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.
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