Abstract
We study the influence of the isovector-scalar meson on the spinodal instabilities and the distillation effect in asymmetric nonhomogenous nuclear matter under strong magnetic fields of the order of ${10}^{18}\text{\ensuremath{-}}{10}^{19}$ G. Relativistic nuclear models both with constant couplings (NLW) and with density-dependent parameters (DDRH) are considered. A strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. It is shown that for neutron-rich matter the inclusion of the \ensuremath{\delta} meson increases the size of the instability region for NLW models and decreases it for the DDRH models. The effect of the \ensuremath{\delta} meson on the transition density to homogeneous $\ensuremath{\beta}$-equilibrium matter is discussed. The DDRH\ensuremath{\delta} model predicts the smallest transition pressures, about half the values obtained for NL\ensuremath{\delta}.
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