Theoretical Calculations of Ion-Atom

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Theoretical Calculationsof Ion-Atom
Atom-Diatom Collisions

• Teck Ghee Lee

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Applications of atomic molecular collisions
cross sections

1. Basic plasma physics
2. Controlled nuclear fusion energy research
3. Astrophysics Atmospheric physics
4. Industrial applications of low-temperature plasma
   such as plasma processing, etching, plasma
   display panel, etc.
5. Lighting science
6. Radiation science and Biological physics
7. Environmental science and technology
8. Surface science, etc.

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Ion-atom and atom-diatom collisions processes are
important in the modeling of many astrophysical
environments
Universe, the final frontier..

• Information of our cosmos comes from
  spectroscopy.
• Absorption lines
• Emission lines
• Knowledge of atomic and molecular physics helps
  to unlock the secrets of the star formation and
  stellar life cycle.
• New tool, new observations required new atomic
  and molecular data.

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Electron capture process in ion-atom collisions
is important in the modeling of many technical
plasmas
Electron capture processes in magnetic fusion
-plasma diagnostics -charge state balance

• The transitions following charge transfer are
  particularly useful for determining the densities
  of the fully stripped low-Z ions and for
  measuring ion temperatures and plasma rotation.

Inside ITER
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Coupled-Channel or Close-Coupling Theory
General 3-body collision system
Elastic
A BC
A BC
A BC
Excited
q
r
AC B
Rearrangement
Solve time-independent Schrodinger Eqn
Born Oppenheimer Approximation

• Take H2 for example
• Base on electronic-nuclear mass ratio 1/1800
  a.u.
• Nuclei of the molecule are virtually standing
  still relative to the electron

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Some general properties
Types of Mechanism Typical Energy (cm-1) Typical Energy (eV)
Electronic 20k 80 k 10
Vibrational 100 4k 0.1
Rotational 0.1 30 0.001
Can write
Use Y to solve the TISE equation with appropriate
boundary conditions.
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Coupled-Channel or Close-Coupling Theory
We write
And
Where
Arrive at a system of coupled-channel equation
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Part I Ion-Atom Collisions at Low Energies
James R. Macdonald Laboratory, Kansas State
University Atomic, Molecular Optical Physics
Funded by the US Department of Energy
e
e
e
A B
B
A
A B
Jacobi Coordinate Systems

• BO/MO represents the wave function in a-set.
  

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Introduction
Energy Regime

• Intermediate energy vo/ve 1.
• Straight-line trajectory approximation.
• Low energy vo/ve ltlt 1.
• Quantum mechanical effect becomes IMPORTANT.
• Non-perturbative quantum mechanical approach is
  required to treat a two-center and 3-Body
  dynamics.

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Ion-Atom collisions at low energy
Rearrangement and Excitation Processes
v
A
B
B
A
B
A
Charge transfer
Elastic, Excitation
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Objectives
Reactions
H D(1s) H(1s) D H(2p) D H D(2p)
H D(1s)
Elastic
Charge Transfer
Direct Excitation

• A proto-type/textbook system and to test our
  theory for weak-channels-transitions.
• Experiment is difficult to perform.
• Behavior of cross sections in low-energy (eV)
  region.

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Previous work B.M. McLaughlin, JPB96 Theory
Semiclassical H H(1s)

• Excitation H(2p) good
• agreement with ORNL data
• except at E lt 1 keV/amu
• Capture H(2p) good
• agreement with ORNL data
• down to 0.6 keV/amu.

Lee et al, JPB2003
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Total charge transfer cross sections
O8 H(1s)
O7(nlm) H

• Data are in reasonable good agreement.
• This general agreement in total cross section
  fails to reveal the significant discrepancies
  among the reported partial cross section.

Lee et al, PRA2004
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Theory Born-Oppenheimer (BO) Method

• Traditional approach is BO

• BO treats collisions by fixing positions of heavy
  nuclei.
• By expanding system wave function
• Scattering wave functions do not satisfy the B.C.
• Existence of long-range spurious couplings.
• Cross sections not being Galilean invariant.

• Solve TISE by expanding system wave function

Ad-hoc electron translation factors
(ETF), defined in terms of nuclear
velocities, have no quantum equivalents.
Arbitrary choice of switching function
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Solutions to B.O. Problems

• Hyperspherical coordinate system accounts for
  the mass dependence.

• Free from the B.O. problems.
• Free from ambiguities.
• Hyperspherical coordinate method can be applied
  to any 3-body systems.

