Atomic and molecular collisions' Present and future'

1
Atomic and molecular collisions. Present and
future!.

• R. Cabrera-Trujillo,
• Quantum Theory Project
• University of Florida

2
Interstellar intercloud gas

• Chemistry
• Reaction rates
• Spectroscopy
• Energy transfer
• Charge transfer

3

• Ionized nebulae
• Electron scattering

• Ionization

• Photon emission

4
Planetary aurorae

• Chemical composition
• Photon emission
• Ionization
• Energy and momentum
• transfer
• Reactivity

5

• Planetary surface processes
• Sputtering
• Aircraft surface effects
• Material degradation

6
Radiotherapy and dosimetry

• Chemical modification
• Energy deposition
• Tumor treatment

7
Microelectronic and metallurgic

• Material modification
• Stress, tension

• Si and Cu implantation
• Microcircuity

8
The problem Energy loss
9
Schematic view of the collision.
10
Potential Energy Surface dynamics
11
Electron-Nuclear Dynamics approach (END)

• Time-dependent treatment of all electrons and
  nuclei.
• Instantaneous forces from the Coulombic
  Hamiltonian. No PESs are needed.
• Choice of molecular wave function in a given
  basis is the only approximation.
• Cartesian laboratory coordinates are used.

12

• Principle of least action produces the quantum
  mechanical equations of motion through the TDVP
• The wave function parameters (complex molecular
  orbital coefficients, z, average nuclear
  positions, R, and momenta, P, e.t.c.) are the
  dynamical variables.

13
Dynamical Equations
Quantum Mechanical Action
Quantum Mechanical Lagrangian
14
Dynamical Equations
Principle of least action or Time-Dependent
Variational Principle
Euler-Lagrange Equations
15
Molecular Coherent State
16
Dynamical Equations
For nuclei description
For electronic structure (complex MO coefficients)
The Lagrangian evaluated at zero width of
the nuclear wave packets.
17
Dynamical Equations (cont.)
18
Analysis of Evolved State
For a time t, when products are well separated
Impact parameter b, collision energy E, and final
state f in the same basis.
19
Classical Cross Section
Where the sum is over trajectories yielding the
same scattering angle
Diverges for
(forward scattering or glory angle)
(Rainbow angle)
and
20
Semi-classical Corrections

• Uniform Airy Approximation (K. W. Ford and J. A.
  Wheeler, Ann. Phys. 7, 259 (1959))
• Schiff Approximation
• (L. I. Schiff, Phys. Rev. 103, 443 (1956))
• includes all the terms of the Born series
• rainbow and glory angle treated in a single
  approach without requiring the separation of
  different scattering regions.

21
angle between and
22
H H2O at 50 eV b1.7 a.u.
23
H H2O at 50 eV b3.0 a.u.
24
H C2H6 at 5 eV b4.0 a.u.
25
H C2H6 at 5 eV b2.0 a.u.
26
Deflection function for H?He and H?He at 0.5 keV
27
Direct differential cross section for H?He at
0.5, 1.5, and 5.0 keV. The experimental points
are fromL. K. Johnson et al., Phys. Rev. A40,
3625 (1989).
28
Direct differential cross section for He ? He for
projectile energies of 0.5, 1.5, and 5.0
keV. The experiment is fromD. E. Nitz et al.,
Phys. Rev. A35, 4541 (1987).
29
Direct differential cross section for He ? Ne for
0.5, 1.5, and 5.0 keV. The experiment is
fromR. S. Gao et al., Phys. Rev. A36, 3077
(1987).
30
Direct differential cross section for H ? N? for
0.5, 1.5, and 5.0 projectile energies. Experiment
al pointsSolid squareL. S. Johnson et al.,
Phys. Rev. A38, 2794 (1988) open circles J. H.
Newman et al., J. Geophys. Res. 90, 8947 (1986).
31
Direct and charge transfer differential cross
section for He at 1.5 keV colliding with Ne.
Experimental points are from Johnson et. al.
PRA, 40, 4920 (1989).
32
Charge transfer differential cross section for H
at 0.5, 1.5, and 5.0 keV colliding with atomic
and molecular oxygen.
Experimental dataLinsay et. al, PRA 53, 212
(1996).
33
Direct and charge exchange differential cross
section for H at 5.0 keV on gaseous water.
Experimental pointsLinsay et. al. PRA 55, 3945
(1997).
34
Total charge exchange cross section for H
colliding with C2H2 as a function of the
projectile energy.
Experimental data Kusakabe et. al. PRA 62,
062715 (2000).
35
State to state total capture cross section for
the projectile in the 2s and 2p state when H
collids with H.

• Experimental data
• Hill et.al. JPB12 L341 (1979).
• Morgan et.al. Phys. Rev. A22, 1460 (1980).

36
State to state total excitation cross section for
the 2s and 2p state when H collides with atomic
H.
37
Trajectory for H colliding with H2 at 200 eV and
b0.5 a.u.
38
Internuclear distances among the collision
partners for H colliding with H2 at 200 eV at
b0.5 a.u.
39
Deflection function and trajectories at the plane
of the collision for H colliding with H2 at 200
eV
40
Energy and impact parameter dependent deflection
function for H colliding with H2
41
Direct differential cross section for H ? H? for
0.5, 1.5, and 5.0 keV projectile energies Dashed
lineCoupled-channel theory (DIM method). M.
Kimura et al., Phys. Rev. A33, 1619
(1986). Experimental dataR. S. Gao et al.,
Phys. Rev. A44, 5599 (1991).
42
Direct differential cross sction for H colliding
with atomic and molecular H at 0.5, 1.5, and 5.0
keV.
Experimental pointsGao et. al. PRA 44, 5599
(1991) and Newman et. al. P J. Geophys. Res. 90,
11045 (1985).
43
Electron capture and electron loss cross sections
for H, H ? H, H? for projectile energies from 10
eV up to 100 keV. Short-dashed lineM. Kimura,
Phys. Rev. A32, 802 (1985)
44
Equilibrium charge fraction in a hydrogen beam on
H2 as a function of the projectile energy.
Experimental data Allison and Garcia-Munoz,
Proc. Roy. Soc. London A232, 423 (1955).
45
Total energy loss for protons colliding with
molecular hydrogen as a function of the
projectile energy and impact parameter.
46
Total stopping cross section for a hydrogen beam
colliding with atomic and molecular hydrogen.
Experimental dataNIMB 69, 18 (1992). PR 92, 742
(1953). PR 127, 792 (1962). NIMB 44, 399
(1990). PR 90, 532 (1953).
47
(No Transcript)
48
SUMMARY

• No restrictions as to projectile or target
  charge state are made.
• No restrictions are made on the collision
  trajectory.
• Projectile energy ranges from eV up to keV (until
  ionization channel opens).
• Results compare well with other theoretical
  approaches and with available experimental data.
• The method is computationally intensive, but very
  general.

• In the works
• Free electrons - ionization and electron
  projectiles.
• State to state, vibrational and rotational energy
  resolution.