Neutrinoless double positron decay and positron emitting electron capture in the interacting boson model

Neutrinoless double-$β$ decay is of fundamental importance for determining the neutrino mass. Although double electron ($β^-β^-$) decay is the most promising mode, in very recent years interest in double positron ($β^+β^+$) decay, positron emitting electron capture ($ECβ^+$), and double electron capture ($ECEC$) has been renewed. We present here results of a calculation of nuclear matrix elements for neutrinoless double-$β^+$ decay and positron emitting electron capture within the framework of the microscopic interacting boson model (IBM-2) for $^{58}$Ni, $^{64}$Zn, $^{78}$Kr, $^{96}$Ru, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba, and $^{136}$Ce decay. By combining these with a calculation of phase space factors we calculate expected half-lives.

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