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I know about the CP-violation experiments from the 60's and the P-violation from the 50's. But, is there a similar experiment which displays (perhaps historically in the same way as the experiements of Wu and Christensen) the violation of Charge conjugation alone?

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There is not, because the combined transformation $CPT$ is a symmetry of all Lorentz-invariant systems. The $P$-violating decay distribution observed by Wu et al. is also a $C$-violating distribution, because polarized anti-cobalt would have had the opposite sign of asymmetry. (However no one has ever made, or probably will ever make, polarized anti-cobalt, so that particular claim is unverified.)

The Garwin, Lederman, and Weinrich experiment published simultaneously with Wu's result measured opposite polarizations for $\mu^+$ and $\mu^-$ produced from unpolarized pions. (Pions are spinless, and therefore unpolarizable.) The existence of the polarization is a $P$-violation; the correlation of polarization with charge is a $C$-violation; the pion-producing decays separately conserve $CP$ and $T$, to conserve $CPT$.

Conservation of $CP$ is an automatic consequence of a weak interaction with only two generations of isospin doublets; three generations are necessary for the CKM matrix to carry a $CP$-violating phase. We have experimental evidence that $CP$-violating phases in our universe are small, but the Sakharov conditions tell us that the evolution of the universe from baryon-symmetric to baryon-asymmetric requires a violation of $CP$ that distinguishes matter from antimatter. So the searches for small $CP$ violation are well-motivated.

The nontrivial phenomena that would fit your description would be processes that violate $C$ and $T$ but not $P$ (or, just as interesting, $P$ and $T$ but not $C$). Off the top of my head I cannot think of any such processes. The role of the $C$- and $P$-violating, mostly-$CP$-conserving weak interaction makes it unlikely that any such process exists.

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