We discuss electron redistribution during the semiconductor-to-Dirac semimetal transition in Na-Sb-Bi alloys using x-ray Compton scattering experiments combined with first-principles electronic structure modeling. A robust signature of the semiconductor-to-Dirac semimetal transition is identified in the spherically averaged Compton profile. We demonstrate how the number of electrons involved in this transition can be estimated to provide a novel descriptor for quantifying the strength of spin-orbit coupling responsible for driving the transition. The associated theoretical deviation of the Born charge of Na in ${\mathrm{Na}}_3\mathrm{Bi}$ from the expected ionic charge of $+1$ is found to be consistent with the corresponding experimental value of about 10%. Our study also shows the sensitivity of the Compton scattering technique toward capturing the spillover of Bi $6\mathrm{p}$ relativistic states onto Na sites.

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• Coherent potential approximation
• Compton scattering
• Density functional theory
• Korringa-Kohn-Rostoker method