Multichannel Quantum Defect Theory
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Transcript Multichannel Quantum Defect Theory
Multichannel Quantum Defect
Theory
-The Brief Introduction Department of Chemistry
Kim Ji-Hyun
1. What is a channel ?
Any possible grouping of elementary or
composite particles corresponding to a
particular final state
Elastic and Inelastic scatterings
Above threshold : open
Below threshold : closed
Particles : a, b, c
Bound states : (bc), (bc), (ac)
☞channel 0, 1, 2, 3
a + (bc) → a + b + c
→ a + (bc)
→ a + (bc)
→ b + (ac)
(breakup)
(elastic scattering)
(excitation)
(rearrangement)
2. Quantum Defect
For a hydrogenic atom,
En = E∞ - 1/n2
• For an alkaline or alkaline-earth atom,
En = E∞ – 1/(n – m)2
nn = n – m : effective quantum number
m : quantum defect
☞ from short-range interactions with a core
3. Division of Region
☞ system = ionic core + a Rydberg electron
1) The inner region(R ≤ R0)
• the existence of strong short-range
interactions besides a long-range potential
• spanned by regular solutions obtained from
solving the close-coupled equation
2) The outer region (R ≥ R0)
• Channels are decoupled.
• spanned by regular and irregular solutions
obtained from solving the ordinary secondorder differential equation
※ the most famous base pair
⇒ Coulomb functions
4. Boundary conditions
For standing wave channel basis,
the continuity conditions at the matching
radius R0
For fragmentation eigenchannels,
the condition imposing on their
asymptotic forms
The divergence terms must disappears in
asymptotic regions.
5. The power in experiments
From the compatibility equation,
Lu-Fano plot : graphical determination of
discrete levels
• From cross sections,
Reproduction of complex spectra
with the short-range K matrix and
the long-range quantum defect parameters h
and b
<References>
Ch. Jungen, Molecular Application of
Quantum Defect Theory (Institute of
Physics Publishing, Bristol, 1996)
John R. Taylor, Scattering theory(John
Wiley & Sons, New York, 1972)
C. –W. Lee, submitted to Phys. Rev. A