The relativistic nuclear mean-field model with derivative scalar coupl
ing suggested by Zimanyi and Moszkowski is extended to asymmetric nucl
ear matter by including the rho meson degree of freedom in the Lagrang
ian. The extended model is then used to study the Coulomb instability
of asymmetric nuclear matter at finite temperature. The critical tempe
rature for the liquid-gas phase transition in nuclear matter and its d
ependence on the asymmetry parameter are calculated. The limiting temp
erature T(lim), which reflects Coulomb instability of hot nuclei is st
udied. The calculated results are compared with those given by quantum
hadrodynamics (QHD) models.