Why don't we consider electrostatic energy of the pair in the case of pair production? I have seen this Wikipedia article and many others, but in none of them I find any mention of the electro-static energy of the generated pair. Why?
I mean, the energy conservation should be written as 
$h\nu = E_+ + E_- + Electrostatic\  Energy$
 A: The pair production is only possible due to relativistic quantum physics and one needs to describe all these processes by the so-called "quantum field theory" or its generalization (well, string theory is the only example).
In quantum field theory, electromagnetic fields are, just like all other fields, quantized. All of the configurations of the electromagnetic field may be written in terms of states of the particles – in the case of the electromagnetic field, the particles are photons.
The simplest process of pair production is possible in which no photons are generated along with the electron-positron or another pair at all. It is impossible to faithfully translate the statements into a classical electrodynamics language because classical electrodynamics isn't equivalent to the quantum field theory and it's not the right theory to describe pair production. But one could perhaps say that the simplest processes of pair production ultimately produce the two particles without any electrostatic energy in between.
When the particles in the newly created pair are close to one another, in the middle of the process of pair production, it's right to imagine that some electrostatic energy in between them is contributing to the total energy (the Hamiltonian). The form of the Hamiltonian in the Coulomb gauge makes this point explicit. But quantum field theory is a quantum theory so it – completely importantly – avoids the discussion what is there exactly in the middle of the process.
Quantum field theory is a quantum theory so it calculates the probabilities of various final states assuming some knowledge about the initial state and emphasizes that it is right to dismiss all other discussions and questions as scientifically meaningless. In Feynman's formulation, we're summing over all intermediate histories. The intermediate histories are undescribable in any classical, objective way. If we calculate the probability (or the probability amplitude) that we get a pair of well-separated particles in the final state – so that their mutual electrostatic energy drops to zero – we get a finite number which means that the production of extra photons along with the particle pair isn't necessary.
The energy conservation only demands that the initial energy is equal to the final energy. In the calculation of this process, both initial and final energy may be calculated from energy-momenta of well-separated particles so that their interaction energies are negligible. The energy-momenta or similar quantities describing the particles in the middle of the process aren't sharply well-defined. Like always in quantum mechanics, the physical system probes all the possibilities simultaneously, using quantum linear superpositions. It makes no sense to verify the energy conservation in the middle of the process of particle production (or any other process) because we actually aren't measuring the energy in the middle of the process. It's therefore unphysical to talk about it.
A: It depends what you  mean by "electrostatic energy". 
When we are talking of pair production we are talking of physics at the quantum mechanics framework.


FEYNMAN DIAGRAMS for pair production by a gamma ray (left) or an electron (right). These represent the processes in the preceding sketch. 

Lets take the simplest diagram on the left: a photon interacts with the electrostatic field of a nucleus , Z, by scattering off the field an electron and a positron appears to conserve lepton quantum numbers. All three outgoing (Z, e+, e-) conserve energy and momentum.  The electrostatics are taken care of in this balanc
A: I think that in a scattering process it is always understood that we are actually talking about asymptotic states for which mutual interactions are totally negligible (which is the reason why we treat asymptpotic states as free particles). 
Perhaps, a situation closer to what you have in mind is represented by pair production via a long lived bound states or resonances for which the binding energy of the intermediate state is important.
