Excitation of deformation vibrations by radiationless muonic transitions

An investigation is carried out for selected doubly even nuclei in the rare-earth and actinide regions for possible resonances between pairs of muonic levels of the appropriate quantum numbers and certain nuclear collective states. Such resonances can lead to the excitation of the particular nuclear state involved, and could be used as an alternate means of nuclear excitation. Electric monopole excitations were found which can result in the excitation of the nuclear 0⁺ level of the β-band. The muonic states involved, however, are such that the probability of nuclear excitation may be small. An electric quadrupole resonance in ¹⁸²W involving the excitation of the 2⁺ state of the β-band is found to be a very likely candidate. Dipole and octupole resonances were also investigated; however no possible resonances were found. Also unsuccessful was the search for quadrupole excitations of the 2⁺ state in the γ-band. The matrix elements involved in the EO and E2 resonances are calculated, the nuclear contribution being computed using the nuclear collective model of Davydov and Chaban. The probability for nuclear excitation in the E2 resonance in ¹⁸²W is computed.