  Starting with the modified Dirac equations for free massive particles with
the $\gamma_5$-extension of the physical mass $m\rightarrow m_1 + \gamma_5
m_2$, we consider equations of relativistic quantum mechanics in the presence
of an external electromagnetic field. The new approach is developing on the
basis of existing methods for study the unbroken $\cal PT$ symmetry of
Non-Hermitian Hamiltonians. The paper shows that this modified model contains
the definition of the mass parameter, which may use as the determination of the
magnitude scaling of energy $M$. Obviously that the transition to the standard
approach is valid when small in comparison with $M$ energies and momenta.
Formally, this limit is performed when $M\rightarrow\infty$, which
simultaneously should correspond to the transition to a \emph{Hermitian
limit}$m_2\rightarrow 0$. Inequality $m \leq M$ may be considered and as the
restriction of the mass spectrum of fermions considered in the model. Within of
this approach, the effects of possible \emph{observability} mass parameters:
$m_1, m_2$, $M$ are investigated taking into account the interaction of the
magnetic field with charged fermions together with the accounting of their
anomalous magnetic moments.
