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phys documents (dragged) 64 - p → q and is given by A pq...

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58 Physics Formulary by ir. J.C.A. Wevers 3. Ionisation and 3-particles recombination: A p + e - A + + 2e - 4. radiative recombination: A + + e - A p + hf 5. Stimulated emission: A q + hf A p + 2 hf 6. Associative ionisation: A ** + B AB + + e - 7. Penning ionisation: b.v. Ne * + Ar Ar + + Ne + e - 8. Charge transfer: A + + B A + B + 9. Resonant charge transfer: A + + A A + A + 11.5.2 Cross sections Collisions between an electron and an atom can be approximated by a collision between an electron and one of the electrons of that atom. This results in d σ d ( Δ E ) = π Z 2 e 4 (4 πε 0 ) 2 E ( Δ E ) 2 Then follows for the transition p q : σ pq ( E ) = π Z 2 e 4 Δ E q,q +1 (4 πε 0 ) 2 E ( Δ E ) 2 pq For ionization from state p holds to a good approximation: σ p = 4 π a 2 0 Ry 1 E p - 1 E ln 1 . 25 β E E p For resonant charge transfer holds: σ ex = A [1 - B ln( E )] 2 1 + CE 3 . 3 11.6 Radiation In equilibrium holds for radiation processes: n p A pq emission + n p B pq ρ ( ν , T ) stimulated emission = n q B qp ρ ( ν , T ) absorption Here, A pq is the matrix element of the transition
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Unformatted text preview: p → q , and is given by: A pq = 8 π 2 e 2 ν 3 | r pq | 2 3¯ h ε c 3 with r pq = ± ψ p | ± r | ψ q ² For hydrogenic atoms holds: A p = 1 . 58 · 10 8 Z 4 p-4 . 5 , with A p = 1 / τ p = ∑ q A pq . The intensity I of a line is given by I pq = hfA pq n p / 4 π . The Einstein coef±cients B are given by: B pq = c 3 A pq 8 π h ν 3 and B pq B qp = g q g p A spectral line is broadened by several mechanisms: 1. Because the states have a ±nite life time. The natural life time of a state p is given by τ p = 1 / ∑ q A pq . From the uncertainty relation then follows: Δ ( h ν ) · τ p = 1 2 ¯ h , this gives Δ ν = 1 4 πτ p = ∑ q A pq 4 π The natural line width is usually ³ than the broadening due to the following two mechanisms:...
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