Delbrück scattering of 30–100 MeV photons by Pb through angles of 15°–30°

Delbrück scattering at energies of 140–450 MeV

“…However, the accuracy of cross section measurements achieved in experiments [14][15] is essentially smaller than the accuracy of the theoretical predictions.…”

Relativistic oscillator model and Delbrück scattering

“…It was found that the Coulomb corrections at Zα ∼ 1 drastically change the amplitude as compared to the Born approximation. (3) At high energies and momentum transfers (ω, q ≫ m e ), the amplitude was also found to all orders in Zα [15,16,17]. In this case the Delbrück amplitude has a scaling behavior [18] and becomes inversely proportional to the photon energy.…”

“…(ii) In order to extract an information on nuclear structure from differential cross sections of photon scattering on nuclei, a precise knowledge of the Delbrück amplitude may be required because of its interference with the nuclear amplitude. In some cases, the Delbrück scattering considerably modifies the differential cross section of γA-scattering [6,7,8,9].…”

“…The pole at ω = 2E 0 is nevertheless absent because matrix elements in (10) vanish for the s-wave states n = n ′ = 0. Using (7), we easily calculate the integrals (9) with respect to the variables ǫ, r and r ′ (here the substitutions r = r 1 +r 2 and r ′ = r 1 −r 2 are helpful). It is also convenient to replace s 1 = s(1 + x)/2 and s 2 = s(1 − x)/2, where s 1 and s 2 are proper times in the integral representation of the Green functions in (9).…”

“…We may obtain another form of Eq. (13) by deforming the integration path over ǫ in (9) to transform the integral to − 1 2 ω+i∞ − 1 2 ω−i∞ dǫ. Such a deformation is always possible at low energies ω because the chains of singularities of two Green functions in (9) lying below and above the real axis, i.e.…”