Nuclear Matrix Elements in the Double Beta DecayTe130→Xe130

The nuclear matrix element for the double $\beta$ decay ${\mathrm{Te}}^{130}$→${\mathrm{Xe}}^{130}$ is calculated with a specific Gamow-Teller force. A reasonable strength of this force is unable to give enough reduction in the rate to agree with the experimental half-life. The amount of isospin violation in the wave function owing to the difference of the neutron and proton single-particle energies is calculated. The number and isospin problems are discussed in connection with the use of the random-phase approximation in a $\beta$-decay calculation. It is shown that the $\beta$-decay operator has no spurious terms due to number or isospin dispersion.