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Adiabatic hyperspherical potential curves
n2
H(1s)D
DE3.7meV
D(1s)H
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(No Transcript)
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Newman et al HD(1s)
HSCC8
ORNL HH(1s)
TDDFT
Newman et al HH(1s)
Dalgano SCA
Charge transfer from D(1s) to H(1s)
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O8 H(1s) collision
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Part II Atom-Diatom Collisions at Low Energies
v
X
R
H
q
r
O
H
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Energy Levels of H2

• The aim of this work is to obtain both accurate
  and comprehensive molecular collisional rate
  coefficients, that are needed to understand
• H2 spectral line formation
• rovibrational level populations
• the effects of H2 on surrounding gas (e.g.,
  heating and cooling)

• Since these data are potential sources of error
  in astrophysical models such as a those developed
  with the plasma simulation code Cloudy. The
  current uncertainties in collision rates have
  been known to affect the interpretation of the
  molecular spectra and our understanding of the
  conditions in interstellar gas.

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Le Bourlot MNRAS 99

• Plot of column density (population) ratio
  N(H2v0,j3)/ N(H2v0,j1) as functions of
  total column density N(H2).
• Scatters represent the results of 100 times
  changes in the collision rates, an uncertainty
  representative of current dispersion in collision
  rates at 100 K.
• Consequently, over a broad range of column
  densities uncertainties in collision rates
  preclude the use of the H2 absorption spectra as
  probes of the high-redshift universe.

Rescaled collisional data
Observed data
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Contour plots of the He-H2 surface as function of
H-H separation r and He-H2 separation R, at angle
g 90o.
He
R
H
g
r
O
H
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Quenching rate coefficients of He-H2 collisions
Transition v1,j0 to v0,j
v1,j0
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l-dependent potential couplings
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Transition v2,j0 to v1,j

• 2 characteristics contribute to large 1,0 to
  0,8 transition
• Small energy gap between 1,0 and 0,8 level.
• Large potential coupling.

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Elastic cross sections
De-excitation cross sections
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Summary

• Coupled-Channel method is a powerful tool for
  evaluating and generating reliable cross
  sections for many atomic and molecular collisions
  systems.
• Serve as a diagnostic tool for other theoretical
  methods.
• Accurate collisional cross sections data are
  important.
• Provide a guide to experimental measurement.
  Improvement of experimental apparatus and
  techniques.
• Turn-key theoretical tool to create benchmark
  collision data needed for applications.
• Theoretical calculations are economical, provided
  the computing power is available.

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Future Plan
Ro-vibrational transitions
H H2(v,j)
H H2(v,j)
H HD(v,j)
H HD(v,j)
H2(v,j) H2(v,j)
H2(v,j) H2(v,j)
He HD(v,j)
He HD(v,j)
H2(v,j) HD(v,j)
H2(v,j) HD(v,j)
Collision Induced Dissociation of H2 and HD
molecules
H H2(v,j)
H H H
H HD(v,j)
H H D
H2(v,j) H H
H2(v,j) H2(v,j)
He HD(v,j)
He H D
H2(v,j) H D
H2(v,j) HD(v,j)
H HD(v,j)
D H2(v,j)
(Rearrangement)
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Collaborators
Gary J. Ferland
N. Balakrishnan
Phillip C. Stancil
Robert C. Forrey
A. Dalgarno
David R. Schultz
Harvard-Smithsonian Center for Astrophysics
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• NASAs space astrophysics missions
• have the goal of meeting bold scientific
  challenges
• represent a very large investment
• require large arrays of laboratory astrophysics
  data to improve interpretation of observations
  and to enable modeling and simulation

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Background

• In brief, the availability of the required
  laboratory astrophysics data falls significantly
  short of what is actually needed and sponsorship
  for this research is also far less than what is
  required
• Therefore there is an opportunity and a need for
  the community to address this shortfall of
  laboratory astrophysics research
• Southeast Laboratory Astrophysics Community
  (SELAC)

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The Southeast Laboratory Astrophysics Community

• SELAC is a community of researchers seeking to
  address the laboratory astrophysics needs of NASA
  space missions ground-based observatories, and
  the modeling and simulation efforts required to
  make significant advances in astrophysics
• SELAC is a new organization, but is built on the
  foundation of longstanding strength in laboratory
  astrophysics in the Southeast
• SELAC has been formed and will develop
• in order to provide a forum for communication
  between and within the laboratory astrophysics
  and the astrophysics communities
• in response to the need to increase awareness of
  the underpinning nature of laboratory
  astrophysics in seeking answers to important,
  present challenges in astrophysics

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A three-level approach to reach our goals

• National level
• Need to increase the awareness that laboratory
  astrophysics underpins the interpretation and
  modeling of a wide range of astrophysics
  observations
• Need national committees to view laboratory
  astrophysics as a priority and advocate in its
  favor
• Need to stimulate new funding initiatives at NASA
  (NSF, DOE)
• Need to translate the LAW process findings into
  concrete actions
• Regional/broad level
• Leverage the regional strength in laboratory
  astrophysics by setting up an organization to
  improve communications and undertake new
  initiatives - SELAC
• Organize SELAC to benefit all its members,
  sponsoring institutions, the astrophysics
  community, and the mission agencies
• Regional/focused level
• Encourage and promote individual or multilateral
  laboratory astrophysics initiatives

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www.orau.org/selac

• UK workshop announcement from first page of the
  SELAC website