  After briefly reviewing $\beta \beta$ decay as a test of the neutrino mass, I
examine the nuclear structure involved in this process. Simple formulas (\`{a}
la Pad\'{e}) are designed for the transition amplitudes and the general
behavior of $\beta \beta$ decay amplitudes in the quasiparticle random phase
approximation are discussed. Results of a calculation for $^{48}Ca$, $^{76}Ge
$, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei are presented, in
which the particle-particle interaction strengths have been fixed by invoking
the partial restoration of the isospin and Wigner SU(4) symmetries. An upper
limit of $ <m_{\nu}>\approx 1$ eV is obtained for the effective neutrino mass.
