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A particle-core Hamiltonian is used to describe the lowest parity partnerbands $K^{\pi}=1/2^{\pm}$ in  $^{219}$Ra, $^{237}$U and $^{239}$Pu, and three parity partner bands,$K^{\pi}=1/2^{\pm}, 3/2^{\pm}, 5/2^{\pm}$, in $^{227}$Ra. The core is describedby a quadrupole and octupole boson Hamiltonian which was previously used forthe description of four positive and four negative parity bands in theneighboring even-even isotopes. The particle-core Hamiltonian consists of fourterms: a quadrupole-quadrupole, an octupole-octupole, a spin-spin and arotational $\hat{I}^2$ interaction, with $\hat {I}$ denoting the total angularmomentum. The single particle space for the odd nucleon consists of threespherical shell model states, two of positive and one of negative parity. Theproduct of these states with a collective deformed ground state and theintrinsic gamma band state generate, through angular momentum projection, thebands with $K^{\pi}=1/2^{\pm},3/2^{\pm},5/2^{\pm}$, respectively. In the spaceof projected states one calculates the energies of the considered bands. Theresulting excitation energies are compared with the corresponding experimentaldata as well as with those obtained with other approaches. Also, we searchedfor some signatures for a static octupole deformation in the considered oddisotopes. The calculated branching ratios in $^{219}$Ra agree quite well withthe corresponding experimental data.

The CSM extension for description of the positive and negative parity bands in even-odd nuclei