A Reflection ASymmetric Relativistic Mean Field (RAS-RMF) approach is developed by expanding the equations of motion for both the nucleons and the mesons on the eigenfunctions of the two-center harmonic-oscillator potential. The efficiency and reliability of the RAS-RMF approach are demonstrated in its application to the well-known octupole deformed nucleus $^{226}$Ra and the available data, including the binding energy and the deformation parameters, are well reproduced.
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