We have extended the formalism for the two-neutrino double beta decay by including the weak-magnetism term, as well as other second-forbidden corrections. The weak magnetism diminishes the calculated half-lives in $\sim 10%$, independently of the nuclear structure. Numerical computations were performed within the pn-QRPA, for $^{ 76}Ge$, $^{ 82}Se$, $^{ 100} Mo$, $^{ 128}Te$ and $^{ 130}Te$ nuclei. No one of the second-forbidden corrections modifies significantly the spectrum shapes. The total reduction in the calculated half lives varies from 6% up to 32%, and strongly depend on the nuclear interaction in the particle-particle $S=1,T=0$ channel. We conclude that the higher order effects in the weak Hamiltonian would hardly be observed in the two-neutrino double beta experiments.
Categories: nucl-th hep-ph