Nuclear excitation by the bound muon and the muonic hyperfine structure

For the even-even transition nuclei a theory of the nuclearquadrupole excitation by the bound muon is formulated using a realistic nuclear wave function on the basis of the anharmonic oscillator model. The hyperfine spectrum of the muonic X-ray is predicted for 192Os and the dependence of the nuclear parameters on the spectrum is also discussed. Then we can suggest that it is possible to discriminate the nuclear model and to find out some nuclear properties in comparison with more precise measurement of muonic X-rays.