  Let $\Omega_+\subset\mathbb{R}^{3}$ be a fixed bounded domain with boundary
$\Sigma = \partial\Omega_{+}$. We consider $\mathcal{U}^\varepsilon$ a tubular
neighborhood of the surface $\Sigma$ with a thickness parameter
$\varepsilon>0$, and we define the perturbed Dirac operator
$\mathfrak{D}^{\varepsilon}_{M}=D_m +M\beta
\mathbb{1}_{\mathcal{U}^{\varepsilon}},$ with $D_m$ the free Dirac operator,
$M>0$, and $\mathbb{1}_{\mathcal{U }^{\varepsilon}}$ the characteristic
function of $\mathcal{U}^{\varepsilon}$. Then, in the norm resolvent sense, the
Dirac operator $\mathfrak{D}^{\varepsilon}_M$ converges to the Dirac operator
coupled with Lorentz scalar $\delta$-shell interactions as $\varepsilon =
M^{-1}$ tends to $0$, with a convergence rate of $\mathcal{O}(M^{-1})$.
