  The consistency condition is tested within the particle-particle random-phase
approximation (RPA), renormalized RPA (RRPA) and the self-consistent RPA
(SCRPA) making use of the Richardson model of pairing. The two-particle
separation energy is calculated in two ways, namely as the energy of the first
addition mode, which adds two particles to a core with N particles, and as the
energy of the first removal mode, which removes two particles from the (N+2) -
particle system to get back to the same N-particle core. The corresponding
transitions generated by the pairing operators are also calculated. It is found
that the results obtained in these two ways of calculations are close to each
other only at large values of particle number N and/or small interaction
strength. At N below 10 for a given value of the interaction strength, the
discrepancy between the results obtained in two ways of calculations within the
SCRPA is much smaller than those given by the RPA and RRPA.
