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Numerical experiments have been performed to investigate the thermal behaviorof a cooled down white dwarf of initial mass $M_{\rm WD} = 0.516 M_{\sun}$which accretes hydrogen-rich matter with Z = 0.02 at the rate $\dot{M}=10^{-8}$\msun \yrm1, typical for a recurrent hydrogen shell flash regime. The evolutionof the main physical quantities of a model during a pulse cycle is examined indetail. From selected models in the mass range $M_{\rm WD} = 0.52\div 0.68$\msunend, we derive the borders in the $M_{\rm WD}$ - $\dot{M}$ plane of thesteady state accretion regime when hydrogen is burned at a constant rate asrapidly as it is accreted. The physical properties during a hydrogen shellflash in white dwarfs accreting hydrogen-rich matter with metallicities Z =0.001 and Z = 0.0001 are also studied. For a fixed accretion rate, a decreasein the metallicity of the accreted matter leads to an increase in the thicknessof the hydrogen-rich layer at outburst and a decrease in the hydrogen-burningshell efficiency. In the $M_{\rm WD}$-$\dot{M}$ plane, the borders of thesteady state accretion band are critically dependent on the metallicity of theaccreted matter: on decreasing the metallicity, the band is shifted to loweraccretion rates and its width in $\dot{M}$ is reduced.Comment: 31 pages and 10 Postscript figures; Accepted for publication on Ap

Hydrogen‐Accreting Carbon‐Oxygen White Dwarfs of Low Mass: Thermal and Chemical Behavior of Burning Shells