Uncertainties in nuclear transition matrix elements for $\beta ^{+}\beta   ^{+}$ and $\varepsilon \beta ^{+}$ modes of neutrinoless positron   double-$\beta $ decay within PHFB model
  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. 
P. K. Rath, R. Chandra, K. Chaturvedi, P. Lohani, P. K. Raina and J.   G. Hirsch
nucl-th