Coherent emission of $γ$ quanta by synchrotron radiation excited nuclei: geometry of nearly backward scattering

A possibility of further development of Synchrotron M\"{o}ssbauer Source (SMS) of $^{57}$Fe 14.4 keV radiation is considered. The principles and detailed description of the SMS device is given in Refs. Phys. Rev. A 84, 053851 (2011) G. V. Smirnov et al, J. Synchrotron Rad., v. 19, 559 (2012) V. Potapkin et al. The perfect crystal of Iron Borate, FeBO$_{3}$, is the central element of this device. The coherent nuclear fluorescence of IB crystal illuminated by synchrotron radiation produces the sharply directed beam of 14.4 keV M\"{o}ssbauer radiation from the crystal set at the pure nuclear Bragg reflection. Up to now the low angle scattering geometry was used for generation of the coherent $\gamma $ radiation. The analysis performed in the present paper shows that the source of about two times larger power can be obtained when nearly backward scattering geometry is employed. This result can be efficiently applied in development of high resolution spectroscopy using synchrotron radiation.