Collectivity of rotational motion in $^{220}$Rn and $^{226}$Ra

Abstract

Calculations to reconstruct rotational level patterns in the $^{220}$Rn and $^{226}$Ra nuclei have been performed using a collective quadrupole+octupole approach with microscopic mass tensor and moments of inertia dependent on deformation and pairing degrees of freedom. The main objective is to quantitatively confirm the known experimental observations that the Rn nucleus passes from octupole vibrational to octupole deformed with increasing rotation frequency, while the Ra nucleus is relatively weakly affected by collective rotation, being octupole deformed from the beginning. The collective potential in a nine-dimensional collective space is determined using the macroscopic-microscopic method with Strutinsky and the BCS with an approximate particle number projection microscopic corrections. The corresponding Hamiltonian is diagonalized based on the projected solutions of the harmonic oscillators coupled with Wigner functions. Such an orthogonalized basis is additionally symmetrized with respect to the so-called intrinsic symmetrization group, specifically dedicated to the collective space used, to ensure the uniqueness of the Hamiltonian eigen-solutions in the laboratory frame. The response of the pairing and deformation degrees of freedom to external rotation is discussed in the variational approach, where the total energy is minimized by the deformation and pairing variables. Consequently, the corresponding microscopic moments of inertia increase with collective spin (Coriolis {\it antiparing} effect), resulting in effectively lower rotational energy levels I$^π$ with respect to pure classical-rotor pattern I(I+1). The obtained comparison of experimental and theoretical rotational energy level schemes, dipole, quadrupole and octupole transition probabilities of B(E$λ$) in $^{220}$Rn and $^{226}$Ra is satisfactory.