The standard mollifier is the function $\rho \in \mathcal{D}(\mathbb{R}^n)$ defined by
\begin{align}
\rho(x) &:= \begin{cases} c \exp\!\left(\dfrac{-1}{1-|x|^2}\right) & \text{if } |x| < 1, \\[4pt] 0 & \text{if } |x| \ge 1, \end{cases}
\end{align}
where $c > 0$ normalises $\int_{\mathbb{R}^n} \rho \, d\mathcal{L}^n = 1$. For $\varepsilon > 0$, the rescaled mollifier is
\begin{align}
\rho_\varepsilon(x) &:= \varepsilon^{-n} \rho(x/\varepsilon).
\end{align}
Then $\rho_\varepsilon \in \mathcal{D}(\mathbb{R}^n)$, $\rho_\varepsilon \ge 0$, $\mathrm{supp}(\rho_\varepsilon) = \overline{B}(0,\varepsilon)$, and $\int \rho_\varepsilon \, d\mathcal{L}^n = 1$.