In the last decade, the manifestation of chirality in atomic nuclei has become the subject of numerous experimental and theoretical studies. The common feature of current model calculations is that the chiral geometry of angular momentum coupling is extracted from expectation values of orientation operators, rather than being a starting point in construction of a model. However, using the particle-hole coupling model for triaxial odd-odd nuclei it is possible to construct a basis which contains right-handed, left-handed and planar states of angular momentum coupling. If this basis is used, the chirality is an explicit rather than an extracted feature as in any other models with non-chiral bases. The time-reversal symmetry, which relates the basis states of opposite handedness, can be used to reduce the dimension of matrices for diagonalization of the model Hamiltonian, proving the effectiveness of this approach. Moreover, the final model eigenstate wave functions show a concentration of amplitudes among a relatively small number (∼1%) of components compared to the full model space. In that sense, the 'chiral' basis provides a useful tool to examine model predictions providing direct insight into the structure of doublet states. In this work, similarities and differences between the rotational behaviour of an axial and triaxial body provide a starting point for derivation of the basis optimal for valence nucleon coupling to an axial and a triaxial core. The derived 'chiral' basis is optimal for coupling of a valence particle and hole to the triaxial core. Model predictions are presented and discussed. A comprehensive review of current experimental data on observed chiral band candidates is also provided.
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