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Neutron-activated sources of $^{103}$Ru and $^{103}$Pd both share theisomeric first-excited state in $^{103}$Rh as a daughter product. Fromindependent measurements of both decays, we have measured the $K$-shell andtotal internal conversion coefficients, $\alpha_K$ and $\alpha_T$, for the39.8-keV $E$3 transition, which de-excites that state in $^{103}$Rh, to be141.1(23) and 1428(13), respectively. When compared with Dirac-Fockcalculations, our new results disagree with the version of the theory thatignores the $K$-shell atomic vacancy, which is consistent with our conclusiondrawn from a series of measurements on high multipolarity transitions in nucleiwith higher $Z$. Calculations that include the atomic vacancy indicate that thetransition actually has a small $M$4 component with mixing ratio $\delta$ =0.023(5).

Precise measurement of $\alpha_K$ and $\alpha_T$ for the 39.8-keV $E$3 transition in $^{103}$Rh: Test of internal-conversion theory