  The overlap of the excited states in quasiparticle random-phase approximation
(QRPA) is calculated in order to simulate the overlap of the intermediate
nuclear states of the double-beta decay. Our basic idea is to use the
like-particle QRPA with the aid of the closure approximation and calculate the
overlap as rigorously as possible by making use of the explicit equation of the
QRPA ground state. The formulation is shown in detail, and the mathematical
properties of the overlap matrix are investigated. Two test calculations are
performed for relatively light nuclei with the Skyrme and volume delta-pairing
energy functionals. The validity of the truncations used in the calculation is
examined and confirmed.
