  The instability, so-called the quantum-phase-like transition, in the Dicke
model with a rotating-wave approximation for finite $N$ atoms is investigated
in terms of the Berry phase and the fidelity. It can be marked by the
discontinuous behavior of these quantities as a function of the atom-field
coupling parameter. Involving an additional field $A^{2}$ term, it is observed
that the instability is not eliminated beyond the characteristic atom-field
coupling parameter even for strong interaction of the bosonic fields,
contrarily to the previous studies.
