Smallness of the nuclear polarization effect in the hyperfine structure of heavy muonic atoms as a stimulus for next-generation experiments

There is renewed interest in studies of muonic atoms, which may provide detailed information on nuclear structure. A major limiting factor in the interpretation of measurements is the nuclear polarization contribution. We propose a method to determine this contribution to the hyperfine structure in muonic atoms from a combination of theory and experiment for hydrogenlike ions and muonic atoms. Applying the method to $^{203,205}$Tl and $^{209}$Bi, for which there are H-like ion and muonic atom hyperfine experimental data, we find that the nuclear polarization contribution for these systems is small, and place a limit on its size of less than $10\%$ the total hyperfine splitting. We have also performed direct calculations of the nuclear polarization contribution using a semi-analytical model, which indicate that it may be as much as two orders of magnitude smaller. Therefore, we conclude that the nuclear polarization correction to the hyperfine structure of muonic atoms does not represent a limiting factor for next-generation experiments.