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A new method has been proposed to determine the strength of the isoscalarproton-neutron pairing interaction applicable to many nuclei. The principle isthe equivalence between the double charge change and the double transfer oflike-particle pair, and a constraint is derived to the effective interactionsused in approximations. This method was applied to the quasiparticlerandom-phase approximation for determining that interaction strength. In thispaper, detail of this method is explained thoroughly, and applications are madeto nuclei of several instances of the double-$\beta$ decays. The systematics ofthe strengths determined for those nuclei is understood in terms of a midshelleffect. The effect of the new interaction strength is examined in two examplesof the Gamow-Teller strength function with comparisons with the experimentaldata. The nuclear matrix elements of the neutrinoless double-$\beta$ decay arealso calculated.

Physical features of strength of isoscalar pairing interaction determined by relation between double charge change and double pair transfer