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FEDLINK - United States Federal Collection jresv72Bn1p79 (User talk:Fæ/IA books#Fork8) (batch 1000-3000 #192074)
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Simple analytic expressions for the total Born approximation cross section for pair production in a Coulomb field
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The total Born approximation cross section for pair production in a Coulomb field given originally by Racah is used to derive two simple and rapidly convergent analytic expansions for this cross section, one valid for high energies, k , of the incident photon , the other for energies near the threshold. For k > 4 mc2 the fractional error involved in using the first four terms in the high energy expansion is < 4.4 x 10-5. For k < 4 mc2 the fractional error committed in using the first five terms of the low energy expansion is <1.1x10-4. The leading terms in these expansions are the well known high energy and low energy limits of this cross section, respectively.