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The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix}0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where$\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic ora general strictly regular boundary condition $(bc)$ has discrete spectrums. Itis known that, for large enough $|n|$ in the disc centered at $n$ of radius1/4, the operator has exactly two (periodic if $n$ is even or antiperiodic if$n$ is odd) eigenvalues $\lambda_n^+$ and $\lambda_n^-$ (counted according tomultiplicity) and one eigenvalue $\mu_n^{bc}$ corresponding to the boundarycondition $(bc)$. We prove that the smoothness of the potential could becharacterized by the decay rate of the sequence $|\delta_n^{bc}|+|\gamma_n|$,where $\delta_n^{bc}=\mu_n^{bc}-\lambda_n^+$ and$\gamma_n=\lambda_n^+-\lambda_n^-.$ Furthermore, it is shown that the Diracoperator with periodic or antiperiodic boundary condition has the Riesz basisproperty if and only if $\sup\limits_{\gamma_n\neq0}\frac{|\delta_n^{bc}|}{|\gamma_n|}$ is finite.

Characterization of the potential smoothness of one-dimensional Dirac operator subject to general boundary conditions and its Riesz basis property