By E. W. McDaniel and M. R. C. McDowell (Eds.)

ISBN-10: 0720402255

ISBN-13: 9780720402254

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**Extra resources for Case Studies in Atomic Collision Physics**

**Sample text**

The correction required is clearly much more complicated. § 1-7. Theoretical and experimental three-body ionic recombination coefficients Numerous authors [6, 16,20] have improperly assumed that the reaction 0 2 + + 0 2 + 0 2 -+ [ 0 4 ] + 0 2 (1-7-1) corresponds to the realistic situation of oxygen ions recombining in oxygen gas. Because of the mass effect, previously discussed, care must be exercised in identification of the possible ions involved. The equilibrium rate constant for 02+ + 0 2 ^ 0 : (1-7-2) has been studied by Yang and Con way [47] whose data show that O4 is the predominant positive ion even at very low neutral densities.

50° — The index gives the power of 10 by which the entry must be multiplied. The form of Jf13 (λ, μ) may be seen from Table 1-6-2 which gives some values of/(A, μ\α, A) which is dimensionless and such that *iz{K μ) = ep*a±(l + a)M;±I(À, μ\α, A). (1-6-37) As would be expected ^13(λ, μ) falls off very rapidly as \λ—μ\ is increased from zero. In the case where symmetrical resonance chargetransfer collisions are responsible for the energy change, the corresponding 50 1-6 THREE-BODY RECOMBINATION function has no pole and its variation with |A—μ| is relatively slow (cf.

The pole in the inte grand of (1-6-1) can be separated out by changing the integration variable to x = rjr (1-6-4) with the result φ = n-2(b/rc) f (l-x2)-*/(x)dx Jo (1-6-5) 1-6 THE RECOMBINATION COEFFICIENT 43 in which f(x) = a-x2)*g(x) (1-6-6) with g(x) = {1 - V(rc/x)IE-b2x2/r2c}-± (1-6-7) is well behaved over the range of integration. Therefore, the integral can be expanded by using the Gauss-Mehler quadrature formula •+ i i+1(l-x2)-*/Wdx = - J-i nj=i Σ/ίοοβ^π) \ In I (1-6-8) where n is an even integer [42] to yield ψ = n-2{bnjnrc) *» £ akg{aj) (1-6-9) 7= 1 with {-—π\9 k = in + l-j (1-6-10) since g(x) is an even function of x.

### Case Studies in Atomic Collision Physics by E. W. McDaniel and M. R. C. McDowell (Eds.)

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