Step 1: Recall how control limits for the R-chart are derived. The range R has mean $E(R) = d_2\sigma$ and standard deviation $\text{SD}(R) = d_3 \sigma$, both $d_2$ and $d_3$ being constants tabulated against sample size $n$.
Step 2: The 3-sigma control limits for the R-chart are then built as $E(R) \pm 3\,\text{SD}(R) = d_2\sigma \pm 3 d_3 \sigma$, and these combined coefficients are themselves tabulated directly as $D_1 = d_2 - 3d_3$ and $D_2 = d_2 + 3d_3$, giving $LCL = D_1\sigma$ and $UCL = D_2\sigma$.
Step 3: This shows clearly that $D_1$ and $D_2$ are control-limit constants built from $d_2$ and $d_3$ together, they are not the constant linking $E(R)$ to $\sigma$ on their own. The constant $d_1$ is not part of standard range notation at all.
Step 4: Therefore the direct relation between the expected range and the standard deviation uses $d_2$ alone.
\[\boxed{E(R) = d_2\sigma}\]