Strength of the isoscalar pairing interaction determined by a relation between double-charge change and double-pair transfer for double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay
J. Terasaki
Abstract
A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double-charge change and the double transfer of like-particle pairs, and a constraint is derived for the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, details of this method are explained thoroughly, and applications to nuclei of several instances of the double-$\ensuremath{\beta}$ decays are shown. The systematics of the strengths determined for those nuclei is understood in terms of a midshell effect. The effect of the new interaction strength is examined in two examples of the Gamow-Teller strength function with comparisons with the experimental data. The nuclear matrix elements of the neutrinoless double-$\ensuremath{\beta}$ decay are also calculated.