where we express the operator of quadrupole deformation through the creation and anihilla- tion operators of bosons with β$_{0}$ = √ ℏ / 2 Bω$_{0}$ . In this work we does not consider the transfer of nucleons in the DNS explicitely. Instead, we assume that the system stays in its lowest state in mass-asymmetry coordinate. The reason for such an assumption is that the energy of α -particle DNS is around 1 MeV higher than the binding energy of $^{220}$Th. The first excited state in mass-asymmetry will appear high enough to neglect its influence on the low-energy part of the spectra. Instead of considering the mass-asymmetry motion we take the effective value of mass-asymmetry η$_{0}$ in our calculations. This value, which must be at least in the interval η$_{α}$ < η$_{0}$ < 1, where η$_{α}$ = ( A − 4) /A is the mass-asymmetry for DNS with alpha-particle, is fixed by the description of the lowest 1 − state. If we neglect the interaction term ˆ V$_{int}$ in (1) the eigenfunctions of the Hamiltonian can be constructed as where | nτn$_{Δ}$I$_{1}$ ) represents the n-boson wave function of the heavy nucleus, with the seniority τ and angular momentum I$_{1}$ . Since the quadrupole oscillations have positive parity, the parity of the states (6) is determined by the angular momentum of the relative rotation of the fragments p = ( − 1) I 2 . The energies of states (6) are given in this approximation by the expresssion The set of wave functions (6) can be used as a basis to construct the eigenfunction of the Hamiltonian ˆ H in the form where coefficients a ( I,p ) n$_{I}$$_{1}$τ$_{I}$$_{1}$I 1 I 2 should be obtained by a diagonalization of ˆ H . The matrix Ψ$_{IM,p}$ = ∑ I 1 I 2 ∑ n$_{I}$$_{1}$τ$_{I}$$_{1}$ a ( I,p ) n$_{I}$$_{1}$τ$_{I}$$_{1}$ I 1 I 2 [ | n$_{I}$$_{1}$τ$_{I}$$_{1}$I$_{1}$ ) × Y$_{I}$$_{2}$ ]$_{(}$$_{IM}$$_{)}$ , (8) 6 E$_{nI}$$_{1}$$_{I}$$_{2}$$_{I}$ = [ ℏ ω$_{0}$n + ℏ 2 2 µR $_{2}$I$_{2}$ ( I$_{2}$ + 1) ] . (7) Ψ IM ( nτn Δ I 1 ) I 2 = [ | nτn$_{Δ}$I$_{1}$ ) × Y$_{I}$$_{2}$ ]$_{(}$$_{IM}$$_{)}$ , (6) ˆ β$_{2}$$_{µ}$ = β$_{0}$ ( d + 2 µ + ˜ d$_{2}$$_{µ}$ ) , (5)