two transitions in $^{224}$Ra and $^{226}$Ra, one in $^{224}$Th), but we hope our work can stimulate interest for new experimental investigations. The reduced matrix element of the quadrupole transition operator ${\cal M}$(E2) between the states $|s,K=0,J \big>$ and $|s^\prime,K=0,J^\prime \big>$ can be evaluated as $$\big( s J |\!|{\cal M}{\rm(E2)} |\!|s^\prime  J^\prime \big) = C_2
\big< s J | \beta_2 | s^\prime J^\prime \big> \ (J |\!| Y_2 |\!| 
J^\prime \big)\ ,
\label{E:14b}$$ with $\big< s, J | \beta_2  |s^\prime ,  J^\prime \big> =
\int \Psi_{ s J} \beta_2 \Psi_{s^\prime ,
J^\prime}\ {\rm d}\tau$ and $C_2$ constant. The volume element ${\rm d}\tau$, in our non-cartesian coordinates, is the product of the differentials of the coordinate variables [*multiplied by*]{} $g=G^{1/2}$, with $G$ the determinant of the matrix of inertia $\cal G$. In our assumptions, the integrals over all variables apart from $\beta_2$ ad $\beta_3$ are independent from one another and from the integral over ${\rm d}\beta_2{\rm d} \beta_3$, and their result is $1$ (if the corresponding wavefunctions are properly normalized). As the electric dipole and quadrupole operators do not contain derivatives, we can exploit the substitution defined in Eq. \[E:5.2\] to express the remaining integral as $$\int\!\Psi_{ s J} \beta_2 \Psi_{s^\prime    
J^\prime}\ 