Coherent forward scattering of synchrotron radiation via cascade of Mِssbauer transitions

Coherent inelastic forward scattering of synchrotron radiation (SR) via a two-transition Mِssbauer cascade (CIMC) is theoretically examined. It is shown that the spectral distribution of the scattered radiation in the vicinity of the second transition frequency occurs which is different for a recoilless scattering and for a scattering accompanied by a creation or annihilation of phonons. The most interesting scattering channel, when quanta of the second transition of the cascade are recoillessly emitted, is examined in detail. In this case, the phase-matching conditions for the recoilless absorption of an initial SR quantum and for a recoil absorption are different. The spectral distributions of the CIMC for the Mِssbauer cascade of 57Fe are calculated and perspectives of the CIMC observation are discussed.