{\rm d}\tau
= \int_0^{\beta_2^w}\!{\rm d}\beta_2    
\!\int_{-\beta_3^w}^{\beta_3^w}\!{\rm d}\beta_3
\Phi_{sJ}\beta_2\Phi_{s^\prime J^\prime}\phantom{.}$$ This integral has been evaluated numerically, for values of $J \leq 18$, with $J^\prime = J-2$ (and also with $J^\prime = J-1$). The reduced matrix element over the angular coordinates has the form $$\begin{aligned}
&&\hspace*{-6mm}\big( J ||Y_L || J^\prime \big) = \\
&&\hspace*{-6mm}\phantom{m}(-1)^J (4\pi )^{-1/2} 
\sqrt{(2J\!+\!1) (2L\!+\!1) (2J^\prime\!+\!1)}
\left( \!\begin{array}{lcr} J&L&J^\prime \\ 0&0&0 \end{array}\!\right)
\nonumber\end{aligned}$$ Finally, the reduced transition probabilities from $J$ to $J^\prime$ are obtained as\
$B({\rm E2},s J\rightarrow s^\prime J^\prime)=(2J+1)^{-1}  
\big( s J ||{\cal M}{\rm(E2)} | |s^\prime  J^\prime \big) ^2$.\
The absolute values of the ratios of E2 reduced matrix elements, $R_J(E2)=(J|\!|\mathcal{M}(E2)|\!|J-2) /
(2^+|\!|\mathcal{M}(E2)|\!|0^+)$, for transitions within the positive– and the negative–parity part of the ground–state band, are depicted, as a function of $b=\beta_3^w/\beta_2^w$, in the fig. \[F:7\]$(a)$. Their limit at $\beta_3^w/\beta_2^w\rightarrow 0$ corresponds, as expected, to the X(5) value.

In addition to the in–band E2 transition, we have to consider the E1 transitions between levels of opposite parity. How to treat E1 transitions in the frame of the geometrical model is a big problem, as all E1 transition moments should vanish for a homogeneous fluid of constant charge density. In this sense, E1 transitions are outside the Bohr 