  The pheomenological Generalized Coherent State Model Hamiltonian is amended
with a many body term describing a set of nucleons moving in a shell model
mean-field and interacting among themselves with paring, as well as with a
particle-core interaction involving a quadrupole-quadrupole and a
hexadecapole-hexdecapole force and a spin-spin interaction. The model
Hamiltonian is treated in a restricted space consisting of the core projected
states associated to the bands ground, $\beta, \gamma,\widetilde{\gamma}, 1^+$
and $\widetilde{1^+}$ and two proton aligned quasiparticles coupled to the
states of the ground band. The chirally transformed particle-core states are
also included. The Hamiltonian contains two terms which are not invariant to
the chiral transformations relating the right handed trihedral $({\bf J_F},
{\bf J_p}, {\bf J_n})$ and the left handed ones $(-{\bf J_F}, {\bf J_p}, {\bf
J_n})$, $({\bf J_F}, -{\bf J_p}, {\bf J_n})$,
  $({\bf J_F}, {\bf J_p}, -{\bf J_n})$ where ${\bf J_F}, {\bf J_p}, {\bf J_n}$
are the angular momenta carried by fermions, proton and neutron bosons,
respectively. The energies defined with the particle-core states form four
chiral bands, two of them being degenerate. Electromagnetic properties of the
chiral bands are investigated. Results are compared with the experimental data
on $^{138}$Nd.
