In the case of the quadrupole transitions we have for the transitions between the states of the ground state band and for the transition between the negative parity states In the last two expressions we have For the dipole transitions between the two bands our calculations yields where The results of calculations of the energy spectra of the ground state band and of the two lowest negative parity bands for the $^{220}$Th are presented in Fig.2 together with the available experimental data. The calculation is done by the exact numerical diagonalization III. RESULTS OF CALCULATIONS B ( E 2 , I g.s. → ( I − 2) $^{g.s.}$) = ( − q (2 , 0) 0 sin [ γ$_{0}$ ( I )] cos [ γ$_{0}$ ( I − 2)] + q (0 , 2) 2 √ I 2 sin [ γ$_{0}$ ( I )] sin [ γ$_{0}$ ( I − 2)] + q (0 , 2) 2 √ ( I − 2) 2 cos [ γ$_{0}$ ( I )] cos [ γ$_{0}$ ( I − 2)]) 2 (25) B ( E 2 , I n.p. → ( I − 2) $^{n.p.}$) = ( − q (2 , 0) 0 √ 6(2 I − 3) 5(2 I 1) sin [ γ$_{0}$ ( I )] cos [ γ$_{0}$ ( I − 2)] + q (0 , 2) 2 √ I − 1 2 sin [ γ$_{0}$ ( I )] sin [ γ$_{0}$ ( I − 2)] + q (0 , 2) 2 √ (2 I − 3)(2 I + 3)( I + 1) 2(2 I − 1)(2 I + 1) cos [ γ$_{0}$ ( I )] cos [ γ$_{0}$ ( I − 2)]) $^{2}$. (26) q (2 , 0) 0 = e$_{eff}$ A 2 $_{1}$Z$_{2}$ + A 2 $_{2}$Z$_{1}$ A 2 R $^{2}$, q (0 , 2) 2 = e$_{eff}$ 3 4 π Z$_{1}$R 2 $_{1}$β$_{0}$ . (27) B ( E 1 , I g.s. → ( I − 1) $^{n.p.}$) = q 2 0 2 I + 1 { √$_{2}$$_{I}$ − 1 sin [ γ$_{0}$ ( I )] cos [ γ$_{1}$ ( I − 1)] + √ 6(2 I + 1) 5 cos [ γ$_{0}$ ( L )] sin [ γ$_{1}$ ( I − 1)] } 2 , B ( E 1 , I n.p. → ( I − 1) $^{g.s.}$) = q 2 0 sin $^{2}$[ γ$_{1}$ ( I )] sin $^{2}$[ γ$_{0}$ ( I − 1)] , (28) q$_{0}$ = e$_{eff}$ A$_{1}$Z$_{2}$ − A$_{2}$Z$_{1}$ A R 10 .