A new method ''two-vacua random-phase approximation'' (TVRPA) for the
description of the two-neutrino nuclear double-beta decay is developed
. The nuclear wave functions of the intermediate odd-odd nucleus are c
onstructed as linear combinations of proton-particle neutronhole excit
ations from the ground state of the initial even-even (N, Z) nucleus a
nd, at the same time, as neutron-particle proton-hole excitations from
the ground state of the final (N - 2, Z + 2) nucleus. The Ritz variat
ional principle is used to obtain RPA-like equations. The ground state
in the initial and final nucleus is approximated with HFB wave functi
ons including proton-neutron pairing. A projection on numbers of proto
ns and neutrons is performed additionally on the wave functions in bot
h nuclei to restore the exact number of particles, broken by the quasi
-particle transformation. The method is applied, as a preliminary test
, to the 2nu double-beta decay in 48(20)Ca28. More realistic B(GT-) an
d B(GT+) Gamow-Teller strength distributions than QRPA and PQRPA are o
btained. No dependence is found on the particle-particle strength para
meter g(pp), renormalizing Brueckner reaction matrix elements of the B
onn potential.