The solar LMA neutrino oscillation solution in the Zee model

We examine the neutrino mass matrix in the version of Zee model where both Higgs doublets couple to the leptons. We show that in this case one can accommodate the large mixing angle (LMA) MSW solution of the solar neutrino problem, while avoiding maximal solar mixing and conflicts with constraints on lepton family number-violating interactions. In the simplified scenario we consider, we have the neutrino mass spectrum characterized by $m_1 \simeq m_2 \simeq \sqrt{\Delta m^2_\mathrm{atm}}/\sin 2\theta$ and $m_3/m_1 \simeq \cos 2\theta$, where $\theta$ is the solar mixing angle.