novel reconstituted FW transformation will be introduced in Sec. \[sec:IIA\]. In Sec. \[sec:IIB\], the single-particle density will be investigated, and as a step further, the relativistic corrections will be also considered. The single-particle scalar density obtained by the reconstituted FW transformation and the corresponding corrections will then be discussed in Sec. \[sec:IIC\]. The results for the single-particle energies and single-particle densities will be presented in Sec. \[sec:IIIA\] and Sec. \[sec:IIIB\], respectively. The single-particle scalar densities with the reconstituted FW transformation will be investigated in Sec. \[sec:IIIC\]. Finally, a summary and perspectives will be given in Sec. \[sec:IV\].

Theoretical Framework {#sec:II}
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Reconstituted FW transformation {#sec:IIA}
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In the relativistic scheme, the Dirac Hamiltonian with the scalar $S$ and vector $V$ potentials for nucleons reads [@Long2004Phys.Rev.C69.034319; @Meng2006Prog.Part.Nucl.Phys.57.470--563; @Zhao2010Phys.Rev.C82.054319; @Liang2015Phys.Rep.570.1--84] $$\label{Hamiltonian}
H=\boldsymbol{\alpha} \cdot \mathbf{p}+\beta(M+S)+V,$$ where $\alpha$ and $\beta$ are the Dirac matrices, and $M$ is the mass of nucleon.

Inspired by the reconstituted SRG method [@Guo2019Phys.Rev.C99.054324], here we develop the reconstituted FW transformation. Replacing the bare mass $M$ with the Dirac mass $M^\ast = M + S$ and considering the Hermitian property of the Hamiltonian, the corresponding operators are defined as $$\begin{aligned}
\tilde{O}=\boldsymbol{\alpha} \cdot \mathbf{p},\quad \tilde{\varepsilon}=V,\quad \tilde{\Lambda}=-\frac{i\beta}{4}(\frac{1}{M^\ast}\tilde{O}+\tilde{O}\frac{1}{M^\ast}),\end{aligned}$$ where the operators $\tilde{O}$ and 