Delbrück scattering
Delbrück scattering is the coherent elastic scattering of photons in the Coulomb field of heavy
nuclei. It is one of the two nonlinear effects of quantum electrodynamics (QED) in the
Coulomb field invested experimentally. The other is the splitting of a photon into two
photons. Delbrück scattering was introduced by Max Delbrück in order to explain
discrepancies between experimental and predicted data in a Compton scattering experiment
on heavy atoms carried out by Meitner and Köster [1]. Delbrück’s arguments were based on
the relativistic quantum mechanics of Dirac according to which the QED vacuum is filled
with electrons of negative energy or - in modern terms – with electron-positron pairs. These
electrons of negative energy should be capable of producing coherent-elastic photon
scattering because the recoil momentum during absorption and emission of the photon is
transferred to the total atom while the electrons remain in their state of negative energy. This
process is the analog of atomic Rayleigh scattering with the only difference that in the latter
case the electrons are bound in the electron cloud of the atom. The experiment of Meitner and
Köster [1] was the first in a series of experiments where the discrepancy between
experimental and predicted differential cross sections for elastic scattering of photons by
heavy atoms were interpreted in terms of Delbrück scattering. From the present point of view
these early results are not trustworthy. Reliable investigations were possible only after modern
QED techniques based on Feynman diagrams were available for quantitative predictions [2,3],
and on the experimental side photon detectors with high energy resolution and high detection
efficiency had been developed. This was the case at the beginning of the 1970th when also
Computers with high computing capacity were in operation which delivered numerical results
for Delbrück scattering amplitudes with sufficient precision. A first observation of Delbrück
scattering was achieved in a high-energy, small-angle photon scattering experiment carried
out at DESY (Germany) in 1973 [4]. Agreement was obtained with the predictions of Cheng
and Wu [5] which later were verified by Milstein and Strakhovenko [6]. These latter authors
[6] make use of a quasi-classical approximation being very different from the one of Cheng
and Wu. It could however be shown that both approximations are equivalent and lead to the
same numerical results. The essential breakthrough came with the Göttingen (Germany)
experiment in 1975 carried out at an energy of 2.754 MeV [7]. In this latter experiment
Delbrück scattering was observed as the dominant contribution to the coherent-elastic
scattering process, in addition to minor contributions stemming from atomic Rayleigh
scattering and nuclear Rayleigh scattering. This experiment [7] was the first where exact
predictions based on Feynman diagrams were confirmed with high precision and, therefore,
has to be considered as the first definite observation of Delbrück scattering. For a
comprehensive description of the present status of Delbrück scattering see [8,9]. Nowadays.
the most accurate measurements of high-energy Delbrück scattering are performed at the
Budger Institue of Nuclear Physics in Novosibirsk (Russia) [10]. The experiment where
photon splitting was really observed for the first time was also performed at the Budger
Institue of Nuclear Physics [11,12].
[1] L. Meitner, H. Köster, (with a comment of M. Delbrück), Z. Physik 84 (1933) 137.
[2] P. Papatzacos, K. Mork, Phys. Rev. D 12 (1975) 206; Phys. Rep. 21 (1975) 81.
[3] H. Falkenberg, et al., Atomic Data and Nucl. Data Tables 50 (1992) 1.
[4] G. Jarlskog, et al., Phys. Rev. D 8 (1973) 3813.
[5] H. Cheng, T.T. Wu, Phys. Rev. Lett. 22 (1969) 666; Phys. Rev. 182 (1969) 1852, 1868,
1873, 1899; Phys. Rev. D 2 (1970) 2444; Phys. Rev. D 5 (1972) 3077.
[6] A.I. Milstein, V.M. Strakhovenko, Phys. Lett. A 95 (1983) 135; Sov. Phys – JETP 58
(1983) 8.
[7] M. Schumacher, et al., Phys. Lett. 58 B (1975) 134.
[8] A.I. Milstein, M. Schumacher, Phys. Reports 234 (1994) 183.
[9] M. Schumacher, Rad. Phys. Chem. 56 (1999) 101.
[10] S.Z. Akhmadalev, et al., Phys. Rev. C 58 (1998) 2844.
[11] S.Z. Akhmadalev, et al., Phys. Rev. Lett. 89 (2002) 061802.
[12 ] R.N. Lee, et al., Phys. Reports 373 (2003) 213.

Delbrück scattering