In this paper we present a calculation of the expected flux of the mono-energetic 14.4 keV solar axions emitted by the M1 type nuclear transition of $^{57}$Fe in the Sun. These axions can be detected, e.g., by inverse coherent Bragg-Primakoff conversion in single-crystal TeO$_2$ bolometers. The ingredients of this calculation are i) the axion nucleon coupling, estimated in several popular axion models and ii)the nuclear spin matrix elements involving realistic shell model calculations with both proton and neutron excitations. For the benefit of the experiments we have also calculated the branching ratio involving axion and photon emission
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