During pair production, a photon steals momentum from a nearby nucleus so that momentum is conserved. My question is: whether the photon can take the momentum from a nearby photon or not?
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$\begingroup$ So you are asking if two interacting photons can make an electron positron pair? If so yes because such a Feynman Diagram can be constructed using only rotations of the allowed vertex type $\endgroup$– JepsilonCommented May 31, 2018 at 8:03
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During pair production, a photon steals momentum from a nearby nucleus so that momentum is conserved.
Does not "steal", it gives momentum for momentum conservation in the center of mass of the produced pair. The nucleus had no momentum before the interaction, and has momentum after it.
My question is: whether the photon can take the momentum from a nearby photon or not?
You have to forget about taking momenta. It is all about conservation of energy and momentum . If two gammas have enough energy they can interact and produce various pairs. Gamma gamma colliders are being proposed to study production of particles..
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$\begingroup$ "The nucleus had no momentum before the interaction, and has momentum after it." Sure, in some reference frame. In another reference frame, it has momentum beforehand and none afterwards, so is this really a meaningful distinction? $\endgroup$– Chris ♦Commented May 31, 2018 at 8:36
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$\begingroup$ @Chris it is at the center of mass of the produced pair that the kinematic inconsistency of a photon decay to a pair appears as the photon has no center of mass and the nuclear field becomes necessary, or any field that can balance energy and momentum. $\endgroup$– anna vCommented May 31, 2018 at 8:55