Calculation of hyperfine magnetic anomaly in many-electron atoms

The precision measurements of the ratio of hyperfine structure constants for $s_{1/2} $ and $p_{1/2} $ states allow us to estimate the difference between hyperfine magnetic anomalies for these levels. We calculate the atomic factor in order to recover the absolute values of the hyperfine magnetic anomalies from their difference. Taking into account the hyperfine anomaly correction allows one to increase the accuracy of determining the $g$ factors of short-lived isotopes by more than an order of magnitude.