Collision geometry scaling of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Au</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Au</mml:mi></mml:mrow></mml:math>pseudorapidity density from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>19.6</mml:mn><mml:mspace width="0.5em"/><mml:mtext>to</mml:mtext><mml:mspace width="0.5em"/><mml:mn>200</mml:mn><mml:mspace width="0.3em"/><mml:mi>GeV</mml:mi></mml:mrow></mml:math>

The centrality dependence of the midrapidity charged particle multiplicity in $\mathrm{Au}+\mathrm{Au}$ heavy-ion collisions at $\sqrt{{s}_{NN}}=19.6$ and $200\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ is presented. Within a simple model, the fraction of hard (scaling with number of binary collisions) to soft (scaling with number of participant pairs) interactions is consistent with a value of $x=0.13\ifmmode\pm\else\textpm\fi{}0.01(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{syst})$ at both energies. The experimental results at both energies, scaled by inelastic $p(\overline{p})+p$ collision data, agree within systematic errors. The ratio of the data was found not to depend on centrality over the studied range and yields a simple linear scale factor of ${R}_{200∕19.6}=2.03\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{syst})$.