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Calculations aimed at reproducing the rotational level patterns in the $^{220}$Rn nucleus were carried out using a collective quadrupole-octupole approach with a microscopic mass tensor and moments of inertia dependent on the deformation and pairing degrees of freedom. The main objective, however, is to quantitatively confirm known experimental facts, according to which the Rn nucleus transitions from octupole oscillations to octupole deformation under external rotation.
The collective potential in nine-dimensional deformation space is determined using the macroscopic-microscopic method with the Strutinsky shell correction and the BCS method with an approximate particle number projection. The corresponding Hamiltonian is diagonalised based on the projected solutions of harmonic oscillators coupled with the appropriate Wigner functions. Such orthogonalised basis is, in addition, symmetrised with respect to the so-called internal symmetry group, specifically assigned to the collective space under consideration, in order to ensure the unambiguity of the Hamiltonian eigensolutions with respect to the laboratory reference frame.
The response of the deformation and pairing degrees of freedom to external rotation is discussed in a variational framework (the total energy is minimised by the pairing and deformation variables).
As the nuclear spin increases, the proton and neutron evaporation gaps decrease from their equilibrium values to zero (no superfluid solution). Consequently, the corresponding microscopic moments of inertia increase with increasing collective spin (the Coriolis anti-parity effect), resulting in effectively lower rotational energy levels $I\pi$ compared with the $I(I+1)$ pattern characteristic of a solution with a pure rigid rotor.
Compared with previous calculations, the spin-dependent moments of inertia and mass parameters were calculated taking into account the fact that proton and neutron evaporation gaps are, in fact, collective quantities.
A general comparison of the experimental and theoretical schemes for rotational energy levels and the probabilities of dipole, quadrupole and octupole transitions BE(ƛ) in $^{220}$Rn is satisfactory.