Holography with γ rays: Simulations versus experiment for $\alpha {-}^{57}\mathrm{Fe}$

The $\gamma$-ray holography was recently applied [P. Korecki et al., Phys. Rev. Lett. $79,$ 3518 (1997)] to image the three-dimensional structure of $\alpha {-}^{57}\mathrm{Fe}$ with an atomic resolution. A simple theory of the hologram formation based on single-scattering cluster formalism taking into account the polarization effects in the resonant nuclear scattering and absorption processes is presented. The high quality of the real-space reconstruction is demonstrated, however, problems arising from the cancellation of real twin images are revealed. The realistic simulations are in a good agreement with the experiment. A method for elimination of the real and twin images cancellation taking advantage of the strong dependence of the scattering phase on the detuning from the resonance in the nuclear scattering is proposed.