Uncertainties in nuclear transition matrix elements for $β^{+}β ^{+}$ and $\varepsilon β^{+}$ modes of neutrinoless positron double-$β$ decay within PHFB model

P. K. Rath, R. Chandra, K. Chaturvedi, P. Lohani, P. K. Raina, J. G. Hirsch

Published 2012-10-19, updated 2012-12-19Version 2

Uncertainties in the nuclear transition matrix elements $M^{(0\nu)}$ and $M^{(0N)}$ of the double-positron emission $(\beta ^{+}\beta ^{+})_{0\nu}$ and electron-positron conversion $(\varepsilon \beta ^{+})_{0\nu}$ modes due to the exchange of light and heavy Majorana neutrinos, respectively, are calculated for $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes by employing the PHFB model with four different parameterization of the pairing plus multipolar two-body interactions and three different parameterizations of the Jastrow short range correlations. In all cases but for $^{130}$Ba, the uncertainties are smaller than 14% for light Majorana neutrino exchange and 35% for the exchange of a heavy Majorana neutrino.