we show how a modification of the heavy Majorana mass matrix can lead to a large mixing angle MSW solution with a LOW mass splitting. In Appendix D we present a different choice of $U(1)_X$ charges and operators which can lead to the SMA MSW solution.

The superpotential of the MSSM with right-handed neutrinos is given by : $$\begin{aligned}
{\cal W} &=& {\cal W}_{MSSM}+{\cal W}_{\nu^c} \label{SRNDSuperPot} \\
{\cal W}_{MSSM} &=&
  q_A (\lambda_u)_{AB} u^c_B h_u 
- q_A (\lambda_d)_{AB} d^c_B h_d 
- l_A (\lambda_e)_{AB} e^c_B h_d 
+ \mu h_u h_d \\
{\cal W}_{\nu^c} &=&
  l_A (\lambda_\nu)_{AB} \nu^c_B h_u
+ {\textstyle {1 \over 2}} \nu^c_A (M_{RR})_{AB} \nu^c_B \end{aligned}$$ where $A,B=1,..,3$ are family indices, $u^c$, $d^c$, $e^c$ and $\nu^c$ are the right-handed $SU(2)_L$ singlet superfields, $q=(u,d)$ and $l=(\nu,e)$ are the $SU(2)_L$ quark and lepton doublets, and $h_u$ ($h_d$) is the up (down) Higgs boson doublet. The Dirac neutrino coupling and the heavy Majorana mass for the right-handed neutrinos are denoted by $\lambda_\nu$ and $M_{RR}$ respectively. When the neutral components of the two MSSM Higgs bosons $h^0_{u,d}$ acquire their vacuum expectation values (VEV)s $v_{2,1}$ ($\tan\beta=v_2/v_1 \sim 40-50$) the superpotential in Eq.  generates the following sum of mass terms : $$\begin{aligned}
{\cal L}_{U,D,E} &=&-U (\lambda_u v_2) 