Double helix level scheme of 171Yb nucleus

We revisit the principles underlying high-spin level schemes, using the case of 171 Yb as an example. We first introduce the least-squares fit of the experimental γ -ray energy bands vs spin as a family of straight lines , 2 c ( 2 I + k − 1 ) . The fit captures the average rotational phenomenology of all the bands. The constant 2 c average slope is the inverse of the effective moment of inertia ℑ e f f ( 2 ) = ħ 2 / 2 c . 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 γ -ray energies can be parametrized as 2 c b a n d ( 2 I + k + k ′ − 1 ) , where the additional integer k ′ contains the deviations of E γ values from the fit lines and c b a n d is the band inertial parameter, which determines the band moments of inertia, ℑ b a n d ( 2 ) = ħ 2 / 2 c b a n d . The new E γ = 2 c b a n d ( 2 I + k + k ′ − 1 ) parametrization leads to a natural 3 D representation of the 171 Yb rotational bands as paths on the double helix structure. These paths contain all information of both the macroscopic and microscopic motions of 171 Yb nucleus.