The microscopic mechanism behind the fission-barrier asymmetry (II): The rare-earth region $50 < Z < 82$ and $82 < N < 126$

It is well known that most actinides fission into fragments of unequal size. The first attempt to understand this difference suggested that division leading to one of the fragments being near doubly magic $^{132}$Sn is favored by gain in binding energy. After the Strutinsky shell-correction method was developed an alternative idea that gained popularity was that the fission saddle might be lower for mass-asymmetric shapes and that this asymmetry was preserved until scission. Recently it was observed [Phys. Rev. Lett. {bf 105} (2010) 252502] that $^{180}$Hg preferentially fissions asymmetrically in contradiction to the fragment-magic-shell expectation which suggested symmetric division peaked around $^{90}$Zr, with its magic neutron number $N=50$, so it was presented as a new type of asymmetric fission. However, in a paper [Phys. Lett. 34B (1971) 349] a simple microscopic mechanism behind the asymmetry of the actinide fission saddle points was proposed to be related the coupling between levels of type [40$LambdaOmega$] and [51$LambdaOmega$]. The paper then generalizes this idea and made the remarkable prediction that analogous features could exist in other regions. In particular it was proposed that in the rare-earth region couplings between levels of type [30$LambdaOmega$] and [41$LambdaOmega$] would favor mass-asymmetric outer saddle shapes. In this picture the asymmetry of $^{180}$Hg is not a new type of asymmetric fission but of analogous origin as the asymmetry of actinide fission. This prediction has never been cited in the discussion of the recently observed fission asymmetries in the new region of asymmetry, in nuclear physics also referred to as the rare-earth region. We show by detailed analysis that the mechanism of the saddle asymmetry in the sub-Pb region is indeed the one predicted half a century ago.