  The theoretical approach to consideration of the Hamiltonian with pairing
forces using a technique of the finite boson representation is developed. It is
shown that a simultaneous description of the pairing vibrational state in
$^{56}$Ni and the pairing rotational states with $T$=0 in the neighboring $N=Z$
nuclei is possible if the pairing Hamiltonian takes into account only isovector
monopole pairing. However, the calculated energies of the pairing rotational
states of $N=Z$ nuclei removed from $^{56}$Ni by 12 and more nucleons exceed
significantly the experimental values. The possible reason of this discrepancy
is discussed.
