and $m_1$ with $m_2 > m_1$. Then the eigenvalue $m_3$ relevant for the atmospheric data is the “isolated” eigenvalue.

The current experimental picture is summarized by the recent three neutrino global analysis in [@Fogli:2005cq]. For the solar neutrino sector we take $$\begin{aligned}
%
\Delta m_{12}^{2} & = & 7.92 (1\pm 0.09) \; \times 10^{-5} {\rm
eV}^2 \label{dm12} \\
%
\sin^{2}\theta_{12} & = & 0.314(1_{-0.15}^{+0.18}) ,
\label{theta12}
%\end{aligned}$$ where all measurements are $\pm 2 \sigma$ (95% C.L.). The last measurement implies a value for the mixing angle $\theta_{12}$ itself of $\theta_{12} \simeq 0.595_{-0.052}^{+0.060}$, well below the maximal mixing value $\theta_{12}^{max}=\pi/4$. We take the upper bound on $\theta_{13}$ to be $$%
\sin^{2} \theta_{13} =0.9_{-0.9}^{+2.3} \times 10^{-2} \; \quad
\Rightarrow |\theta_{13}| < 0.18
%
\label{theta13}$$ at the 2$\sigma$ level. For the atmospheric oscillations $$\begin{aligned}
%
|\Delta m^2_{23}|& =& 2.4 (1_{-0.26}^{+0.21}) \times 10^{-3} {\rm
eV}^{2} \label{dm23} \\
%
\sin^{2}\theta_{23}& =& 0.44 (1_{-0.22}^{+0.41}),
%
\label{theta23} \end{aligned}$$ consistent with maximal mixing ($\sin^2 \theta_{23}^{\rm
max}=0.5$).

With this in mind, let us consider the general off-diagonal Majorana mass matrix $$%
m_{\nu} = \( \begin{array}{ccc} 0 & a & b \\ a & 0 & \epsilon \\ b
& \epsilon & 0
\end{array} \) = m_{\nu}^{T}
%
\label{genoff}$$ with 