total densities {#sec:IIIB}
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![(Color online) (a) Single-particle density for the neutron $2d_{5/2}$ state. The solution of the Dirac equation  is shown with the black solid line, while the result by Eq.  is shown with the olive dashed line. The results by Eq.  with the corrections up to the $1/{M^\ast}^2$ and $1/{M^\ast}^3$ orders are shown with the blue dotted and red dash-dotted lines, respectively. (b) Details around the node of wave function in a smaller scale.[]{data-label="fig2"}](Fig2.eps){width="45.00000%"}

For the discussion on the single-particle density, let us first take the neutron $2d_{5/2}$ state as an example, which has one-node structure and is neither deeply nor weakly bound. The exact single-particle density for the $2d_{5/2}$ state is shown with the black solid line in Fig. \[fig2\]. For comparison, the single-particle density calculated by Eq.  without any relativistic correction (i.e., picture-change-error correction) is shown with the olive dashed line. In contrast, the results calculated by Eq.  with the relativistic corrections up to the $1/{M^\ast}^2$ and $1/{M^\ast}^3$ orders are shown with the blue dotted and red dash-dotted lines, respectively.

For the result without correction, on the one hand, a deviation from the exact density is visible around the first peak of the wave function. On 