Spectroscopic study of CEMP-(s \& r/s) stars. Revisiting classification criteria and formation scenarios, highlighting i-process nucleosynthesis

We have derived the stellar atmospheric parameters, the effective temperature T$_{eff}$, the microturbulent velocity $\zeta$, the surface gravity log g, and the metallicity [Fe/H] for HE 0017+0055, HE 2144-1832, HE 2339-0837, HD 145777, and CD-27 14351 from local thermodynamic equilibrium analyses using model atmospheres. Elemental abundances of C, N, $\alpha$-elements, iron-peak elements, and several neutron-capture elements are estimated using the equivalent width measurement technique as well as spectrum synthesis calculations in some cases. In the context of the double enhancement observed in four of the programme stars, we have critically examined whether the literature i-process model yields ([X/Fe]) of heavy elements can explain the observed abundance distribution. The estimated metallicity [Fe/H] of the programme stars ranges from -1.63 to -2.74. All five stars show enhanced abundance for Ba, and four of them exhibit enhanced abundance for Eu. Based on our analysis, HE 0017+0055, HE 2144-1832, and HE 2339-0837 are found to be CEMP-r/s stars, whereas HD 145777 and CD-27 14351 show characteristic properties of CEMP-s stars. From a detailed analysis of different classifiers of CEMP stars, using a large sample of similar stars from the literature, we have identified the one which best describes the CEMP-s and CEMP-r/s stars. We have also examined if [hs/ls] alone can be used as a classifier, and if there are any limiting values for [hs/ls] ratio that can be used to distinguish CEMP-s and CEMP-r/s stars. In spite of peaking at different values of [hs/ls], CEMP-s and CEMP-r/s stars show an overlap in the range 0.0 < [hs/ls] < 1.5 and hence this ratio alone can not be used to distinguish CEMP-s and CEMP-r/s stars.