  Context. About 0.2-2% of giant stars are Li-rich, whose lithium abundance
(A(Li)) is higher than 1.5 dex. Among them, near 6% are super Li-rich with
A(Li) exceeding 3.2 dex. Meanwhile, the formation mechanism of these Li-rich
and super Li-rich giants is still under debate. Aims. Considering the compact
He core of red giants, attention is paid to the effect of element diffusion on
A(Li). In particular, when the He core flash occurs, the element diffusion
makes the thermohaline mixing zone extend inward and connect to the inner
convection region of stars. Then, a large amount of 7Be produced by the He
flash can be transferred to stellar surface, finally turning into 7Li. Thus,
the goal of this work is to propose the mechanism of A(Li) enrichment and
achieve the consistency between the theoretical and observation data. Methods.
Using the Modules for Experiments in Stellar Astrophysics (MESA), we simulate
the evolution of low-mass stars, with considering the effects of element
diffusion on the Li abundances. The timescale ratio of Li-rich giants to normal
giants is estimated by population synthesis method. Then we get the theoretical
value of A(Li) and make a comparison with observations. Results. Considering
the influence of element diffusion in the model results in the increase of
lithium abundance up to about 1.8dex, which can reveal Li-rich giants.
Simultaneously, introducing high constant diffusive mixing coefficients (Dmix)
with the values from 10e11 to 10e15in the model allows A(Li) to increase from
2.4 to 4.5dex, which can explain the most of Li-rich and super Li-rich giant
stars. The population synthesis method reveals that the amount of Li-rich
giants among giants is about 0.2-2%, which is consistent with observation
estimated levels.
