6 2005).
[7]
D.Vrinceanu, A.Z.Msezane, D.Bessis, J.N.L.Connor and D.Sokolovski,
Pade` reconstruction of Regge poles from scattering matrix
data for chemical reactions, Chem.Phys.Lett., 324, 311 (2000).
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