We find that the shell model and Nilsson-pairing model predictions for the matrix elements mediating the $2\nu$ $\beta \beta$ decay of ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ are in quantitative agreement when the comparison is made for equivalent model spaces. This suggests that further expansion of shell model bases may exacerbate the existing discrepancies between theory and various geochemical rates.

RADIOACTIVITY Double beta decay; ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$, lepton number conservation; comparison of shell and Nilsson-pairing models.

• Received 22 February 1983

DOI:https://doi.org/10.1103/PhysRevC.28.458