The search for solar axions produced by Compton ($\ensuremath{\gamma}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+A$) and bremsstrahlunglike (${e}^{\ensuremath{-}}+Z\ensuremath{\rightarrow}Z+{e}^{\ensuremath{-}}+A$) processes has been performed. The axion flux in both cases depends on the axion-electron coupling constant. The resonant excitation of the low-lying nuclear level of $^{169}\mathrm{Tm}$ was looked for: $A+^{169}\mathrm{Tm}\ensuremath{\rightarrow}^{169}\mathrm{Tm}^{*}\ensuremath{\rightarrow}^{169}\mathrm{Tm}+\ensuremath{\gamma}$ (8.41 keV). The Si(Li) detector and $^{169}\mathrm{Tm}$ target installed inside the low-background setup were used to detect 8.41 keV $\ensuremath{\gamma}$ rays. As a result, a new model-independent restriction on the axion-electron and the axion-nucleon couplings was obtained: ${g}_{Ae}\ifmmode\times\else\texttimes\fi{}|{g}_{AN}^{0}+{g}_{AN}^{3}|\ensuremath{\le}2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$. In the model of the hadronic axion this restriction corresponds to the upper limit on the axion-electron coupling and on the axion mass ${g}_{Ae}\ifmmode\times\else\texttimes\fi{}{m}_{A}\ensuremath{\le}3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{eV}$ (90% C.L.). The limits on the axion mass are ${m}_{A}\ensuremath{\le}105\text{ }\text{ }\mathrm{eV}$ and ${m}_{A}\ensuremath{\le}1.3\text{ }\text{ }\mathrm{keV}$ for the Dine-Fischler-Srednicki-Zhitnitskii- and Kim-Shifman-Vainstein-Zakharov-axion models, correspondingly (90% C.L.).
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