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Multichannel Quantum Defect Theory

Multichannel Quantum Defect Theory. The Brief Introduction - Department of Chemistry Kim Ji-Hyun. 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

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Multichannel Quantum Defect Theory

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  1. Multichannel Quantum Defect Theory The Brief Introduction - Department of Chemistry Kim Ji-Hyun

  2. 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

  3. Particles : a, b, c Bound states : (bc), (bc), (ac) ☞channel 0, 1, 2, 3 a + (bc) → a + b + c (breakup) → a + (bc) (elastic scattering) → a + (bc) (excitation) → b + (ac) (rearrangement)

  4. 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

  5. 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

  6. 2) The outer region(R ≥ R0) • Channels are decoupled. • spanned by regular and irregular solutions obtained from solving the ordinary second-order differential equation ※ the most famous base pair ⇒ Coulomb functions

  7. 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.

  8. 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

  9. <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

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