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Optical precision spectroscopy of isotope shifts can be used to test for newforces beyond the Standard Model, and to determine basic properties of atomicnuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2}\rightarrow {}^2F_{7/2}$ octupole transition of trapped$^{168,170,172,174,176}$Yb ions. When combined with previous measurements inYb$^+$ and very recent measurements in Yb, the data reveal a King plotnonlinearity of up to 240$\sigma$. The trends exhibited by experimental dataare explained by nuclear density functional theory calculations with the Fayansfunctional. We also find, with 4.3$\sigma$ confidence, that there is a seconddistinct source of nonlinearity, and discuss its possible origin.

Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson