Double helix level scheme of 171Yb nucleus

Abstract

We revisit the principles underlying high-spin level schemes, using the case of ¹⁷¹Yb as an example. We first introduce the least-squares fit of the experimental $\gamma$-ray energy bands vs spin as a family of straight lines, $2c(2I+k-1)$. The fit captures the average rotational phenomenology of all the bands. The constant $2c$ average slope is the inverse of the effective moment of inertia ${\Im }_{eff}^{\left(2\right)}={ħ}^2/2c$. The inclusion of the additional integer parameter $k$ transforms the Bohr–Mottelson ideal rotor into a double helix structure that can accommodate all combinations of spin, parity, and signature quantum numbers for the rotational levels. Finally, the experimental $\gamma$-ray energies can be parametrized as $2c_{band}(2I+k+k^{\prime }-1)$, where the additional integer $k^{\prime }$ contains the deviations of $E_{\gamma }$ values from the fit lines and $c_{band}$ is the band inertial parameter, which determines the band moments of inertia, ${\Im }_{band}^{\left(2\right)}={ħ}^2/2c_{band}$. The new $E_{\gamma }=2c_{band}(2I+k+k^{\prime }-1)$ parametrization leads to a natural $3D$ representation of the ¹⁷¹Yb rotational bands as paths on the double helix structure. These paths contain all information of both the macroscopic and microscopic motions of ¹⁷¹Yb nucleus.