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

TL;DR

This paper models the rotational behavior of $^{220}$Rn and $^{226}$Ra nuclei using a collective quadrupole+octupole approach, confirming experimental observations of shape evolution with rotation and providing detailed energy level and transition probability calculations.

Contribution

It introduces a comprehensive microscopic model incorporating deformation, pairing, and collective motion, with a symmetrized basis ensuring unique solutions for these nuclei.

Findings

The Rn nucleus transitions from octupole vibrational to deformed with increasing rotation.

The Ra nucleus remains octupole deformed from the start, showing weak rotational effects.

Theoretical energy levels and transition probabilities agree well with experimental data.

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$^{\pi}$ 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$\lambda$) in $^{220}$Rn and $^{226}$Ra is satisfactory.