We present extensive sets of stellar models for 0.8 - 9.0 M _ { \odot } in mass and -5 \leq \textrm { [ Fe / H ] } \leq - 2 and Z = 0 in metallicity .
The present work focuses on the evolutionary characteristics of hydrogen mixing into the helium-flash convective zones during the core and shell helium flashes which occurs for the models with \textrm { [ Fe / H ] } \la - 2.5 .
Evolution is followed from the zero age main sequence to the thermally pulsating AGB phase including the hydrogen engulfment by the helium-flash convection during the RGB or AGB phase .
There exist various types of mixing episodes of how the hydrogen mixing sets in and how it affects the final abundances at the surface .
In particular , we find hydrogen ingestion events without dredge-ups that enables repeated neutron-capture nucleosynthesis in the helium flash convective zones with ^ { 13 } { C } ( \alpha,n ) { } ^ { 16 } { O } as neutron source .
For Z = 0 , the mixing and dredge-up processes vary with the initial mass , which results in different final abundances in the surface .
We investigate the occurrence of these events for various initial mass and metallicity to find the metallicity dependence for the helium-flash driven deep mixing ( He-FDDM ) and also for the third dredge-up events .
In our models , we find He-FDDM for M \leq 3 M _ { \odot } for Z = 0 and for M \la 2 M _ { \odot } for -5 \leq \textrm { [ Fe / H ] } \leq - 3 .
On the other hand , the occurrence of the third dredge-up is limited to the mass range of \sim 1.5 M _ { \odot } to \sim 5 M _ { \odot } for \textrm { [ Fe / H ] } = -3 , which narrows with decreasing metallicity .
The paper also discusses the implications of the results of model computations for observations .
We compared the abundance pattern of CNO abundances with observed metal-poor stars .
The origins of most iron-deficient stars are discussed by assuming that these stars are affected by binary mass transfer .
We also point out the existence of a blue horizontal branch for -4 \la \textrm { [ Fe / H ] } \la - 2.5 .