I saw today in book that the momentum in pair production is conserved.
My question is, how could it be possible that the momentum is conserved?
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3$\begingroup$ Wikipedia: “The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron–positron pair produced in free space cannot both satisfy conservation of energy and momentum.” $\endgroup$– G. SmithCommented Mar 10, 2020 at 21:24
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It seems that your intuition is saying that it's not possible for a gamma ray to turn into a pair of particles without some additional mechanism to balance the energy and momentum equations, and your intuition is right. Real pair production from a gamma ray always involves another particle such as a heavy nucleus.
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$\begingroup$ Or just another gamma ray (which might as well come from a nucleus) $\endgroup$ Commented Mar 10, 2020 at 21:36
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1$\begingroup$ Except that gamma ray - gamma ray interactions have a very low cross section. "Very" is an understatement. $\endgroup$ Commented Mar 10, 2020 at 23:44
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$\begingroup$ pair producing $\gamma$'s like the large $Z^2$ of a heavy nucleus, but the heavy part is not important, for $\hbar\omega > 4m_ec^2$. At that threshold, pair production in the fields of atomic electrons also occurs. See: rcwww.kek.jp/research/shield/photon_r.pdf $\endgroup$– JEBCommented Mar 11, 2020 at 0:50