Abstract
The nuclear matrix element for the double $\ensuremath{\beta}$ decay ${\mathrm{Te}}^{130}$\ensuremath{\rightarrow}${\mathrm{Xe}}^{130}$ 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 $\ensuremath{\beta}$-decay calculation. It is shown that the $\ensuremath{\beta}$-decay operator has no spurious terms due to number or isospin dispersion.
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