Shift between emission and absorption lines at natural strong narrowing of Mössbauer lines. Way to the exclusion of systematic errors in experiments with natural strong narrowing

The natural strong narrowing of Mössbauer lines on long-lived isomers, which was correctly detected in [Yu. D. Bayukov, A. V. Davydov, Yu. N. Isaev, G. R. Kartashov, M. M. Korotkov, and V. V. Migachev, JETP Lett. $\mathbf{90}$, 499 (2009)] and consistently explained in [S. V. Karyagin, JETP Lett. $\mathbf{98}$, 174 (2013)] is additionally studied. It is shown that the chemical shift $\delta$ between $\gamma$ emission and absorption lines appears in experiments with natural strong narrowing in the homogeneous medium of a $\gamma$ source. This shift was previously thought to be impossible. The theory of the $\gamma$-resonance gravitational spectrum is developed with allowance for the shift $\delta$. The shift $\delta$ and new linewidth $k$ including this shift are determined; this new linewidth is noticeably smaller than that without the shift $\delta$. It is shown that the lifetimes of isomers in experiments with natural strong narrowing are strongly limited from above by the suppression of the $\gamma$ resonance by the shift $\delta$. The smallness of $\delta$ confirms the recently revealed effect of strong natural suppression of monopole broadening [S. V. Karyagin, JETP Lett. $\mathbf{103}$, 213 (2016)]. It is shown that the electron density on the Ag nucleus inside grains is lower than that at their periphery by $\sim10^{-14}\,\%$. To detect thinner effects, experiments of a new type are proposed to exclude systematic errors.