The effect of hyperfine displacement of the X-ray lines excited in an internal conversion, caused by non-statistical population of the components of the atomic hyperfine structure is predicted (A.A.Rodionov, A.I.Smirnov) and is first observed experimentally [48]. The theory of such effects is originated and developed (V.V.Fedorov, A.A.Rodionov, A.S.Ryl'nikov [49-53]), that has allowed to create a new method of measurements of the magnetic moments of nuclear states practically with the any lifetimes.
Using the spectrometer GSK-3 for measurements of the hyperfine shifts of the X-ray lines excited by internal conversion, a number of the magnetic moments of short-living states of nuclei, including unknown earlier, was measured [49,54].
Recently, using a prism beta-spectrometer [55], the hyperfine displacement of the electron K-conversion lines of 169Tm, equal to (0.32 ± 0.15) eV, is measured for the first time (A.A.Rodionov [56]). This activity completed by defending the Candidate thesis by A.A.Rodionov in 1996 titled "Study of hyperfine structure of atomic X-ray levels and new possibility of determining the nuclear electromagnetic moments". The solution of the problem of a further improvement of accuracy of measurement of hyperfine displacements of the conversion lines, concerned with the creation of a new beta-spectrometer, which is under construction now, would essentially expand the opportunities of the method, because the electron conversion line, contrary to the X-ray one, unequivocally selects the studied nuclear transition.