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Background: Magnetic dipole (M1) excitation is the leading mode of nuclearexcitation by the magnetic field, which couples unnatural-parity states. Sincethe M1 excitation occurs mainly for open-shell nuclei, the nuclear pairingeffect is expected to play a role. As expected from the form of operator, thismode may provide the information on the spin-related properties, including thespin component of dineutron and diproton correlations. In general, the sum rulefor M1 transition strength has not been derived yet. Purpose: To investigatethe M1 excitation of the systems with two valence nucleons above theclosed-shell core, with pairing correlation included, and to establish the M1sum rule that could be used to validate theoretical and experimentalapproaches. Possibility to utilize the M1 excitation as a tool to investigatethe pairing correlation in medium is also discussed. Method: Three-body model,which consists of a rigid spherical core and two valence nucleons, is employed.Interactions for its two-body subsystems are phenomenologically determined inorder to reproduce the two-body and three-body energies. We also derive the M1sum rule within this three-body picture. Conclusion: The introduced M1 sum rulecan be utilized as a benchmark for model calculations of M1 transitions in thesystems with two valence nucleons. The total sum of the M1 transition strengthis related with the coupled spin of valence nucleons in the open shell, wherethe pairing correlation is unnegligible. The three-body-model calculations for18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairingcorrelations on the low-lying M1 transitions. Therefore, further experimentalstudies of M1 transitions in those systems are on demand, in order to validateproposed sum rule, provide a suitable probe for the nuclear pairing in medium,as well as to optimize the pairing models.

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons