theoretical estimate (see Table \[T:e1\]). These results is encouraging, but would obviously need to be validate by a more extensive check, involving higher–lying levels, which, at the moment, is not possible.

A comparison of the two E1 transition from the lowest level $1^-$ to the $0^+$ and to the $2^+$ states is possible for the three isotopes, as well as for the E1 branches from the $3^-$ in $^{226}$Ra. All these amplitude ratios for transitions within the ground–state band, shown in the upper part of Table \[T:e1\], are in very good agreement with the calculated values. However, they are not significantly different from those expected for a rigid asymmetric rotor (as shown in the last column of Table \[T:e1\]) and also from those reported by Lenis and Bonatsos [@lenis06] on the basis of a rather different model.

![\[F:e1e2\] (Color online) Ratios of the absolute value of the transition matrix elements (normalized to the Weisskopf Unit) for E1 and E2 transitions in the g.s bands of $^{224,226}$Ra and $^{224}$Th, from $J_i$ to $J_i\!-\!1$ and $J_i\!-\!2$, respectively: $R_J(E1/E2)=$ $(J_i|\!|[\mathcal{M}(E1)|\!|J_i\!-\!1)/\mathcal{M}_W(E1)]
/[(J_i|\!|\mathcal{M}(E2)|\!|J_i\!-\!2)/\mathcal{M}_W(E2)]$. The dotted lines join the calculated values of the ratio (normalized to obtain the best fit with the ensemble of experimental values). 