Download 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